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.
Hello,
1
.65 + 0.20(65) = 65 + 13 = 78(65 - 60) / 65 = 5/65 = 0.0769 x 100 = 7.69 rounds to 7.7 % decrease compared to the 65 pizza's sold yesterday
2.
I posted a file to help you on this question!
3. <span>Find principal by using the formula </span><span>I=P⋅i⋅t</span><span>, where </span>I<span> is interest, </span>P<span> is total principal, </span>i<span> is rate of interest per year, and </span>t<span> is total time in years.
</span>
So basically your answer is
600.I truley hope this helps.
Have a good day!
-Jurgen
Answer:
hardd sorry
Step-by-step explanation:>..
Answer:
Step-by-step explanation:equivalent expressions
Answer
I believe B.)8in3 is the right answer according to the square-cube law.
Step-by-step explanation: