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.
Answer:
Step-by-step explanation:
Using the area model and standard algorithm, we have:
332 (tenths)
<u> × 21 </u>
332
<u> 664 </u>
<u> 6972 </u> tenths = 697.2
<u />
30 + 3 tenths
1 300 32 332
20 600 64 664
33.2 × 21 =<u> 30 </u> × <u> 1 </u> = <u> 30 </u>
Answer:
d)15 apples
Step-by-step explanation:
We know that she gives 2 red apples and 1 green apple to 5 friends and has no more left over. you add 2+1=3 Then you multiply 3x5=15.
Hope this helps! Have a great day ahead. Tell me if I'm wrong :) Stay Safe <3