13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
1 answer:
Answer:
Step-by-step explanation:
The equation of a periodic function is in the form:
y = Asin(Bx + C) + D
Where A = amplitude, B = 2π / period, D = vertical shift, phase shift = -C / B.
Given that:
amplitude: 4, period 4 phase shift = vertical shift = -2
Hence:
A = amplitude = 4, B = 2π / period = 2π / 4 = π / 2, D = vertical shift = -2.
Phase shift = -C / B
C = -phase shift * B = - * -2 * π / 2 = π.
Therefore substituting gives:
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Answer:
k = 168
Step-by-step explanation:
rewrite the equation
Multiply 42 to isolate k. Do the same on the other side
42 * 4 = 168 When you do that you get 168.
Answer:
256
Step-by-step explanation:
A calculator works well for this.
_____
None of the minus signs are subject to the exponents (because they are not in parentheses, as (-1)^5, for example. Since there are an even number of them in the product, their product is +1 and they can be ignored.
1 to any power is still 1, so the factors (1^n) can be ignored.
After you ignore all of the things that can be ignored, your problem simplifies to ...
(2^2)(2^-3)^-2
The rules of exponents applicable to this are ...
(a^b)^c = a^(b·c)
(a^b)(a^c) = a^(b+c)
Then your product simplifies to ...
(2^2)(2^((-3)(-2)) = (2^2)(2^6)
= 2^(2+6)
= 2^8 = 256
