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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:
The left end approaches to + Infinite being an exponential function, and the right end to 0
Step-by-step explanation:
we have to remember the exponential function, the best way to find the answer is plotting the graph or arranging a table of values.
As you can see in the attached graph the y axis gets closer and closer to 0 as it moves forward in the x axis, and as it moves to the left the y axis starts increasing rapidly.
Also you got to keep in mind the way that functions behave in terms of the sign of its variable. for example the 10 in this equation only makes the curve to get wider, but if you change the sign to minus, the answer would be different.
<h2>Given :</h2>
- length = 200 cm
- breadth = 150 cm
- height = 100 cm
Through the statement above we have,
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