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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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Answer: I believe the answer is b. 55%

Step-by-step explanation:

200/ (550-200) * 100

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How do you write 8.04 × 104 in standard form?<br> (plzzz help) (NO LINKS)
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Step-by-step explanation:

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3 years ago
In the accompanying diagram of rectangle ABCD, diagonal AC is drawn, DE = 8, DE 1 AC, and m2 DAC = 55. Find the area of rectangl
Aneli [31]

Answer:

sin (55)  =  DE / AD

AD  =  DE / sin (55)

AD  =  8 / sin (55)

And  

tan (55) = DC / AD

tan (55)  = DC / [8 / sin (55) ]

DC  =  8 tan (55) / sin (55)    

AD * DC  =

[8 /sin (55) ]  [ 8 tan (55) / sin (55) ]   =    136 units^2  

Step-by-step explanation:

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7 0
3 years ago
Can anyone help me??? <br><br> PLZ….
bezimeni [28]
7. Obtuse
8. Acute
9. No, because it’s the hypotenuse
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4 0
3 years ago
License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is
Helga [31]

Answer:

26^3\times10^2 = 1757600

option B is correct

Step-by-step explanation:

We have 5 spaces in the license plate:

_ _ _ _ _

we have 26 available letters, and 10 available numbers.

starting with letters:

  • how many choices do i have to place the 1st letter? 26.

26 _ _ _ _

  • how many choices do i have to place the 2nd letter? 26 (since we're allowed to repeat letters)

26 26 _ _ _

  • how many choices do i have to place the 3rd letter? 26

26 26 26 _ _

we've used all the places for letters, (note: the exact position of the letters doesn't matter here, the first letter could've been placed anywhere in _ _ _ _ _, but the amount of possible choices for letters would always be 26).

let's move on to numbers.

  • how many choices do i have to place the 1st number? 10

26 26 26 10 _

  • how many choices do i have to place the 2nd number? 10

26 26 26 10 10

we've completed our number plate. Next we'll simply multiply all these numbers to get all the possible arrangements in which numbers and letters can be displayed on a license place.

26^3\times10^2 = 1757600

option B is correct

8 0
3 years ago
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