the sine function is a many-to-one function and therefore has no inverse function.
However if the domain is restricted to -90° ≤ x ≤ 90°
Then the function is one-to-one for this domain
Thus,
x is defined as the angle such that - π/2 ≤ x ≤ π/2
5π/6 is therefore outwith the domain
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:
a)20 is the answers for the question
Step-by-step explanation:
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Answer:
The answer is 62.8
Step-by-step explanation:
C=2(3.14)(r)
c=6.28(10)
c=62.8
10 to the 5th power means 5 times zero, place 8 before that and it will be 800000 then multiply with 0.5 it will be 400000. In scientific notation it will be like 4x10 the 5th power.