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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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the diameter of a piston for an automobile is 3 11/16in with tolerence of 1/64in. find the upper and lower limits of the pistons
padilas [110]

Upper Tolerance

Remark

The 11/16 is the only thing that will be affected. The three won't go up or down when we add 1/64 so we should just work with the 11/16. We need only add 11/16 and 1/64 together to see what the upper range is. Later on we can add 3 into the mix.

Solution

<u>Upper Limit</u>

\dfrac{11}{16} +  \dfrac{1}{64}

Now change the 11/16 into 64. Multiply numerator and denominator or 11/16 by 4

\dfrac{11*4}{16*4} +  \dfrac{1}{64}

\dfrac{11*4}{16*4} +  \dfrac{1}{64} Which results in

\dfrac{44}{64} +  \dfrac{1}{64}

With a final result for the fractions of 45/64

So the upper tolerance = 3 45/64

<u>Lower Tolerance</u>

Just follow the same steps as you did for the upper tolerance except you subtract 1/64 like this.

\dfrac{11}{16} - \dfrac{1}{64}

Your answer should be 3 and 43/64


4 0
3 years ago
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x-intercept (-250, 0)

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If I was given 50 dollars and they bought 12.00 and 6.50 and 4.50 how much do I owe them
larisa [96]
Answer is:
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7 0
3 years ago
Read 2 more answers
8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the comm
Ilya [14]

Answer:

a₁ = 38

Step-by-step explanation:

Given AP, where:

  • 8a₈ = 12a₁₂
  • d = -2,
  • a₁ = ?

=============

<h3>Solution</h3>

aₙ = a₁ + (n-1)d

  • a₈ = a₁ + 7d = a₁ + 7*(-2) = a₁ - 14
  • a₁₂ = a₁ + 11d = a₁ + 11*(-2) = a₁ - 22

8a₈ = 12a₁₂

  • 8(a₁ - 14) = 12(a₁ - 22)
  • 2(a₁ - 14) = 3(a₁ - 22)
  • 2a₁ - 28 = 3a₁ - 66
  • 3a₁ - 2a₁ = -28 + 66
  • a₁ = 38
6 0
3 years ago
The parallel boxplots below display the quiz grades (out of 30) for two of Mrs. Smith’s statistics classes.
stich3 [128]

Answer:

The quiz grades for class 1 have more variability than the quiz grades for class 2.

Step-by-step explanation:

8 0
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