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Anarel [89]
3 years ago
6

AP Calc pls help Find the area of the region bounded by the graphs of y = x2 − 4x and y = x − 4.

Mathematics
1 answer:
pishuonlain [190]3 years ago
7 0

Answer:

9/2

Step-by-step explanation:

First, you want to graph these two functions and find where they intersect so you can figure out the lower and upper bounds you need on your integral. I just entered it in on my TI-84 and had it figure out the intersections for me: (1, -3) and (4, 0). You could also set these two equations equal to one another and figure out their intersection point algebraically.

This means your integral should have an upper bound of 4 and a lower bound of 1, since I want to integrate with respect to x. You could also integrate with respect to y; it depends on your preference. Since the equations are already solved for y, it's easier to integrate with respect to x. To find the area between two curves, you want to integrate the height of the space between these two curves, so what you do is the curve on top minus the curve on the bottom. In our case, x - 4 is the above the area between the curve, and x^2 - 4x is below the area between the curve. So the integral looks like this:

\int\limits^4_1 {(x - 4) - (x^2 - 4x)} \, dx

My result is that the area is 9/2, which you can find by simplifying the integral. I'd be happy to do it for you, but using the formula thing on this site is kind of a huge pain. It'll take me a second to write down the work if you need it, but hopefully just seeing how the integral is set up will be enough to get you there!


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A student says that the sum difference, product and quotient of two
anastassius [24]

Answer:

The quotient of two integers may not always be an integer.

Therefore, I do not agree when a student says that the sum difference, product, and quotient of two are always integers.

Step-by-step explanation:

The student is not largely correct!

The sum, difference, and product of two integers is indeed always an integer.

But, the quotient of two integers may not always be an integer.

  • For example, the quotient of integers 4 and 2 will be an integer.

i.e.

4/2 = 2

  • But, if we take the quotient of 2 and 3, the result will not be an integer.

i.e.

2/3 = 0.67

Therefore, I do not agree when a student says that the sum difference, product, and quotient of two are always integers.

7 0
2 years ago
Store display volume of each cube shaped box is 125 cubic inches of the display has six layers of boxes how high is the display
Doss [256]

Answer:

30 inches

Step-by-step explanation:

We know that the formula for calculate the volume of a cube is:

∨=8³

Where "s" is the length of each side.

Since the volume of each cube-shaped box is 125 cubic inches, we can find "s":

125 in³=8³

∛125 in³=8

8=5 in

We know that  the display has six layers of boxes, then , to calculate the height of the display, we can multiply the value of "s" obtained before by 6.

Then:

height= (5 in)(6)=30 in

8 0
2 years ago
I NEED HELP LIKE NOW PLS!<br> I'll give you brainliest answer if you can help me ((:
Marta_Voda [28]
The first word of the question is cut out of the picture, so we don't exactly know what the assignment is. But we can see that the graph of f(x) will do something weird when x=-3, because the denominator will be zero, and division by zero doesn't even have a definition or meaning. Just for fun, you should go ahead and calculate the numerator when x=-3, and that totally blows your mind, because the numerator is zero too. So you've got. f(-3)= 0/0 , and I can pretty much guarantee that you won't be able to plot that point anywhere on the graph. (I'm pretty sure that f(-3) is actually going to turn out to be -13, but even if I'm correct, you probably haven't learned that little calculus trick yet, so don't worry about it. As far as you're concerned, f(-3) is 0/0, and can't be plotted.)
7 0
3 years ago
Read 2 more answers
Q6 Q20.) Solve the equation for x in the interval ​[0,2π).
Marysya12 [62]
Hello there!

See picture below...

Let me know if you have any questions about the answer. As always, it is my pleasure to help students like you!


8 0
3 years ago
When a 757 passenger jet begins its descent to the Ronald Reagan National Airport in Washington, D.C., it is 3900 feet from the
Svetradugi [14.3K]

Answer:

Option A. 37106 ft.

Step-by-step explanation:

Given: An 757 passenger jet at the height of 3900 feet from the ground means vertical height = 3900 feet.

Angle of descent to the airport in Washington,D.C. is 6 degrees.

To find: Horizontal distance the plane will cover to reach the run way.

Solution: As we know tan ∅  = \frac{Height}{Base}

Then tan 6° = \frac{3900}{x}

0.105 = \frac{3900}{x}

x = \frac{3900}{.105}

x = 37106 ft

3 0
3 years ago
Read 2 more answers
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