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musickatia [10]
3 years ago
5

Then find the area bounded by the two graphs of y=2x^2−24x+42 and y=7x−2x^2

Mathematics
1 answer:
vodka [1.7K]3 years ago
3 0
To find the area under a curve, we integrate the function. To find the area bound between two curves, we integrate the difference of the functions. That is, we find:

\int\limits^a_b {(f(x)-g(x))} \, dx

If you think about it, we are really doing this with all integration, only the second function is just y=0.

First, we need to figure out which function is on top. In this case we know that 2x^2-24x+42 is a positive parabola while 7x-2x^2 is negative, so the negative parabola will be on top. It is always a good idea to draw a rough sketch of the graphs because the curves could intercept multiple times, flipping which graph is on top at different intervals.

Next, we need to determine the bounds. These will be where the two graphs intercept, so we can just set them equal to each other and solve for x:

2x^2-24x+42=7x-2x^2

Combine like terms:

4x^2-31x+42

Now factor and find the zeros. We can use the quadratic formula:

\frac{31+ \sqrt{31^2-4(4)(42)} }{8}

and

\frac{31- \sqrt{31^2-4(4)(42)} }{8}

x = 1.75 and 6

\int\limits^6_{1.75} {((7x-2x^2)-(2x^2-24x+42))} \, dx

\int\limits^6_{1.75} {(-4x^2+31x-42)} \, dx

Solve:

\frac{-4x^3}{3} + \frac{31x^2}{2} - 42x

Plug in bounds:

\frac{-4(6)^3}{3} + \frac{31(6)^2}{2} - 42(6)-(\frac{-4(1.75)^3}{3} + \frac{31(1.75)^2}{2} - 42(1.75)) = 51.17708





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Find three positive consecutive integers such that the product of the smallest and the largest is 17 more than three times the m
trapecia [35]
There are two answers to this question
the first possible answer is 5, 6, and 7 and the second possible answer is -4, -3, and -2


Step-by-step explanation:

let the three numbers be (x-1), x, and (x+1)
the product of the smallest and largest number is 17 more than 3 times the middle number, or
(x-1)(x+1) = 3x+17, or
x^2-1 = 3+17, or
x^2-3x-18 = 0
(x-6)(x+3) = 0
So x = 6 or -3
Then just subtract one and add one to get the other integers. the three numbers are 5, 6, and 7 or -4, -3, and -2
3 0
2 years ago
Select the correct answer. One factor of the polynomial 213 3r2 – 3x + 2 is (t – 2), which expression represents the other facto
Darina [25.2K]

Answer:

(x - 2)(x + 1)(2x -1)

Step-by-step explanation:

We use synthetic division as a tool for factoring the given expression.  The coefficients of the terms given are {2, -3, -3, 2}.  If x - 2 is a factor of this expression, then 2 is a root.  We perform synthetic division as follows:

2   /    2     -3      -3     2

                  4       2     -2

    -------------------------------

          2      1        -1      0

Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s).  Using -1 as divisor, we get:

-1    /     2     1     -1

                   -2    1

     ---------------------

             2     -1     0

Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor.  Answer D is correct.

4 0
2 years ago
Describe how a point on a graph is related to a table and an equation that represent the same relationship.
castortr0y [4]

Answer:

because everything is relative to each other.

Step-by-step explanation: Graphing ordered pairs is only the beginning of the story. Once you know how to place points on a grid, you can use them to make sense of all kinds of mathematical relationships. A linear relationship is a relationship between variables such that when plotted on a coordinate plane, the points lie on a line. Let’s start by looking at a series of points in Quadrant I on the coordinate plane. Look at the five ordered pairs (and their x– and y-coordinates) below.

4 0
3 years ago
Read 2 more answers
2. Find the unit rate demonstrated in the graph<br> below.
MaRussiya [10]

Answer:B is the answer for this question

6 0
3 years ago
Mrs. White's students are making school spirit packs. They have 24 bumper stickers and 18 window clings. Every pack must have th
ExtremeBDS [4]

Answer:

6 packet.

Step-by-step explanation:

Given:

Mrs. White's students are making school spirit packs.

They have 24 bumper stickers and 18 window clings.

Every pack must have the same contents and there should be no leftover items.

Question asked:

What is the greatest number of packs they can make?

Solution:

To find the<u> </u><u>greatest number</u> of packs could be made by 24 bumper stickers and 18 window clings by using<u> </u><u>same contents</u> in each pack with<u> </u><u>no left over </u>items, we will simply use<u><em> Highest Common Factor.</em></u>

Factor of 24 - 2, 3, 4, <em><u>6</u></em>, 8, 12, 24

Factor of 18 - 2, 3, <em><u>6</u></em>, 9, 18

Highest Common Factor is 6.

Thus, they can make 6 packet at most.

3 0
2 years ago
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