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3 years ago

9

At 57 degrees fahrenheit, a certain insect chirps at a rate of 100 times per minute, and at 65 degrees, they chirp 156 times per

minute. Write an equation in slope-intercept form that represents the situation.

1 answer:

Elan Coil [88]3 years ago

5 0

Answer:

57= 100 65=156-8=158

Step-by-step explanation:

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Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

$A=w\ell$

Where <em>w</em> is the width and <em>l</em> is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>

$\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]$

By the Product Rule:

$\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w$

Since we know that dl/dt = 6 and that dw/dt = 5:

$\displaystyle \frac{dA}{dt}=5\ell + 6w$

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

$\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}$

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

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The old city park is rectangular. It has a length of 350 meters. It has a width of 125 meters. What is the perimeter, in meters,

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The question as you wrote it doesn't fit the answers. However, one of the answers fits if you meant
"elapsed time from 5:34 to 10:11".

There are many ways to do this. Try first taking the time from 5:34 to 6:11, and after that finding the time from 6:11 to to 10:11.

In a way, 6:00 is the same thing as 5:60. Add 11 to that and you can see that 6:11 is the same as 5:71. Now that you have an easy way to find the time from 5:34 to 6:11.
6:11 - 5:34 isn't easy.
But 5:71 - 5:34 is quite easy. 71 - 34 is 37.

So, from 5:34 to 6:11 there are 37 minutes.

Now the easy part, finding the time from 6:11 to 10:11. Since the minutes are the same, just subtract the hours. 10 - 6 = 4 hours.

Now you have the hours and minutes, which number 4 hours and 37 minutes.

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