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2 years ago

How do the average rates of change for f(x) = -0.5x² and g(x) = -1.5x² over the interval -5 ≤ x ≤ -2 compare?

1 answer:

8 0

Pick an x-value between the interval givens. I’ll choose “1”. If you sub in one for both f(x) and g(x) you get that f(1) = -1.5 and g(1) = -0.5. Now you can divide f(1) by g(1) to get average rate of change. -1.5/-0.5 = 3.

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3 years ago

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4 years ago

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3 years ago

Kathy is fencing in her yard that has an area of 800 square feet. Her yard is in the shape of a rectangle where the length is 60

anygoal [31]

Answer:

The dimensions of the yard are W=20ft and L=40ft.

Step-by-step explanation:

Let be:

W: width of the yard.

L:length.

Now, we can write the equation of that relates length and width:

$L=5W-60$ (Equation #1)

The area of the yard can be expressed as (using equation #1 into #2):

$Area=W*L=W*(5W-60)$ (Equation #2)

Since the Area of the yard is $800 ft^2$ , then equation #2 turns into:

$800=W*(5W-60)$

Now, we rearrange this equation:

$800=W*(5W-60)//800=5W^2-60W//5W^2-60W-800=0$

We can divide the equation by 5 :

$W^2-12W-160=0$

We need to find the solution for this quadratic. Let's find the factors of 160 that multiplied yields -160 and added yields -12. Let's choose -20 and 8, since $(-20)*8=160$ and $-20+8=-12$ . The equation factorised looks like this:

$(W-20)(W+8)=0$

Therefore the possible solutions are W=20 and W=-8. We discard W=-8 since width must be a positive number. To find the length, we substitute the value of W in equation #1:

$5*20-60=40$

Therefore, the dimensions of the yard are W=20ft and L=40ft.

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3 years ago

How do the average rates of change for f(x) = -0.5x² and g(x) = -1.5x² over the interval -5 ≤ x ≤ -2 compare?​

How do the average rates of change for f(x) = -0.5x² and g(x) = -1.5x² over the interval -5 ≤ x ≤ -2 compare?