Answer:
t = 1.55 sec
Step-by-step explanation:
Because we are asked to find the time it will take for the rocket to travel horizontally, we are only concerned with the x-dimension here.
We are told that the initial velocity is 50 ft/s and the angle is 75 degrees.
The equation we are going to need to solve this involves the displacement, the initial velocity, the acceleration, and the time...all in the x dimension:
Δx = V₀t + 1/2at²
We have the displacement, we can solve for the initial velocity, we know acceleration, and time is what we are solving for.
Let's work to fill in these values:
Δx = 20 feet
V₀x = V₀ cos Ф (that's the closest thing I could find to theta)
a = 0 (acceleration is always 0 in the horizontal dimension)
t = ?
From the information we can determine the initial velocity in the x dimension using the formula
[tex]V_{0x}=V_{0}cos(\theta)[/tex]
Solving for the initial velocity in the x-dimension:
[tex]V_{0x}=50cos(75)[/tex], which gives us from our calculators that initial velocity in the x-dimension is 12.941 (I am not paying attention to significant digits here since 50 has only 1).
Now we can fill in our equation with the info:
[tex]20=12.941t+\frac{1}{2}(0)t^2[/tex]
Because a = 0, the whole portion of the equation after the plus sign equals 0, so we can disregard and simply solve:
20 = 12.941t so
t = 1.55 seconds
The time it will take for the rocket to travel 20 feet horizontally is 1.545 seconds.
What is the equation of motion?There are three equations of motion, v= u +at, s = ut +(1/2)at²and v² = u²+2as.
The initial velocity is 50 ft/s
The angle is 75 degrees.
s = ut +(1/2)at²
v= u cos [tex]\rm \theta[/tex]
v = 50 cos 75
v = 12.94 ft/s
a = 0 in horizontal direction
s = 20
20 = 12.94 *t
t = 20/12.94
t = 1.545 seconds.
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Evaluate the expression.
Answer:
C
Step-by-step explanation:
at least two have to be in the same place (i think), and that’s the only one that does that
Answer:
55/56 ≈ 0.982143
Step-by-step explanation:
nPk = n!/(n-k)!
Your expression is ...
1 - (6·5·4·3)/(8·7·6·5·4·3) = 1 - 1/(8·7) = 1 - 1/56 = 55/56 ≈ 0.982143
Suppose you have a bucket of sand containing 5.5 billion grains of sand ( 5.5×109 grains). Most of the grains of sand are white, but there are some brown grains mixed evenly throughout. If the concentration of brown sand is 2.0% , how many grains of brown sand are in the bucket?
Answer:
1.1×10^8
Step-by-step explanation:
2% of 5.5 billion is ...
2×10^-2 × 5.5×10^9 = 11×10^7 = 1.1×10^8
About 1.1×10^8 grains of brown sand are in the bucket.
Answer:
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Step-by-step explanation:
Total number sand grains in the bucket =[tex] 5.5\times 10^9 grain[/tex]
Concentration of brown sand grains = 2.0%
Number of brown brain in the bucket be x
[tex]\%=\frac{\text{Brown sand grains}}{\text{Total sand grains}}\times 100[/tex]
[tex]2.0\%=\frac{x}{5.5\times 10^9 grain}\times 100[/tex]
[tex]x=1.1\times 10^8 grains[/tex]
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Please answer this question for 30 points and brainliest!!
Answer:
2.5 cm
Step-by-step explanation:
The ratio of side lengths of similar figures is the same as the ratio of any linear measure on those figures, including perimeter. The second figure's perimeter is 10/16 of that of the first figure, so the shortest side of the second figure will also be 10/16 of the length of the shortest side of the first figure.
(10/16)×(4 cm) = 2.5 cm
The shortest side of the second polygon has a length of 2.5 cm.
Given the conditional statement: p → ~q Choose the logically equivalent statement.
A. p → q
B. ~p → q
C. q → p
D. q → ~p
Answer: The correct option is
(D) q → ~p.
Step-by-step explanation: We are given to select the statement that is logically equivalent to the conditional statement p → ~q.
We know that
two conditional statements are said to be logically equivalent if the truth tables of both the statements are same.
That is, they have same truth values under similar conditions.
The truth table is given by
p q ~p ~q p → ~q p → q ~p → q q → p q → ~p
T T F F F T T T F
T F F T T F T T T
F T T F T T T F T
F F T T T T F T T
So, the truth values of p → ~q is same as the truth values of q → ~p. They must be logically equivalent.
Thus, option (D) is CORRECT.
Answer:
D). q → ~p
Step-by-step explanation:
I just did the assignment on Edge... It's 100% correct... Hope this helps!!
Also heart and rate if you found this answer helpful... Have a nice day!! :)
An hour of CFL use consumes 10-2 kWh (kilowatt – hour), if each kilowatthour of electricity use is equivalent to 3.6 X 106 joules of energy, then find out the energy in joules used by the CFL in one hour
Answer:
[tex]3.6*10^{4}\ joules[/tex] or [tex]36,000\ joules[/tex]
Step-by-step explanation:
Let
x -----> the energy in joules used by the CFL in one hour
we know that
using proportion
[tex]\frac{1}{3.6*10^{6}}\frac{kWh}{joules} =\frac{10^{-2}}{x}\frac{kWh}{joules}\\ \\x=(3.6*10^{6})(10^{-2})\\ \\x=3.6*10^{4}\ joules[/tex]
or
[tex]36,000\ joules[/tex]
Need help with this one, no clue how to solve this. If someone could explain what's going on like I'm 5 it'd be much appreciated.
Find x.
Question 10
cos 45 = x/10
cos 45(10) = x
(1/sqrt{2})*10 = x
10/sqrt{2} = x
Rationalize the denominator.
[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x
10•sqrt{2} ÷ 2 = x
5• sqrt{2} = x
If [tex]\alpha[/tex] = 65° and j = 11 mm, what is the value of h to the nearest tenth of a millimeter?
A. 4.7 mm
B. 12.1 mm
C. 5.1 mm
D. 8.6 mm
Answer:
C. 5.1 mm
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan alpha = opposite/ adjacent
tan alpha = j/h
tan 65 = 11/h
Multiply both sides by h
h tan 65 = 11/h *h
h tan 65 = 11
Divide each side by tan 65
h tan 65 / tan 65 = 11 / tan 65
h = 11 / tan 65
h =5.12938424
To the nearest tenth
h = 5.1
Answer:
12.1
Step-by-step explanation:
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.
Answer with explanation:
Temperature in the living room =68°F
The equation which satisfies ,the room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies
t=2 Cos (0.21 m) +68----------(1)
⇒To determine the period of the function
Z= A cos (sx+q)+r
As period of cos x is 2 π.
So,the given function has period
[tex]=\frac{2\pi}{s}[/tex]
So, the period of function 1, is given by
[tex]=\frac{2\pi}{0.21}[/tex]
⇒The meaning of period of the function is that after every period of [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.
⇒Cosine function has maximum value of 1 , and Minimum value of -1.
-1 ≤ Cos x ≤ 1
So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature
And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature
Final answer:
The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.
Explanation:
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.
The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.
The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.
PLEASE HELP
In the proof of the Law of Cosines, the equation c^2=h^2+(b-x)^2was created using the Pythagorean theorem. Which equation is a result of expanding (b-x)^2?
A.c^2=h^2+b^2-x^2
B.c^2=h^2+b^2-2bx+x^2
C. c^2=h^2+b^2+x^2
not D
Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth.
9.0 yd
16.1 yd
22.1 yd
23.7 yd
Answer:
Q1 B
Q2 23.7yd
Step-by-step explanation:
Solution of Q2 is in the picture
Answer:
a) [tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) TP = 23.7 yards
Step-by-step explanation:
a) We can rewrite [tex](b-x)^{2}[/tex] as (b-x)(b-x), so we have a product of two binomials. We can use the FOIL method to multiply it:
[tex](b-x)(b-x)=b^{2}-bx-bx+x^{2}=b^{2}-2bx+x^{2}[/tex]
so the the Law of Cosines equation will be write as:
[tex]c^{2}=h^{2}+(b-x)^{2}=h^{2}+b^{2}-2bx+x^{2}[/tex]
Therefore letter B is the correct answer.
b) Here we can use the Law of sines.
TP is the distance between Tyrone and the pianoDP is the distance between Diego and the pianoTD is the distance between Diego and Tyrone.∠A angle between TD and TP = 65°
∠B angle between TD and DP = 77°
∠C angle between TP and DP = 180° - 77° - 65° = 38°
The equation is:
[tex]\frac{TP}{sin(B)}=\frac{TD}{sin(C)}[/tex]
[tex]\frac{TP}{sin(77)}=\frac{15}{sin(38)}[/tex]
Solving it for TP, we have:
[tex]TP=sin(77)\frac{15}{sin(38)}=23.7 yards[/tex]
I hope it helps you!
Really trying to pass this exam and graduate can someone smart please help me with these problems im running out of time ..
Answer:
1172.08 square inches
Step-by-step explanation:
Total surface area is area of all the surfaces.
Cylinder:
Top surface = πr^2 = π(4)^2 = 16(3.14) = 50.24
Lateral Surface = 2πrh = 2π(4)(9) = 72π = 72(3.14) = 226.08
Rectangular Prism:
2 sides = 2*(11*11) = 242
front and back = 2*(16*11) = 352
bottom = 16 * 11 = 176
Top part (it is top rectangle - bottom of cylinder) = (16*11) - (π(4)^2) = 125.76
Adding all up, we get:
50.24 + 226.08 + 242 + 352 + 176 + 125.76 = 1172.08 square inches
For the function f(x)=[tex]\frac{\sqrt{x} }{5} +2[/tex]
A. ƒ –1(x) = 25(x – 2)2, x ≥ 2
B. ƒ –1(x) = 25x2 – 2, x ≥ 0
C. ƒ –1(x) = 5(x – 2)2, x ≥ 0
D. ƒ –1(x) = 25(x – 2)2, x ≥ 0
Answer:
[tex]f^{-1}(x)=25(x-2)^2[/tex]
Step-by-step explanation:
The inverse function can be found by solving ...
f(y) = x
(√y)/5 +2 = x
(√y)/5 = x -2 . . . . . subtract 2
√y = 5(x -2) . . . . . . multiply by 5
y = 25(x -2)² . . . . . square both sides
The inverse function is ...
[tex]f^{-1}(x)=25(x-2)^2[/tex]
_____
About the graph
The inverse of a function is its mirror image across the line y = x.
He function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes. Explain what h(10) means in the context of the real-world scenario, and how to find its value.
Answer:
Step-by-step explanation:
h(10) would be the height of the balloon at 10 seconds
Determine the height of the triangle.
Round to the nearest foot.
a. 12 ft c. 10 ft
b. 14 ft d. 18 ft
Please select the best answer from the choices provided
Answer:
Option B is correct.
Step-by-step explanation:
We need to find the height of triangle.
The triangle is right angled triangle
We are given Hypotenuse = 25
Perpendicular = h
and angle Ф = 34°
We know that sinФ = Perpendicular / Hypotenuse
sin 34° = h / 25
0.56 = h/25
=> h = 0.56 * 25
=> h = 14 ft
So, the height of triangle is h= 14 ft
So, Option B is correct.
Answer:
It's B!
Step-by-step explanation:
I just took it! Have a good day.
What is 3/4 times 710?
Answer:
532.5 or 532[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
3/4 x 710
= 3 x 710 ÷ 4
= 532.5 or 532[tex]\frac{1}{2}[/tex]
Final answer:
To find 3/4 times 710, multiply 710 by 3 to get 2130, then divide that result by 4 to get 532.5. Therefore, 3/4 times 710 equals 532.5.
Explanation:
The question asks for the result of multiplying 3/4 with 710. To perform this calculation we simply take the number 710 and multiply it by the fraction 3/4. Multiplying a whole number by a fraction involves multiplying the numerator of the fraction by the whole number and then dividing the result by the denominator of the fraction.
Here's a step-by-step breakdown:
Multiply the whole number 710 by the numerator of the fraction, 3.Therefore, 3/4 times 710 is 532.5.
Using the graph below, select all statements that are true.
A. f(0.6)=0
B. f(-3.2)=-3
C. f(5.1)=5
D. This is the graph of the greatest integer function.
E. This graph is one-to-one.
Answer:
A. f(0.6)=0
C. f(5.1)=5
D. This is the graph of the greatest integer function.
Step-by-step explanation:
The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.
The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.
Answer:
C, D, E
Step-by-step explanation:
Tony spent $100 on books to give away as prizes to his students. At the store, he bought 4 more books than planned, spending $5 per book. Which equation can be used to find the number of books he originally wanted to buy. X
Answer:
[tex]5x=100[/tex]
[tex]x=20\ books[/tex]
Step-by-step explanation:
I'm going to assume that all books cost the same.
Let
x ------> the number of books he originally wanted to buy
we know that
[tex](x+4)(5)=100+4(5)[/tex]
[tex]5x+20=100+20[/tex]
[tex]5x=100[/tex] -----> equation that can be used to find the number of books he originally wanted to buy
solve for x
[tex]x=100/5[/tex]
[tex]x=20\ books[/tex]
Nick has 21 pencils and Lance has 63 pencils.
Tony spent a total of $100 on books. Since he bought 4 more books than he originally planned, and each book cost $5, let's denote the original number of books he planned to buy as x. Therefore, the total number of books he ended up buying would be x + 4. Given that the cost of each book is $5, we can establish the equation 5(x + 4) = 100 to represent the total expenditure on books.
To find the number of books he originally wanted to buy, we will solve for x in the equation above:
Multiply 5 by the quantity x + 4 to obtain the left side of the equation.
Set that result equal to 100, as this is the total amount spent.
Solve the equation for x by first distributing the 5, which gives us 5x + 20 = 100, and then subtracting 20 from both sides of the equation to get 5x = 80.
Finally, divide both sides by 5 to find the value of x, which results in x = 16.
Therefore, Tony originally planned to buy 16 books.
I don't understand this. Can someone please help me?
Answer:
a) 16 in²
b) 20 cm²
Step-by-step explanation:
In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)
a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².
__
b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².
what is the quotient? 4x^2+3x+2 divided by x-3
For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.
quotient: [tex]4x + 15[/tex]
Divisor: x-3
Dividend: [tex]4x ^ 2 + 3x + 2[/tex]
Remainder: 47
It must be fulfilled that:
Dividend = Quotient * Divisor + Remainder
Answer:
See attached image
The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1.5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.
A. 1
B. 5
C. 10
D. 15
Answer: D. 15
Step-by-step explanation:
Given : The revenue each season from tickets at the theme part is represented by [tex]t(x) = 5x[/tex] .
The cost to pay the employees each season is represented by [tex]r(x) = (1.5)x[/tex].
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
The correct option is d. 15, is the estimated profit after four seasons, rounded to the nearest integer.
Given : The revenue each season from tickets at the theme part is represented by t(x) = 5x .
The cost to pay the employees each season is represented by r(x) = (1.5)x.
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
Match the red graph above to the corresponding equation
Answer:
y = -1/3·x³
Step-by-step explanation:
The function is odd (symmetrical about the origin), so corresponds to a function of odd degree. It is shorter and wider than the parent x³ function, so has a vertical scale factor less than 1. The appropriate choice is ...
y = -1/3x³
The corresponding equation that matches the red graph include the following: A. [tex]y=-\frac{1}{3} x^3[/tex].
What is a cubic root function?In Mathematics and Euclidean Geometry, a radical function, cubic function or a cube root function can be represented by using the following mathematical equation:
[tex]f(x)=a\sqrt[3]{x-h} +k[/tex]
where:
h represent the horizontal shift.k represent the vertical shift.By critically observing the graph shown above, we can logically deduce that the red graph represents a cubic function with an odd degree because it is symmetrical about the origin. Also, the parent cubic function [tex]f(x)=x^3[/tex] was vertically compressed by a factor that is less than 1, which is 1/3;
[tex]y=-\frac{1}{3} x^3[/tex]
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Please Help!! 35 Points!!!
Insert <, >, or = to make the sentence true.
12 __ 25
>
=
[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]
The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].
Hope this helped!
~Just a girl in love with Shawn Mendes
A random sample of 64 freshmen spent an average of 14 hours per week watching television. the sample standard deviation was 32 hours per week. what is the critical value for a 95% confidence interval for the population mean?
Answer:
+/- 1.9983
Step-by-step explanation:
The critical values for a confidence interval for the population mean, with population standard deviation not known, are obtained from the student's t distribution.
The sample size is given as 64. The degrees of freedom will thus be;
sample size - 1 = 64 - 1 = 63
The confidence level is given as 95%. The level of significance will thus be;
100 - 95 = 5%.
The area in the right-tail will thus be 2.5%. Therefore, we looking for a t-value such that the area to its right is 2.5% and the degrees of freedom being 63. From the t-tables we have;
+/- 1.9983
Evaluate the line integral c (2x3 − y3) dx + (4x3 + y3) dy where c is the unit circle, and verify green's theorem for this case
Parameterize [tex]C[/tex]
[tex]x=\cos t[/tex]
[tex]y=\sin t[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\langle2x^3-y^3,4x^3+y^3\rangle[/tex] along [tex]C[/tex] is
[tex]\displaystyle\int_0^{2\pi}\langle2\cos^3t-\sin^3t,4\cos^3t+\sin^3t\rangle\cdot\langle-\sin t,\cos t\rangle\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}(4\cos^4t-2\cos^3t\sin t+\cos t\sin t^3+\sin^4t)\,\mathrm dt=\boxed{\frac{15\pi}4}[/tex]
By Green's theorem, the line integral is equivalent to
[tex]\displaystyle\iint_{x^2+y^2\le1}\left(\frac{\partial(4x^3+y^3)}{\partial x}-\frac{\partial(2x^3-y^3)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le1}(12x^2+3y^2)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(12r^2\cos^2\theta+3r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(9r^3\cos^2\theta+3r^3)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{15\pi}4}[/tex]
To evaluate the line integral along the unit circle, we can parametrize the circle using x = cos(t) and y = sin(t). The resulting integral is 6 times the integral of cos squared(t) times cos(t).
Explanation:To evaluate the line integral, we need to parametrize the unit circle. Let's use x = cos(t) and y = sin(t) as the parameterization. The differential arc length is given by ds = √(dx² + dy²) = dt. Substituting these into the line integral, we get:
∫(2cos³(t) - sin³(t)) dt + ∫(4cos³(t) + sin³(t)) dt = ∫(6cos³(t)) dt
Since the unit circle can be parameterized from 0 to 2π, the integral becomes:
∫[6cos³(t)] dt = 6 ∫[(cos(t))³] dt = 6 ∫[cos³(t)] dt = 6[∫(cos²(t)cos(t)) dt]
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20 points One diagonal of a rhombus has endpoints (-10, 1) and (2, 9).
What are the endpoints of the other diagonal?
(-7, 7) and (-1, 3)
(-4, 7) and (2, 7)
(-2, 2) and (-6, 8)
(-6, 2) and (-2, 8)
Final answer:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other. The endpoints of the other diagonal are (-7, 7) and (-1, 3). Therefore, Option A is the correct answer.
Explanation:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other, meaning they intersect at their midpoints. We can find the midpoint by taking the average of the x-coordinates and the average of the y-coordinates of the given endpoints of the first diagonal.
For the given endpoints (-10, 1) and (2, 9), the midpoint would be ((-10 + 2)/2, (1 + 9)/2), which simplifies to (-4, 5).
Since the diagonals bisect each other, the other diagonal would have the same midpoint. Therefore, the endpoints of the other diagonal would be (-4, 5) and the reflection of (-4, 5) across the midpoint of the given diagonal, which is the midpoint of (-10, 1) and (2, 9). Thus, the correct answer is (-4, 5) and its reflection across (-4, 5), which is (-7, 7) and (-1, 3).
The longer leg of a 30°-60°-90° triangle measures [tex]9\sqrt{3}[/tex] inches. What is the length of the shorter leg?
A. 18 inches
B. [tex]18\sqrt{3}[/tex] inches
C. [tex]9\sqrt{3}[/tex] inches
D. 9 inches
Answer:
D. 9
Step-by-step explanation:
The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x). The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse). If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:
9√3 = x√3 and solve for x. Divide both sides by the √3 to get that x = 9
Answer:
The correct answer is option D. 9
Step-by-step explanation:
Points to remember
It a right triangle with angles 30°, 60 and 90° the n the sides are in the ratio,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2
To find the length of shorter leg
Here it is given that, longer length = 9√3
We have,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2 = Shorter leg : 9√3: hypotenuse
Therefore shorter leg = 9√3/√3 = 9
The ages of sunitha and raseeda are in ratio of 7:8 ten years from now there ages will be 9:10 find there present age
Answer:
Sunitha: 35Raseeda: 40Step-by-step explanation:
Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...
Sunitha: 7·5 = 35
Raseeda: 8·5 = 40
_____
If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:
s/r = 7/8(s+10)/(r+10) = 9/10These can be translated to standard form, which may make some methods of solution easier:
7r -8s = 09r -10s = 10These have solution (r, s) = (40, 35).
A rectangular garden measures 3 feet by 15 feet the gardener decides to extend the garden 1 foot in each of the four directions what is the perimeter of the new garden in feet
The perimeter of the new garden after extension is 44 feet.
Explanation:To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.
To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:
P = 2(l + w)
where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:
P = 2(5 + 17) = 2(22) = 44 feet
Therefore, the perimeter of the new garden is 44 feet.
HELP!! I don't understand this question!!
Answer:
The answer would be c.
Step-by-step explanation:
What I'm understanding from this question is,
In the first attachment, Which has the questions selected on Shows there are two shapes.
Those two shapes have to go in to the identify the tessellation Created using the given regular polygons.
As you can see in answer C. Both shapes are represented in that tessellation.
For example, In the attachment below ] I will be showing you an example of what the question might look like for This certain tessellation.
You obviously know that square is tiltedMake a diamond shaped. That is why the diamond and hexagon is correct!
hope this helps! if it helps in any way plz mark as branliest !
.Tom is throwing darts at a target. In his last 30 throws, Tom has hit the target 20 times. You want to know the estimated probability that exactly one out of the next three throws does not hit the target.
Step-by-step explanation:
In his last 30 throws, Tom hit the target 20 times and missed 10 times.
p = probability he misses the target = ⅓
q = probability he hits the target = ⅔
Using binomial probability:
P = nCr (p)^r (q)^(n-r)
Given n = 3, r = 1, p = ⅓, and q = ⅔:
P = ₃C₁ (⅓)¹ (⅔)³⁻¹
P = (3) (⅓) (⅔)²
P = 4/9
There is a 4/9 probability that he misses exactly 1 of his next 3 throws.
By applying binomial probability, the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target is 4/9.
How to determine the estimated probability?In order to determine the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target, we would apply binomial probability equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Based on the information given, we can deduce the following points:
Probability that Tom misses the target (p) = 10/30 = ⅓Probability that Tom hits the target (q) = 20/30 = ⅔Number of next throws (n) = 3.Number of throws taken at a time (r) = 1.Substituting the given parameters into the equation, we have;
P = ³C₁ × (⅓)¹ × (⅔)³⁻¹
P = 3 × (⅓)¹ × (⅔)²
P = 3 × ⅓ × (⅔)²
P = 1 × 4/9
P = 4/9.
Read more on probability here: https://brainly.com/question/25870256
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The student council at Sparrowtown High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $72. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
(Algebra 2)