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3 years ago

The braking distance Dv (in meters) for a certain car moving at velocity v (in meters/second) is given by =Dvv234.

Mathematics

1 answer:

MaRussiya [10]3 years ago

8 0

Answer:

S(t)= $\frac{9t^2}{34}$

Step-by-step explanation:

We are given that

Th braking distance for a certain car moving at velocity v(in m/s) is given by

$D(v)=\frac{v^2}{34}$

The velocity of car B(t) t seconds after starting = $B(t)=3t$

We have to find the value for braking distance S(t) after t seconds.

To find the formula for braking distance we will substitute the value of velocity B(t) in place of v in D(v)

Substitute the value of velocity then we get

Then, we get

The formula for the braking distance S(t) after t seconds= $\frac{(3t)^2}{34}$

The formula for the braking distance S(t) after t seconds= $\frac{9t^2}{34}$

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Answer:

$12.65

Step-by-step explanation:

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3 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

3 years ago

Write in slope-intercept form an equation of the line that passes through the points (−1,12) and (1,2).

zzz [600]

Answer:

$y=-5x+7$

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

the points (−1,12) and (1,2)

substitute

$m=\frac{2-12}{1+1}$

$m=\frac{-10}{2}$

$m=-5$

step 2

we know that

The equation of the line in slope intercept form is equl to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=-5$

$point\ (1,2)$

substitute in the linear equation and solve for b

$2=-5(1)+b$

$b=2+5=7$

therefore

$y=-5x+7$

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3 years ago

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solmaris [256]

Answer:

2/5

Step-by-step explanation:

The experimental probability is

P (heads) = number of heads/ total tosses

= 8/20

= 2/5

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Answer:

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