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

5

10

15

20

25

30

35

40

45

50

55

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x