Answer:
[tex](x,y) - (x + 4, y-3)[/tex]
Step-by-step explanation:
Given:
A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down.
It is translated 4 units right and 3 units down.
We need to find the rule of translation.
Solution:
Now to the right of the axis which is positive of X axis and 4 units to the right means 4 units are added to X co-ordinate.
Also to the Down of the axis which is negative of Y axis and 3 units to the down means 3 units are Subtracted to Y co-ordinate.
Hence The co-ordinates at which triangle is drawn is [tex](x + 4, y-3)[/tex]
If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = 10x5 + 7x4 + 5
A) Degree: 10; leading coefficient: 5
B) Not a polynomial function
C) Degree: 9; leading coefficient: 10
D) Degree: 5; leading coefficient: 10
Answer:
It's D; degree- 5; leading coefficient-10 :)
Step-by-step explanation:
I just took the test and got it right
The given polynomial function f(x) = 10x⁵ + 7x⁴ + 5 has Degree: 5; leading coefficient: 10 which is the correct answer would be option (D).
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The degree of a polynomial is the highest exponent of the variables in the polynomial. In this case, the highest exponent is 5, so the degree of the polynomial is 5.
The leading coefficient is the coefficient of the term with the highest degree.
In this case, the coefficient of the term with the highest degree (x⁵) is 10, so the leading coefficient is 10. Therefore, the correct answer is D).
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Jacob and Ayden work at a dry cleaners ironing shirts. Jacob can iron 25 shirts per hour, and Ayden can iron 35 shirts per hour. Ayden worked twice as many hours as Jacob and they ironed 380 shirts between them. Determine the number of hours Jacob worked and the number of hours Ayden worked.
Answer:
Step-by-step explanation:
Start with the unknown, which is the number of hours J worked and the number of hours A worked. If A worked twice as many hours as J, then J worked x hours and A worked 2x hours. If J can iron 25 shirts per hour, x, then the number of shirts he can iron in his shift is 25x. If A can iron 35 shirts per hour, x, then the number of shirts he can iron in his shift is 35(2x). The number of shirts they iron together in x hours is
25x + 35(2x) = 380 and
25x + 70x = 380 and
95x = 380 so
x = 4
This means that J worked 4 hours and A worked 8 hours.
Analytic function on unit disk with power series has pole on unit circle, then power series diverges on unit circle.
Answer:
The function
{\ displaystyle f (z) = {\ frac {z} {1- | z | ^ {2}}}} {\ displaystyle f (z) = {\ frac {z} {1- | z | 2}
It is an example of real and bijective analytical function from the open drive disk to the Euclidean plane, its inverse is also an analytical function. Considered as a real two-dimensional analytical variety, the open drive disk is therefore isomorphic to the complete plane. In particular, the open drive disk is homeomorphic to the complete plan.
However, there is no bijective compliant application between the drive disk and the plane. Considered as the Riemann surface, the drive disk is therefore different from the complex plane.
There are bijective conforming applications between the open disk drive and the upper semiplane and therefore determined as Riemann surfaces, are isomorphic (in fact "biholomorphic" or "conformingly equivalent"). Much more in general, Riemann's theorem on applications states that the entire open set and simply connection of the complex plane that is different from the whole complex plane admits a bijective compliant application with the open drive disk. A bijective compliant application between the drive disk and the upper half plane is the Möbius transformation:
{\ displaystyle g (z) = i {\ frac {1 + z} {1-z}}} {\ displaystyle g (z) = i {\ frac {1 + z} {1-z}}}
which is the inverse of the transformation of Cayley.
if an analytic function on the unit disk has a pole on the unit circle, its power series representation diverges on the unit circle, as the singularity prevents the power series from converging outside the disk of convergence.
To understand why a power series diverges on the unit circle when the analytic function it represents has a pole on the unit circle, we can use the concept of analytic continuation and the properties of poles and singularities.
Here's a step-by-step explanation:
1.Analytic function on the unit disk: Let's consider an analytic function defined on the open unit disk, denoted by[tex]\(D = \{z \in \mathbb{C} : |z| < 1\}\)[/tex]. This means the function is holomorphic (complex differentiable) at every point within this disk.
2.Power series representation: Since the function is analytic on[tex]\(D\)[/tex], it can be represented by a power series expansion around any point [tex]\(z_0\) in \(D\)[/tex]. Let's denote this function by[tex]\(f(z)\)[/tex], and its power series representation centered at[tex]\(z_0\) by \(\sum_{n=0}^{\infty} a_n (z - z_0)^n\)[/tex].
3.Pole on the unit circle: Suppose[tex]\(f(z)\)[/tex] has a pole (a point where the function becomes unbounded) on the unit circle[tex]\(|z| = 1\)[/tex], i.e., there exists a point [tex]\(z_1\)[/tex] on the unit circle such that [tex]\(f(z_1)\)[/tex] is infinite. Without loss of generality, let's assume [tex]\(z_1 = 1\)[/tex] (since the unit circle is symmetric about the origin).
4.Behavior near the pole: Near the pole at [tex]\(z = 1\)[/tex], the function[tex]\(f(z)\)[/tex]can be expanded in a Laurent series, which includes negative powers of [tex]\((z - 1)\)[/tex]. This expansion will have infinitely many terms with negative powers, indicating the singularity at [tex]\(z = 1\)[/tex].
5.Radius of convergence: The radius of convergence of the power series representation of [tex]\(f(z)\)[/tex]is at least the distance from the center of convergence to the nearest singularity. In this case, since the singularity (pole) is on the unit circle, the radius of convergence of the power series cannot exceed 1.
6.Divergence on the unit circle: Since the radius of convergence of the power series representation of [tex]\(f(z)\)[/tex] is at most 1, the power series diverges at every point on the unit circle (except possibly at the point of singularity itself, where it may converge by definition). This divergence occurs because the function has a singularity (pole) on the unit circle.
Therefore, if an analytic function on the unit disk has a pole on the unit circle, its power series representation diverges on the unit circle, as the singularity prevents the power series from converging outside the disk of convergence.
I need help with this math question
Answer:
a.) y = 3/(2ˣ)
b.) y = 1/(2ˣ)
c.) y = (π^π)ˣ
d.) y = (1/27)(1/√(3))ˣ
e.) y = .002908/(.119025ˣ)
f.) y = .00000004808/(.0413ˣ)
Step-by-step explanation:
Concept need to know is:
a negative exponent will flip the numerator with the denominatora fraction as an exponent is just a root. so if the exponent is x^(1/2) then the root is 2 and x^(1/3) is a cube rootadding and subtracting exponent is the same thing as multiplying the same base. so x^(1+2) = (x^1)(x^2)and x^(1-2) = (x^1)(x^-2)What is the common difference of an AP which has its first term as 100 and the sum of its first 6 terms = 5 times the sum of its next six terms Pick one of the choices 1. 10 2. -10 3. 12 4. 15
Answer:
The common difference of given AP is Option 2) -10.
Step-by-step explanation:
We are given the following information in the question:
First term of AP, a = 100
The sum of its first 6 terms = 5(the sum of its next six terms)
We have to find the common difference of AP.
The sum of n terms of AP is given by:
[tex]S_n = \dfrac{n}{2}\big(2a + (n-1)d\big)[/tex]
where a is the first term and d is the common difference.
Thus, we can write:
[tex]S_6 = 5 (S_{12}-S_6)\\\dfrac{6}{2}\big(200 + (6-1)d\big) = 5\bigg(\dfrac{12}{2}\big(200 + (12-1)d\big)-\dfrac{6}{2}\big(200 + (6-1)d\big)\bigg)\\\\600 + 15d =5(1200+66d-600-15d)\\600+15d=3000+255d\\2400 = -240d\\d = -10[/tex]
Thus, the common difference of given AP is -10.
One card is selected from a deck of cards. Find the probability of selecting a black card or a jack.
The probability of selecting a black card or a jack is 15/26.
Given that, one card is selected from a deck of cards.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Total number of outcomes =52
The number of black cards in a deck =26
The number of jack cards in a deck =4
Probability of an event = 26/52 +4/52
= 30/52
= 15/26
Therefore, the probability of selecting a black card or a jack is 15/26.
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Final answer:
The probability of selecting a black card or a jack from a standard deck of 52 cards is 7/13.
Explanation:
To find the probability of selecting a black card or a jack from a standard deck of 52 cards, we need to consider the number of favorable outcomes and the total number of possible outcomes.
In a deck, there are 26 black cards (13 clubs and 13 spades) and a total of 4 jacks.
However, since two of the jacks are black, we must avoid counting them twice.
The probability becomes:
P(Black or Jack) = P(Black) + P(Jack) - P(Black and Jack)
P(Black) = 26/52, P(Jack) = 4/52, and P(Black and Jack) = 2/52
Thus, the probability is:
P(Black or Jack) = (26/52) + (4/52) - (2/52) = 28/52 = 7/13
Therefore, the probability of selecting a black card or a jack from a standard deck is 7/13.
13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude: 4, period 4 phase shift = vertical shift = -2
Answer:
[tex]y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2[/tex]
Step-by-step explanation:
Let's start with the original function.
[tex]y=a sin\frac{2\pi t}{T}[/tex]
We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4[tex]\pi[/tex] respectively.
[tex]y=4sin(\frac{2\pi t}{4\pi } )[/tex]
Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:
[tex]y=4sin(\frac{2\pit }{4\pi } )-2[/tex]
Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:
[tex]y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2[/tex]
This function has vertical shift -2, phase shift -4/3 [tex]\pi[/tex], amplitude 4, and period 4[tex]\pi[/tex].
Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.
The perimeter of a rectangle is 360m. If it's length is decreased by 20% and it's breadth is increased by 25%, we get the same perimeter. Find the dimensions of the rectangle.
Answer:the length of the rectangle is 100m
the width of the rectangle is 80m
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + B)
The perimeter of a rectangle is 360m. This means that
2(L + B) = 360
L + B = 180 - - - - - - - - - -1
If it's length is decreased by 20%, its new length would be
L - 0.2L = 0.8L
it's breadth is increased by 25%, it means that the new breadth
B + 0.25B = 1.25B
Since the perimeter remains the same,
2(0.8L + 1.25B) = 360
0.8L + 1.25B = 180 - - - - - - - - -2
Substituting L = 180 - B into equation 2, it becomes
0.8(180 - B) + 1.25B = 180
144 - 0.8B + 1.25B = 180
- 0.8B + 1.25B = 180 - 144
0.45B = 36
B = 36/0.45 = 80
L = 180 - B = 180 - 80
L = 100
Josh has a rope that is 43 feet long. He cuts off a piece that is 10 feet long and gives it to his brother. He wants to cut the rest of the rope into pieces measuring exactly 5 feet each. How many pieces can he cut?
Answer:
6
Step-by-step explanation:
Answer:
Step-by-step explanation:
The initial length of Josh's rope was 43 feet. He cuts off a piece that is 10 feet long and gives it to his brother. This means that the length of the remaining rope would be
43 - 10 = 33 feet.
He wants to cut the rest of the rope into pieces measuring exactly 5 feet each. To determine the number of pieces that he can cut, it becomes
33/5 = 6.6
Therefore, only 6 pieces measuring exactly 5 feet each can be cut.
Suppose that the current equilibrium price of silver is $34 per ounce. If silver is produced under conditions of perfect competition and the industry is in long-run equilibrium, the average total cost of producing silver: a. is less than $34 per ounce. b. is $34 per ounce. c. is indeterminate. d. exceeds $34 per ounce.
Answer:
b. is $34 per ounce
Step-by-step explanation:
If the production cost were less, a competitor would drive the price down. If the production cost were more, the supplier would go out of business.
Since we're at equilibrium, the production cost must be equal to $34 per ounce.
Which of the following must also be known in order to compute the standard deviation?A) ModeB) MeanC) RangeD) Median
Answer:
B) Mean
Step-by-step explanation:
Standard Deviation is the measure of the amount of variation or dispersion of a set of values. Standard Deviation is represented by lower case Greek alphabet sigma σ. Standard Deviation is the square root of variance. Variance is the average of the squared differences or variation or dispersion from the Mean. Therefore, to compute standard deviation, the mean of the given data must be known.
Standard Deviation, σ = [tex]\sqrt{Variance}[/tex]
σ = [tex]\sqrt({\frac{1}{N-1}}[/tex] ∑[tex]_{i = 1}^{N}(x_{i} - X)^{2})[/tex]
where
[tex]x_{1},x_{2},x_{3}, ...x_{N},[/tex] are the values of the sample observed,
X is the mean value of these observations, and
N is the number of observations in the sample.
Which of the following ordered pair could NOT be included in this set if it is a function? { (-4, 2), (3, 6), (4, 3), (x, y) }
(x, y) = (4, -3)
(x, y) = (3, 6)
(x, y) = (1, 2)
(x, y) = (-3, 6)
Why is this the answer?
The x value x = 4 shows up in the point (4, 3), which is in the given function set. Adding (4, -3) to this set will have x = 4 show up twice. We cannot have one x value pair up with more than one y value. In other words, any input cannot map to more than one output. Visually, the two points (4,3) and (4,-3) will fail the vertical line test, which means we wouldnt have a function.
If $-5\leq a \leq -1$ and $1 \leq b \leq 3$, what is the least possible value of $\displaystyle\left(\frac{1}{a} \frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) $
Answer:
The least possible value is -2, obtained for a = -1 and b = 1.
Step-by-step explanation:
We want the minimum of [tex] \displaystyle\left(\frac{1}{a} \frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) [/tex] , where
[tex] -5 \leq a \leq -1 [/tex][tex] 1 \leq b \leq 3 [/tex]First, lets simplify the expression given, we use common denominator on the second part, using ab as the common denominator. We obtain
[tex] \frac{1}{b} - \frac{1}{a} = \frac{a-b}{ab} [/tex]
As a result
[tex] \displaystyle\left(\frac{1}{a} \frac{1}{b}\right)\left(\frac{1}{b}-\frac{1}{a}\right) = \frac{a-b}{(ab)^2} [/tex]
we need the minimum of the function
[tex] f(a,b) = \frac{a-b}{(ab)^2} [/tex]
with the restrictions [tex] -5 \leq a \ -1, 1 \leq b \leq 3 [/tex]
First, we calculate the gradient of f and find where it takes the zero value.
[tex]\nabla{f} = (f_a,f_b) [/tex]
with
[tex]f_a = \frac{(ab)^2 - (a-b) 2ab^2}{(ab)^2} = -1 + 2 \frac{b}{a}[/tex]
Since it has the reversed sign, we get
[tex]f_b = - (-1 + 2 \frac{a}{b}) =1 - 2 \frac{a}{b}[/tex]
In order for [tex] \nabla{f} [/tex] to be zero, we need both [tex] f_a [/tex] and [tex] f_b [/tex] to be zero, observe that
[tex]f_b = 0 \, \rightarrow 1 -2\frac{a}{b} = 0 \, \rightarrow 1 = 2 \frac{a}{b} \, \rightarrow b = 2a [/tex]
Which is impossible with the given restrictions. Hence, the minimum is realized in the border.
If we fix a value a₀ for a, with a₀ between -5 and -1 the function g(b) = f(a₀,b) wont have a minimum for b in [1,3] because the partial derivate of f over b didnt reach the value 0 in the restrictions given. On the other hand. by making a similar computation that before, we can obtain that the partial derivate of f over the variable a doesnt reach the value 0 either. This means that f doesnt reach the minimum on the sides. As a consecuence, it reach a minimum on the corners.
The 4 possible corner values are (-5,1), (-5,3), (-1,1) and (-1,3)
[tex] f(-5,1) = \frac{-6}{25} = -0.24 [/tex]
[tex] f(-5,3) = \frac{-8}{225} = -0.0355 [/tex]
[tex] f(-1,1) = \frac{-2}{1} = -2 [/tex]
[tex] f(-1,3) = \frac{-4}{9} = -0.444 [/tex]
Clearly the least possible value between the four corners is -2.
During a football game a concert in stenciled family three hamburgers and two white dogs for a total of $13 and another family two hamburgers and five hotdogs for a $ $16 what are the prices of a hamburger and a hotdog
Answer:
Price of hamburgers = $2
Price of white-dogs = $3
Step-by-step explanation:
Let
The number price of hamburgers be x
The number price of white-dogs be y
Then the first family buys 3 hamburgers and 2 white -dogs for $13
3x + 2y = 13-----------------------------(1)
Another first family buys 2 hamburgers and 5 white -dogs for $16
2x + 5y = 16----------------------------(2)
To solve let us multiply eq(1) by 2 and eq(2) by 3, we get
6x + 4y = 26-----------------------------(3)
6x + 15y = 48----------------------------(4)
subracting (3) from (4)
6x + 15y = 48
6x + 4y = 26
(-)
-------------------------
11y = 22
---------------------------
[tex]y =\frac{22}{11}[/tex]
y =2
Now substituting the value of y in eq(1),
3x + 2(2) = 13
3x + 4 = 13
3x = 13-4
3x = 9
x =[tex]\frac{9}{3}[/tex]
x =3
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
Answer:
There were 22 men in the sight-seeing tour
Step-by-step explanation:
If the number f women on the sight-seeing tour was less than 30, the closest number that can be divided by 5 is 25, so we suppose that there were 25 women, so with the ratio women(5): children(2) we can apply a rule of three, so we multiply 25*2 divided by 2, now we know that there were 10 children, now with the ratio of men(11): children(5) we apply another rule of three, and multiply 10*11 and then divide it by 5, and now we know that there were 22 men in the sight-seeing tour.
(NOTE: this symbol "*" will be used to express variables that go under the number, like a reverse exponent.)Find the 4th term in the sequence with the following definition:
a*1=2
a*n=(a*n-1)^2
Answer:
256
Step-by-step explanation:
a₁ = 2
aₙ = (aₙ₋₁)²
a₂ = (a₂₋₁)²
a₂ = (a₁)²
a₂ = (2)²
a₂ = 4
a₃ = (a₃₋₁)²
a₃ = (a₂)²
a₃ = (4)²
a₃ = 16
a₄ = (a₄₋₁)²
a₄ = (a₃)²
a₄ = (16)²
a₄ = 256
Find the measure of each angle indicated.
Answer: the measure of the indicated angle is 100 degrees
Step-by-step explanation:
The sum of angles in a triangle is 180 degrees. Let x represent the unknown angle in the bigger triangle. Therefore,
x + 80 + 25 = 180 degrees
x + 105 = 180
x = 180 - 105 = 75 degrees.
Let z represent the other unknown angle in the smaller triangle. Since the sum of the angles on a straight line is 180 degrees, therefore
75 + 55 + z = 180
130 +z = 180
z = 180 - 130 = 50 degrees
Let y represent the unknown angle that we are looking for. Therefore,
50 + y + 30 = 180
80 + y = 180
y = 180 - 80 = 100 degrees
Answer:
55
Step-by-step explanation:
Two school buses leave the same school at the same time, but are headed in opposite directions. One bus traveled 45 miles per hour and the other bus traveled 40 miles per hour.
How long until the buses are 170 miles apart?
Answer:
2 hours
Step-by-step explanation:
45x + 40x = 170
85x = 170
x = 2
Answer:
40 mph: 4 hours 15 minutes
45 mph: 3 hours 46 minutes 40 seconds
Step-by-step explanation:
The rate of separation = 45 + 40 = 85 mph
speed = distance / time
85 = 170 / t
t= 170/85 hour
The third term in a geometric sequence is -81. The common ratio is 1/3
What is the second term of the sequence?
If you answer, can you explain it?
Answer:
Step-by-step explanation:
The formula for the nth term of a geometric sequence is expressed as follows
Tn = ar^(n - 1)
Where
Tn represents the value of the nth term of the sequence
a represents the first term of the sequence.
n represents the number of terms.
From the information given,
r = 1/3
T3 = - 81
n = 3
Therefore,
- 81 = a× 1/3^(3 - 1)
-81 = a × (1/3)^2
-81 = a/9
a = -81 × 9 = - 729
The exponential equation for this sequence is written as
Tn = - 729 * (1/3)^(n-1)
Therefore, to find the second term,T2, n = 2. It becomes
T2 = - 729 * (1/3)^(2-1)
T2 = - 729 * (1/3)^1
T2 = - 729 * (1/3)
T2 = - 243
Consider the vector field ????(x,y,z)=(5z+y)????+(4z+x)????+(4y+5x)????.
a. Find a function ???? such that ????=∇???? and ????(0,0,0)=0.
b. Suppose C is any curve from (0,0,0) to (1,1,1). Use part a. to compute the line integral ∫????????⋅????????.
Answer:
a) [tex]5xz + xy + 4yz[/tex]
b) 10
Step-by-step explanation:
a) Here [tex]F(x,y,z)=(5z+y)i+(4z+x)j+(4y+5x)k[/tex]
Since the case [tex]F[/tex] = ∇[tex]f[/tex] holds, then
∇[tex]f = f_xi+f_yj+f_zk[/tex] = [tex](5z+y)i+(4z+x)j+(4y+5x)k[/tex]
So, [tex]f_x = 5z + y[/tex]
If we integrate [tex]f_x[/tex] with respect to x, we will get an integration constant C which is also a function that depends to y and z.
Hence,
[tex]f = \int f_xdx = 5xz + xy + g(y,z)[/tex]
Now we need to find g(y,z).
So first let's take the derivative of g(y,z) with respect to y.
[tex]f_y = x + g_y(y,z) = 4z + x[/tex]
Hence, [tex]g_y(y,z) = 4z[/tex]
So now, if we integrate [tex]g_y[/tex] with respect to y to find g(y,z)
[tex]g = \int g_ydy = 4yz + C[/tex]
Thus,
[tex]f = 5xz + xy + g(y,z) = 5xz + xy + 4yz + C[/tex]
And since [tex]f(0,0,0)=0[/tex], then [tex]C=0[/tex]
Thus,
[tex]f = f(x,y,z) = 5xz + xy + 4yz[/tex]
b) By the Fundamental Theorem of Line Integrals, we know that
[tex]\int\limits^a_b F. dr = F[r(b)]-F[r(a)][/tex]
Hence,
[tex]\int\limits^a_b F. dr = F(1,1,1)-F(0,0,0) =[(5+1+4)-(0+0+0)]=10[/tex]
To find ????, solve the system of partial differential equations. Use the function ???? from part a to compute the line integral.
Explanation:To find a function ???? such that ????=∇???? and ????(0,0,0)=0, we can solve the system of partial differential equations. Let ????=????????+????????+????????, then compute the partial derivatives of ???? with respect to each variable. Equating these partial derivatives to the given vector field components, we can solve for the unknown function ???? and find its value at the point (0,0,0).
To compute the line integral ∫????????⋅????????, we can use the fundamental theorem of calculus for line integrals. Since ????(x,y,z) is the gradient of ????, the line integral is equal to the change in ???? along the curve C from (0,0,0) to (1,1,1). We can use the function ???? found in part a to evaluate this change in ????.
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Not good at this need some help
Answer:
216 sq. units
Step-by-step explanation:
From the figure, we can see that only one pair of opposite angles are equal. So, the quadrilateral is a kite.
Formula to find the area of a kite:
Area, A = [tex]$ \frac{1}{2} \times d_1 \times d_2 $[/tex]
where, [tex]$ d_1 $[/tex] and [tex]$ d_2 $[/tex] are the lengths of the diagonals.
Here, [tex]$d_1 = 18 $[/tex] units.
And, [tex]$ d_2 = 24 $[/tex] units.
Therefore, the area A = [tex]$ \frac{1}{2} \times 18 \times 24 $[/tex]
= [tex]$ \frac{432}{2} $[/tex]
= 216 sq. units which is the required answer.
A baker uses 2 1/3 cups of cookie dough and 1/4 cup of chocolate chips to make 10 cookies. If the baker has 3 cups of chocolate chips, how much dough will he need
Answer: he will need 28 cups of dough for 3 cups of chocolate.
Step-by-step explanation:
The baker uses 2 1/3 cups of cookie dough and 1/4 cup of chocolate chips to make 10 cookies. Converting 2 1/3 cups of cookie dough into improper fraction, it becomes 7/3 cups of cookie dough.
It means that for every 1/4 cup of chocolate, 7/3 cups of cookie dough is needed.
Let x represent the amount of cookie dough needed for 3 cups of chocolate chips.
If 7/3 dough = 1/4 cup of chocolate
x dough = 3 cups of chocolate
x × 1/4 =7/3 × 3
x/4 = 7
x = 7×4 = 28 cups of dough
PLEASE ANSWER; MAY NOT BE HARD
Find the sum of all positive 3-digit numbers whose last digit is 2
Answer:
Step-by-step explanation:
102+202+302+402+502+602+702+802+902(4518)
+112+212+312+...+ 812+912(4608)
+122+222+322+...+822+922(4698)
+132+232+332+...+932(4788)
..........................................
+192+292+392+...+992(5328)
4518+4608+4698+...+5328
n=10
[tex]s=\frac{10}{2}(4518+5328)\\=5(9846)\\=49230[/tex]
Final answer:
To find the sum of all positive 3-digit numbers ending in 2, we calculate the total for each digit's place and sum them up, resulting in a total sum of 8280.
Explanation:
The problem requires finding the sum of all positive 3-digit numbers with a last digit of 2. To calculate this, we can identify that the first such number is 102 and the last is 992. There are 90 such numbers because they correspond to the tens digit going from 0 to 9 for each of the nine possible hundreds digits (1-9).
Since each number ends in 2, we can think of them as (100x + 10y + 2), where x is the hundreds digit (1 through 9) and y is the tens digit (0 through 9). To find the sum, we calculate the sum of the hundreds digits times their frequency, the sum of the tens digits times their frequency, and add 2 times the number of terms (90). The formula would be:
Sum = (Sum of hundreds values) * 10 * 9 + (Sum of tens values) * 1 * 90 + 2 * 90
The hundreds values are 1 through 9, whose sum is 45, and the tens values are 0 through 9, whose sum is 45 as well. Plugging these values into the formula, we get:
Sum = 45 * 10 * 9 + 45 * 1 * 90 + 2 * 90 = 4050 + 4050 + 180 = 8280.
2. A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.
Answer:
Step-by-step explanation:
Initial amount that was deposited into the savings account is $600 This means that the principal,
P = 600
The account earns 2.1 % interest compounded annually.. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 2.1%. So
r = 2.1/100 = 0.021
It was compounded for t years. So
t = t
a) The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 600 (1+0.021/1)^1×t
A = 600(1.021)^t
b)when A =$800, it becomes
800 = 600(1.021)^t
Dividing both sides by 600, it becomes
1.33 = (1.021)^t
Taking the tth root of both sides
t = 14 years
It will take 14 years
Two cars enter the Delaware turnpike at shoreline drive at 8 am, each heading for ocean city. One cars average speed is 10 mph faster than the other. The faster car arrives at ocean city at 11 am, a half hour before the slower car. What is the average speed of each car?
Average speed of slower car = 60 mph
Average speed of faster car = 70 mph
Solution:
Given that Two cars enter the Delaware turnpike at shoreline drive at 8 am, each heading for ocean city
Given that One cars average speed is 10 mph faster than the other
Let "x" be the average speed of slower car
Then x + 10 is the average speed of faster car
The faster car arrives at ocean city at 11 am, a half hour before the slower car
Time taken by faster car:
The faster car arrives at ocean city at 11 am but given that they start at 8 a.m
So time taken by faster car = 11 am - 8am = 3 hours
Time taken by slower car:
The faster car arrives at ocean city at 11 am, a half hour before the slower car
So slower car takes half an hour more than faster car
Time taken by slower car = 3 hour + half an hour = [tex]3\frac{1}{2} \text{ hour}[/tex]
Now the distance between Delaware turnpike at shoreline drive and ocean city will be same for both cars
Let us equate the distance and find value of "x"
The distance is given by formula:
[tex]distance = speed \times time[/tex]
Distance covered by faster car:
[tex]distance = (x + 10) \times 3 = 3x + 30[/tex]
Distance covered by slower car:
[tex]distance = x \times 3\frac{1}{2} = x \times \frac{7}{2} = 3.5x[/tex]
Equating both the distance,
3x + 30 = 3.5x
3x - 3.5x = -30
-0.5x = -30
x = 60
Thus average speed of slower car = 60 mph
Average speed of faster car = x + 10 = 60 + 10 = 70 mph
Howdy! Id love to have these questions answered asap! Thank you for the help!
1) Which angle is not coterminal to 120 degrees?
A. 840
B. -180
C. 480
2) Use the unit circle and the reference angle to determine which of the following trigonometric values is correct when theta = -90
A. Cos theta = undefined
B. Sin theta = -1
C. Tan = 0
Answer:
1. B.
2. B.
Step-by-step explanation:
Trigonometry
1) Coterminal angles can be found by adding or subtracting 360° (or 2\pi radians) to a given angle. If we have 120°, adding 360° gives 480°, adding again 360° gives 840°. There is no way to get -180°, so this option is not a coterminal angle to 120°
2)
A. [tex]Cos (-90^o)=0[/tex], and not undefined
B. [tex]Sin (-90^o)=-1[/tex]. This is correct
C. [tex]Tan (-90^o)[/tex] is undefined, not zero
Thus the only correct option is B.
You interview four people. You find that person A is a married 24-year-old white female with 2 pets and whose college GPA was 2.4. Person B is a single 44-year-old Asian female with 5 pets and whose college GPA was 2.5. Person C is a single 35-year-old Hispanic male with 4 pets and whose college GPA was 2.2. Person D is a single 48-year-old Asian male with 3 pets and whose college GPA was 3.8. Construct a data file for the characteristics number of pets and ethnic group for this sample.
Answer:
The data file is included in attached excel file.
Step-by-step explanation:
There are seven variables in the data file for four persons interviewed. Person type, marital status, ethnic group and gender are categorical variables while age, number of pets and GPA are quantitative variables. Person type is classified as A,B,C and D. Marital status consists of category married and single. Age of persons lies between 20-50. Ethic group has three categories that are white, Asian and Hispanic. Gender of persons has two categories male and female. Number of pets for the persons interviewed lies in the range of 2 to 5. Last GPA variable ranges from 2.2 to 3.8.
James and Lucas competed in climbing a mountain and coming back. James climbed at an average rate of 3 mph and ran back at 4 mph. Lucas climbed at an average rate of 2 mph and ran back at 5 mph. If the path from the bottom to the top of the mountain was 2 miles, how much time did each take to finish and who was faster? Answer:
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Step-by-step explanation:
Given,
Climbing rate of James = 3 mph
Running back rate of James = 4 mph
Climbing rate of Lucas = 2 mph
Running back rate = 5 mph
Total distance = 2 miles
We know that;
Distance = Speed * Time
As we have to find, we will rearrange the formula in terms of time
[tex]Time=\frac{Distance}{Speed}[/tex]
Time took by James for climbing = [tex]\frac{2}{3}\ hours[/tex]
Time took for running back = [tex]\frac{2}{4}\ hours[/tex]
Total time = [tex]\frac{2}{3}+\frac{2}{4}=\frac{8+6}{12}=\frac{14}{12}[/tex]
Total time taken by James = [tex]\frac{7}{6}\ hours[/tex]
1 hour = 60
Total time taken by James = [tex]\frac{7}{6}*60=70\ minutes[/tex]
Time took by Lucas for climbing = [tex]\frac{2}{2}=\ 1\ hour[/tex]
Time took by Lucas for climbing = 60 minutes
Time took on return = [tex]\frac{2}{5} of\ an\ hour=\frac{2}{5}*60=24\ minutes[/tex]
Total time taken by Lucas = 60+24 = 84 minutes
Therefore,
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Keywords: distance, speed
Learn more about distance at:
brainly.com/question/1021953brainly.com/question/10480770#LearnwithBrainly
Answer:
Step-by-step explanation:
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.
Step-by-step explanation:
Given,
Climbing rate of James = 3 mph
Running back rate of James = 4 mph
Climbing rate of Lucas = 2 mph
Running back rate = 5 mph
Total distance = 2 miles
We know that;
Distance = Speed * Time
As we have to find, we will rearrange the formula in terms of time
Time took by James for climbing =
Time took for running back =
Total time =
Total time taken by James =
1 hour = 60
Total time taken by James =
Time took by Lucas for climbing =
Time took by Lucas for climbing = 60 minutes
Time took on return =
Total time taken by Lucas = 60+24 = 84 minutes
Therefore,
It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.®
Which equilibrium at one atmosphere pressure is correctly associated with Kelvin temperature at which it occur?a. ice-water equilibrium at 0 K
b. ice-water equilibrium at 32 K
c. steam-water equilibrium at 212 K
d. steam-water equilibrium at 373 K
The correct equilibrium at one atmosphere pressure associated with its Kelvin temperature is the steam-water equilibrium at 373 K.
Explanation:The equilibrium at one atmosphere pressure that is correctly associated with the Kelvin temperature at which it occurs is option d. steam-water equilibrium at 373 K. To explain, in the Kelvin temperature scale, the freezing point of water is 273.15 K and the boiling point is 373.15 K, both under standard atmospheric conditions (1 atmosphere pressure). So, at 373 K, the situation would be a steam-water equilibrium, not an ice-water equilibrium as in options a and b. The Kelvin temperature for ice-water equilibrium is 273.15 K and not 0 K and 32 K as stated in options a or b. Similarly, steam-water equilibrium does not occur at 212 K as suggested in option c.
Learn more about Kelvin Temperature here:https://brainly.com/question/30395875
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Option d. steam-water equilibrium at 373 K. The steam-water equilibrium at one atmosphere pressure occurs at 373 K.
The correct answer is:
Steam-water equilibrium at 373 KLet's break down the reasons:
Ice-water equilibrium: This occurs at 0°C, which is 273.15 K, not 0 K or 32 K.Steam-water equilibrium: The boiling point of water is 100°C, which is 373.15 K. At one atmosphere of pressure, water and steam are in equilibrium at this temperature.Thus, the correct association is the steam-water equilibrium occurring at 373 K at 1 atmosphere pressure.
Find the rate of change for x³. You need to work out the change in f(x)=x³ when x is increased by a small number h to x+h. So you will work out f(x+h)-f(x). Then do some algebra to simplify this. Then divide this by h to get the average rate of change of f(x) between x and x+h. The average rate of change of f(x) from x to x+h is:
Answer:
3x² +3xh +h²
Step-by-step explanation:
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^3-x^3}{h}=\dfrac{(x^3+3x^2h+3xh^2+h^3)-x^3}{h}\\\\=\dfrac{3x^2h+3xh^2+h^3}{h}=3x^2+3xh+h^2[/tex]