Answer:
50 minutes
Explanation:
We can set this up as a rate * time = distance problem. We can set the rate at which Amanda travels to work to be x, since that quantity is unknown. The time it takes is given to be 60 minutes. This means that the total distance she travels to get to work is 60x. On the other hand, the way back home has more unknown quantities. The exact rate is unknown, but we do know that it is 20% more than the rate at which Amanda travels to work. This means that the rate is x + .20x, or 1.2x. We can set the time to be y, which means the total distance she travels to get back home is 1.2xy. We are told that Amanda uses the same route to get to and from work, which means 60x = 1.2xy. All we have to do now is solve this equation:

If we divide through by x and then isolate y, we get that it takes Amanda 50 minutes to get home
Using sum and difference identities from trigonometric identities shows that; Asin(ωt)cos(φ) +Acos(ωt)sin(φ) = Asin(ωt + φ)
<h3>How to prove Trigonometric Identities?</h3>
We know from sum and difference identities that;
sin (α + β) = sin(α)cos(β) + cos(α)sin(β)
sin (α - β) = sin(α)cos(β) - cos(α)sin(β)
c₂ = Acos(φ)
c₁ = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
c₁² + c₂² =
(Asin(φ))² + (Acos(φ))²
= A²(sin(φ)² +cos(φ)²)
= A² * 1
= A²
Using common factor as shown in the trigonometric identity above for Asin(ωt)cos(φ) +Acos(ωt)sin(φ) gives us; Asin(ωt + φ)
Complete Question is;
y(t) = distance of weight from equilibrium position
ω = Angular Frequency (measured in radians per second)
A = Amplitude
φ = Phase shift
c₂ = Acos(φ)
c₁ = Asin(φ)
Use the information above and the trigonometric identities to prove that
Asin(ωt + φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Read more about Trigonometric Identities at; brainly.com/question/7331447
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The expression which represent the polar form of complex number -4i when converted into the polar form is 4(cos π+ isin π)
<h3>What is complex number?</h3>
A complex number is the combination of real and imaginary number. In a complex number, real part and imaginary part of number is written together. For example,
a+bi
Here, (a) is the real part while (b) is the imaginary part.
The complex number which need to convert into its polar representation is,
n=-4i
It can be rewritten as,
n=0-4i
The radius r of the polar form is,
r²=0²+(-4)²
r²=0+16
r=4
The value of cos theta is,
tan θ=0/-4
θ=tan⁻¹(0)
θ=π
Thus, the polar form is,
z=rcos θ+(r sin θ)i
z=-4(cos π+ isin π)
Thus, the expression which represent the polar form of complex number -4i when converted into the polar form is 4(cos π+ isin π)
Learn more about the complex number here;
brainly.com/question/2218826
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