Find the exact value of the slope of the line which is tangent to the curve given by the equation

r = 1 - 2cos θ at theta equals pi over 2 .

Thank you in advance!

-2

Step-by-step explanation:

x = r cos θ

y = r sin θ

dx/dθ = -r sin θ + r' cos θ

dy/dθ = r cos θ + r' sin θ

dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)

At θ = π/2, cos θ = 0, sin θ = 1, and r = 1.  So the derivative simplifies to:

dy/dx = (r') / (-1)

dy/dx = -r'

dy/dx = -2 sin θ

dy/dx = -2

according to this law, when unemployment goes up by 1%, gdp drops by 2%. in the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the gdp drops by 6%. thus the effect is a drop in gdp by 6%.

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.