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Ulleksa [173]
3 years ago
9

HELP ME!!!

Mathematics
1 answer:
larisa [96]3 years ago
5 0

Answer:

  -2, 8/3

Step-by-step explanation:

You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...

  A = (1/2)(f(a) +f(4))(4 -a)

  = (1/2)((3a -1) +(3·4 -1))(4 -a)

  = (1/2)(3a +10)(4 -a)

We want this area to be 12, so we can substitute that value for A and solve for "a".

  12 = (1/2)(3a +10)(4 -a)

 24 = (3a +10)(4 -a) = -3a² +2a +40

  3a² -2a -16 = 0 . . . . . . subtract the right side

  (3a -8)(a +2) = 0 . . . . . factor

Values of "a" that make these factors zero are ...

  a = 8/3, a = -2

The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.

_____

<em>Alternate solution</em>

The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.

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Step-by-step explanation:

10x² + 11x − 6 = 0

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5 0
1 year ago
The area of a particular rectangle is 72. If the length of the rectangle is twice
soldier1979 [14.2K]

Answer:

6

Step-by-step explanation:

Suppose the width is "a".  Then the length is 2a.

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4 0
2 years ago
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kvv77 [185]
56.3% hope it helped ok
3 0
3 years ago
I try to find it but I could PLEASE help I’ll say the answer when I’m done
Margaret [11]

Answer: false

Step-by-step explanation:

6 0
2 years ago
Can some please answer this
Sonbull [250]

9514 1404 393

Answer:

  B  (2 violet)

Step-by-step explanation:

Let the colors be represented by their first letter. Then the balances give rise to two equation:

  o +y +b +v = r +g +b

  o +y +v = g +v

Subtracting the second equation from the first gives ...

  (o +y +b +v) -(o +y +v) = (r +g +b) -(g +v)

  b = r +b -v

Adding v-b to both sides, we have ...

  b +(v -b) = r +b -v +(v -b)

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Multiplying this result by 2, we can match the final balance:

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7 0
2 years ago
Read 2 more answers
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