What is 2x if x is -3
2 answers:
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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.
For this question we will use the following relations.
100 centimeters=1 meter (or 1 centimeter= 0.01 meter)
10 millimeter=1 centimeter (or 1 mm=0.1 cm)
60 minutes = 1 hour (or 1 min= hour)
Now, Jackson's speed is 1350 meters per hour. This can be converted to cm per minute as follows:
...Equation 1
Likewise, Jonah's swim speed in cm/min can be calculated as:
...Equation 2
As we can see clearly after comparing Equation 1 and Equation 2, Jonah's swim speed of 7500 cm/min is faster than that of Jackson.
Thus, option B is correct.