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.
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<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.
3/33 can be reduced to 1/11 by dividing by 3 on the top and bottom.
1/11 is not equal to 1/10. Although they have the same numerator or number on top, 1, they don't have the same number in the bottom.
So they are not equivalent.
Hope this helps.
Answer:
Step-by-step explanation:
3x + 1 = 10
3x = 10 - 1
3x = 9
x = 9/3
x = 3
hope this helps
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Answer:
c
Step-by-step explanation:
cvvvbbnh
Where's the "triangle with alt. BD?" This problem can be solved without the diagram, but the solution would be easier with it.
BD is the altitude. Find the length of BD by finding the dist. between (-1,4) and (2,4); it is 2-(-1), or 3. |BD| = 3.
I've graphed the triangle myself and have found that the "base" of the triangle is the vertical line thru (2,1) and (2,6); its length is 6-1, or 5.
Thus, the area of this triangle is A = (b)(h) / 2, or A = (5)(3) / 2 = 10/3 square inches.