Evaluate the function f(x) =-x/2 -7x -2 find f(-9)
1 answer:
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By using the motion equations, we conclude that she will make the goal.
<h3>Will she make the goal?</h3>
First, we know that the goal is 20ft away, and the position in x is given by:
Let's find the time in which the ball will travel these 20 ft.
So the horizontal distance is covered in 1.35 seconds, now let's see which is the height of the ball at that time.
The height equation is:
Evaluating in t = 1.35 we get:
And the goal is 5ft tall, so we can conclude that she will make the goal.
If you want to learn more about motion equations:
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Answer: Choice C
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Explanation:
The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve
Think of the blue region as the floor of this weirdly shaped 3D room.
We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is where 0 < x < 1
Let's compute the area of each general cross section.
We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.
This is what we want to compute
Apply a u-substitution
u = -2x
du/dx = -2
du = -2dx
dx = du/(-2)
dx = -0.5du
Also, don't forget to change the limits of integration
- If x = 0, then u = -2x = -2(0) = 0
- If x = 1, then u = -2x = -2(1) = -2
This means,
I used the rule that which says swapping the limits of integration will have us swap the sign out front.
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Furthermore,
In short,
This points us to choice C as the final answer.
