Mathematics College

A car travels down a highway at 25 m/s. An observer stands 100m from the highway.

a) How fast is the distance from the observer to the car increasing when the car passes in front of the observer?

(Use decimal notation.)

The rate is =

(b) How fast is the distance increasing 10s later?

(Use decimal notation. Give your answer to three decimal places.)

The rate is =

Answers

Answer 1
Let x be the distance (in meters) along the road that the car has traveled andh be the distance (in meters) between the car and the observer.


Part (a):
Before the car passes the observer, we have [tex] \frac{dh}{dt} \ \textless \ 0[/tex]; after it passes, we have [tex]\frac{dh}{dt} \ \textgreater \ 0[/tex].
So at the instant it passes we have [tex]\frac{dh}{dt} = 0[/tex], given that [tex]\frac{dh}{dt} = 0[/tex] varies continuously since the car travels at a constant velocity.
Therefore, the rate the distance from the observer to the car increasing when the car passes in front of the observer is 0m/s



Part (b):

By the Pythagorean Theorem, we have
[tex]h^2=x^2+100^2[/tex]
Thus,
[tex]2h\frac{dh}{dt}=2x\frac{dx}{dt} \\ \\ \Rightarrow\frac{dh}{dt}= \frac{x}{h} \frac{dx}{dt}[/tex]

where: [tex]\frac{dx}{dt}[/tex] is the velocity at which the car is travelling.

Since the car travels at 25 m/s, so after 10 seconds, the distance (in meters) along the road that the car has traveled, x, is given by

[tex]x=speed\times time=25\times10=250 \ meters.[/tex]

and

[tex]h^2=250^2+100^2=62,500+10,000=72,500 \\ \\ \Rightarrow h= \sqrt{72,500} =269.26 \ m[/tex]

Therefore,

[tex]\frac{dh}{dt}= \frac{x}{h} \frac{dx}{dt} \\ \\ = \frac{250}{269.26} (25) \\ \\ =0.9285(25) \\ \\ =23.212 \ m/s[/tex]
Answer 2
Final answer:

The rate at which the distance from the observer to the car is increasing is 25 m/s, both when the car passes in front of the observer and 10 seconds later.

Explanation:

To find the rate at which the distance from the observer to the car is increasing, we need to use the concept of relative velocity. When the car passes in front of the observer, its velocity is perpendicular to the line connecting the observer and the car. Therefore, the rate at which the distance is increasing is equal to the speed of the car. In this case, the rate is 25 m/s.

To find how fast the distance is increasing 10 seconds later, we need to consider the fact that the car is still moving at a constant velocity of 25 m/s. Therefore, the rate at which the distance is increasing remains the same. So, the rate is still 25 m/s.

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Related Questions

expand and simplify: 5(x-3)+2(2x+1)

Answers

First you have to distribute.
5(x - 3) + 2(2x + 1)
5x - 15 + 4x + 2
Then you combine like terms.
9x - 13
This is your final answer. I hope this helps love! :)
5(x-3)+2(2x+1)
5x-15 +2(2x+1)
 5x-15 +4x +2
      9x-13

9x-13 is your answer

If the average of 12 consecutive odd integers is 328, what is the least of these integers

Answers

x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9+x+10+x+11+x+12/12
12x+78/12 = 132 times 12 is
12x+78 = 1,548 minus 78
12x = 1,506 divide by 12
x = 125.5 I believe is the answer, sorry if it is wrong



how is adding integers similar to adding whole numbers? how is it different

Answers

Integers use positive and whole numbers like whole numbers, but also use negative numbers, unlike whole numbers.

Hope this helps!

Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer. 40 POINTS

Answers

3x + 1 = y

x: 1 | 2 | 3  |
------|---|--- |----------------
y: 4 | 7 | 10|

so make points at (1,4) (2,7) and (3,10), and connect them to get the line

4x + 1

x: 1 | 2 | 3
----------------
y: 5 | 9 | 13

Make points at (1,5) (2,9) and (3,13)

IF they do not intersect yet, continue making points until they intersect. Make note of the point in which they intersect, and that is your answer

hope this helps

Lisa drew a picture of a boat. She used the scale 1 inch: 6.5 feet the boat in her picture is 7:25 inches long. What is the length, in feet of the actual boat?

Answers

Okay. So, using the scale, we can solve for the length of the actual boat by writing and solving a proportion. Let’s write it out like this: 1/6.5 = 7.5/x. This is because you’re looking for the real length of the boat, so the x would be lined up horizontally with 6.5, as shown in the proportion. Let’s cross multiply. 6.5 * 7.5 is 48.75. 1 * x is 1x. 48.75 = 1x. Now, let’s divide each side by 1 to isolate the “x”. When you do that, you get x = 48.75. There. The length of the actual boat is 48.75 feet.
you can write this as a proportion  1 inch is to 6.5 feet as 7.25 in is to X               1/6.5 = 7.25/X                     7.25 times 6.5 = X           X = 47.125 feet

Carly sold 18 rolls of wrapping paper. that is 2 time as many as may rolls as Jasmine sold.

Answers

Jasmine sold 9 rolls.
18x2 would equal 36 if its a word problem that's supposed to be solved. hope it helps!


What is a point estimate of the difference between the mean annual premium in pennsylvania and the national mean (to the nearest dollar)?

Answers

Given that the mean annual premium for automobile insurance in the United States is $1503 and that a sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1440

Then the point estimate of the difference between the mean annual premium in pennsylvania and the national mean (to the nearest dollar) is $1,440 - $1,503 = -$63.
Final answer:

A point estimate is a single value used to estimate an unknown parameter. The point estimate of the difference between the mean annual premium in Pennsylvania and the national mean can be calculated by taking the difference between the two means.

Explanation:

A point estimate is a single value that is used to estimate an unknown parameter of a population. In this case, the point estimate of the difference between the mean annual premium in Pennsylvania and the national mean can be calculated by taking the difference between the two means. Let's say the mean annual premium in Pennsylvania is $1000 and the national mean is $1500. The point estimate of the difference would be $1500 - $1000 = $500.

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if (-4,5) is the only solution to a system of two linear equations, then the graphical solution would show:

Answers

What shape do linear equations make? To picture the solution visually, you can imagine two of those shapes meeting on a graph at one (and only one) point, (-4,5).
Final answer:

The graphical solution to a system of two linear equations with the point (-4,5) as the only solution will show two lines intersecting at this point on a two-dimensional graph.

Explanation:

If the point (-4,5) is the only solution to a system of two linear equations, this means that the two lines represented by these equations intersect at this point. On a Two-Dimensional (x-y) Graphing system, this point would be plotted on the graph where the x-coordinate is -4 and the y-coordinate is 5.

These two equations when plotted as lines in a two-dimensional space (with x as the independent variable and y as the dependent variable) will intersect at this point (-4,5). If you draw a line from the origin to the point (-4,5), it will intersect the two lines at this point. This is how the graphical solution would look like.

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Raffle tickets are being sold for a fundraiser. The function a(n) relates the amount of money raised to the number of tickets sold, n. 

It takes as input the number of tickets sold and returns as output the amount of money raised. 

a(n) = 3n – 15 

Which equation represents the inverse function n(a), which takes the money raised as input and returns the number of tickets sold as output?


Answers

Answer:

For apex it is N(a)= [tex]\frac{a+15}{3}[/tex]

Final answer:

To find the inverse function, solve the equation a = 3n - 15 for n. The inverse function is n(a) = (a + 15) / 3.

Explanation:

To find the inverse function, we need to solve the equation n(a) = 3n - 15 for n.

Step 1: Replace n(a) with a: a = 3n - 15

Step 2: Solve for n.

Add 15 to both sides of the equation.a + 15 = 3nDivide both sides of the equation by 3.(a + 15) / 3 = n

Therefore, the inverse function is n(a) = (a + 15) / 3.

Ms.Smith has 132 stickers to give to her students.Shehas 5 students.If she gives the same number of stickers to each of her students how many stickers will she have leftover

Answers

If Ms. Smith hands out 130 of her stickers between all 5 of her students each will have 26. Which means she will have 2 remaining
She'll have 24.6 stickers left over because you divide the 132 stickers with the 5 students

Which expression is equivalent to 6 – (–8)?

Answers

[tex] 6 -(-8)[/tex] 

[tex]6+8 [/tex] 

[tex]=14[/tex]

The expression 6 – (–8) will be equivalent to 14.

What is an expression?

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

For example 3x +5y

The constraint of expression is represented as = or <, >.

Given the expression,

6 – (–8)

By multiplication,

Negative signs become positive

6 – (–8) = 6 + 8 = 14

Hence "The expression 6 – (–8) will be equivalent to 14.".

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The question asked what is 1/4 % of 2000

Answers

1/4% of 2000 is 5

Hope this helps!
do u mean 25% if so its 500 if u mean .25% then 5

A microwave is placed on top of two boxes. One box is 2 feet 5 inches tall the other box is 3 feet 11 inches tall and the microwave is 3 feet 3 inches tall. How tall are they combined ?

Answers

Okay, so looking at the numbers.
1 foot =12 inches 

2*12= 24+5= 29 inches

Second box
3*12= 36+3=39

Adding both of those numbers, 29 and 39 you get 68 inches.

So, if you combine the boxes, you get 5 feet and 8 inches.

The answer in inches is 68, and the answer in feet and inches is 5 feet, 8 inches.

Hope this helps!

15 points and will mark brainliest
solve this system of linear equations. separate the x- and y- values with a coma. -9x=5-2y
15x=-11+2y

Answers

Solve the following system:{-9 x = 5 - 2 y | (equation 1)15 x = 2 y - 11 | (equation 2)
Express the system in standard form:{-(9 x) + 2 y = 5 | (equation 1)15 x - 2 y = -11 | (equation 2)
Swap equation 1 with equation 2:{15 x - 2 y = -11 | (equation 1)-(9 x) + 2 y = 5 | (equation 2)
Add 3/5 × (equation 1) to equation 2:{15 x - 2 y = -11 | (equation 1)0 x+(4 y)/5 = (-8)/5 | (equation 2)
Multiply equation 2 by 5/4:{15 x - 2 y = -11 | (equation 1)0 x+y = -2 | (equation 2)
Add 2 × (equation 2) to equation 1:{15 x+0 y = -15 | (equation 1)0 x+y = -2 | (equation 2)
Divide equation 1 by 15:{x+0 y = -1 | (equation 1)0 x+y = -2 | (equation 2)
Collect results:Answer:  {x = -1                {y = -2

Please note the { are supposed to span over both equations but it interfaces doesn't allow it. Please see attachment for clarification.

A company manufactures photo cells it uses the expression

Answers

What expression it’s not completed

Hello Brainly,
Please send the details for the area of each shape.
Sincerely,
Leanoriaia

Answers

This type of problems are solved by partitioning the figure into rectangles, whose areas we can find easily.

Picture 1)

From the point denoted by E, draw two altitudes towards the sides AG and AC.

Since ED is 3, then BC is 3. Thus, AB=4-3=1. 

Since EF is 1, then HG is 1, so AH=3-1=2.


The area of the figure is equal to the area of rectangle ACDH + the area of the square HEFG.

That is, the area of the figure is 4*2+1*1=8+1=9 (square in).

Picture 2)

As in the first part, draw the altitudes EB and EH from point E.

GF is 5, so AB is 5. This means that BC=7-5=2 (in).

FE is 3, so GH is 3, that is HA=6-3=3.

Thus, Area(figure)=Area(ABFG)+Area(BCDE)=5*6+2*3=30+6=36 (square in.)

Answer: 9 (square in); 36 (square in.)

How to divide 715÷25 using partial quotient

Answers

Attached a solution and showed work.

What is the answer to the distributative operation of 85 divided by 5

Answers

85(2)+85(3)=255 but if u divide it normally it would be 17

Evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 2 (t + 2)(t − 6) dt

Answers

do you mean 2(t+2)(t-6) dt?
if yes then,
expanding you have
2 { t² -4t -12} dt
2 ∫ t²-4t-12 dt
2 [ t³ -4t² -12t +c]

Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?

Answers

Since the amount of money it costs for the forks are 1.70f (if f is the number of forks, due to that we add 1.70 for each fork) and the spoons is 1.30s (with s being the number of spoons), the total money spent is
1.7f+1.3s=37.9 and the total money made is
5.6f+5.4s=147.20 dollars (since forks sell for 5.6 dollars and spoons 5.4)

Multiplying the first equation by -5.4/1.3 and adding it to the second, we end up with -1.46153846154f=-10.2307692308 and by dividing both sides by -1.46153846154, we get f=7. Plugging that into 1.7f+1.3s=37.9, we get 1.7*7+1.3s=37.9. Subtracting 1.7*7 from both sides and then dividing them by 1.3, we end up with (37.9-1.7*7)/1.3=s=20

The environment club is selling indoor herbs gardens for Earth Day. Each member is encouraged to sell at least 10 gardens. You sell 3 on Monday and 4 on Tuesday. Write and solve an inequality to find the possible number of gardens you can sell to reach your goal.

Answers

The inequality is looking for a value of "at least 10" gardens. This means something "greater than or equal to" 10 (>=10). After selling 3 on Monday plus 4 on Tuesday, this leaves "x" to be sold to reach the goal. By setting this on the same side as the 7, we can create the inequality to find out how many more are needed, at minimum, to reach our stated goal: 7 + x >= 10, which, when subtracting the 7 out from both sides of the inequality, leaves x >= 3 gardens.

There is a positive correlation between the number of times the Striped Ground Cricket chirps per second and the temperature in degrees Fahrenheit. If a scatter plot is made with the number of chirps on the horizontal axis and the trend line is found to be y = 3x + 25, then what would you predict the number of chirps per second to be when the temperature is 55 degrees Fahrenheit?

Answers

y=10. Hope this answer helps.

Answer:

As per the statement:

If a scatter plot is made with the number of chirps on the horizontal axis and

the trend line is given by:

[tex]y = 3x+25[/tex]              ....[1]

where,

y represents the temperature in degrees Fahrenheit

x represents the number of chirps per second.

We have to find  the number of chirps per second to be when the temperature is 55 degrees Fahrenheit.

Substitute y = 55 degree Fahrenheit in [1] we have;

[tex]55 = 3x+25[/tex]

Subtract 25 from both sides we have;

[tex]30= 3x[/tex]

Divide both sides by 3 we have;

10 = x

or

x = 10

Therefore, the number of chirps per second to be when the temperature is 55 degrees Fahrenheit is, 10

3(2x+4)-7=-2(x-5)+3x what does x equal? A.1 B.-1 C.-5 D.5

Answers

Solve for x:3 (2 x + 4) - 7 = 3 x - 2 (x - 5)
3 (2 x + 4) = 6 x + 12:6 x + 12 - 7 = 3 x - 2 (x - 5)
Add like terms. 12 - 7 = 5:6 x + 5 = 3 x - 2 (x - 5)
-2 (x - 5) = 10 - 2 x:6 x + 5 = 3 x + 10 - 2 x
3 x - 2 x = x:6 x + 5 = x + 10
Subtract x from both sides:(6 x - x) + 5 = (x - x) + 10
6 x - x = 5 x:5 x + 5 = (x - x) + 10
x - x = 0:5 x + 5 = 10
Subtract 5 from both sides:5 x + (5 - 5) = 10 - 5
5 - 5 = 0:5 x = 10 - 5
10 - 5 = 5:5 x = 5
Divide both sides of 5 x = 5 by 5:(5 x)/5 = 5/5
5/5 = 1:x = 5/5
5/5 = 1:Answer: x = 1

2x + y = -2
x + y = 5
 The x-coordinate of the solution to the system shown is _____.
 -7
-3
3
7

Answers

Subtract equation (2) from equation (1)
Subtract the like terms (ie subtract straight down)

2x - x = 1x = x
y - y = 0y = 0 so the y terms go away
-2 - 5 = -7

We end up with x = -7

Answer:

-7

Step-by-step explanation:

If 3 tons of flower bed mulch cost $480, what is the price per pound?

Answers

1 ton = 2,000 pounds 
3 tons = 6,000 pounds
$480/6,000 = 0.08 
per pound is $0.08

The second angle of a triangular kite is four times as large as the first. The third angle is 45 degrees more than the sum of the other two angels. Find the measurement of the second angle.

Answers

the  ANSWER is
92.5 degrees
because second angle = 4x = 4*17.5 = 70 deg
so 
third angle = 5x+5 = 5*17.5 + 5= 92.5 deg

Solve 8d + 4d – 5d – 4 = 3d.

Answers

8d + 4d - 5d - 4 = 3d
12d - 5d - 4 = 3d
7d - 4 = 3d
7d = 3d + 4
4d = 4
d = 1
8d+4d-5d-4=3d
 7d-4=3d
 7d-3d=4
 4d=4
 d=1

Find two positive numbers whose product is 81 and whose sum is a minimum. (if both values are the same number, enter it into both blanks.)

Answers

Answer:

The two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.

Step-by-step explanation:

81 is divisible by 1 and 81, since 81/1 = 81 and 81/81 = 1.

81 is divisible by 3 and 27, since 81/3 = 27 and 81/27 = 3.

81 is divisible by 9, since 81/9 = 9.

Their sums are.

81 + 1 = 82.

3 + 27 = 30

9 + 9 = 18.

So the two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.

Answer:

The two positive numbers will be 9 and 9.

Step-by-step explanation:

Let the two positive numbers be x and y.

It is given that the product of the number is 81 the sum of them is minimum.

So, the product can be written as [tex]xy=81[/tex].

The sum can be written as [tex]x+y=x+\dfrac{81}{x}[/tex]. It is required to minimize the sum.

Differentiate the sum as,

[tex]x+y=x+\dfrac{81}{x}\\1+y'=1-\dfrac{81}{x^2}=0\\x^2=81\\x=9\\y=\dfrac{81}{x}\\y=9[/tex]

Now, the second derivative of the sum will be,

[tex]y''=2\times \dfrac{81}{x^3}>0[/tex]

So, the second derivative is positive and hence, the sum will be minimum at x=9.

Therefore, the two positive numbers will be 9 and 9.

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Marlene is a tennis player who has win 55% of her matches. What istje probability that she will lose her next tennis match

Answers

Since she has won 55% of her matches and lost 45, the probability is 9/20 which is 45%

Answer:

45% probability that Marlene will lose her next tennis match.

Step-by-step explanation:

For each match that Marlene plays, there is a 55% probability that she wins and a 45% probability that she loses.

These probabilities for each match are independent.

So there is a 45% probability that Marlene will lose her next tennis match.

Need help solving this :/

Answers

[tex]\bf \begin{array}{cccll} x&171x-337778&\textit{internet users}\\ ----&-------&------\\ 2004&171(2004)-337778&4906\\ 2005&171(2005)-337778&5077\\ 2006&171(2006)-337778&5248\\ 2007&171(2007)-337778&5419\\ 2008&171(2008)-337778&5590\\ 2009&171(2009)-337778&5761\\ 2010&171(2010)-337778&5932\\ \end{array}[/tex]

now, that's using the table of values, let's do so using N = 5932

[tex]\bf N=171x-337778\implies 5932=171x-337778 \\\\\\ 5932+337778=171x\implies 343710=171x\implies \cfrac{343710}{171}=x \\\\\\ 2010=x[/tex]
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