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3 years ago

10

Which equation represents a line that passes through (–9, –3) and has a slope of –6?

1 answer:

IgorC [24]3 years ago

6 0

Answer:

<h2>y + 3 = -6(x + 9) - point-slope form</h2><h2>y = -6x - 57 - slope-intercept form</h2>

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

<em>m</em><em> - slope</em>

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

========================================

We have the slope <em>m = -6</em> and the point (-9, -3).

Substitute:

$y-(-3)=-6(x-(-9))\\\\y+3=-6(x+9)$

Convert to the slope-intercept form (<em>y = mx + b</em>):

$y+3=-6(x+9)$ <em>use the distributive property</em>

$y+3=-6x-54$ <em>subtract 3 from both sides</em>

$y=-6x-57$

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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:

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

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

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

$S_{n}=910.22\ ft$

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2 years ago