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1 year ago

Assume these are weekly. Matthew worked 8 hours at $9 a hour. Taxes were 16%. How much money was left?

Mathematics

1 answer:

guapka [62]1 year ago

6 0

Number of hours worked: 8

earning per hour = $9

tax = 16%

First, multiply the number of hours by the earnings per hour:

8 x 9 = $72 (total earnings)

Now, find the tax amount by multiplying the total earnings by the tax percentage in decimal form (divided by 100)

72 x (16/100)= 72 x 0.16 = $11.52

Finally, subtract the tax amount to the total earnings:

Money left: 72-11.52 = $ 60.48

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When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.

Differentiate these with respect to θ :

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In polar coordinates, we have

y(θ) = r(θ) sin(θ)

x(θ) = r(θ) cos(θ)

and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.

The slope of the tangent line to the curve is dy/dx. By the chain rule,

dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)

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

When θ = π/3, the slope is

dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))

dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

dy/dx = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

y - 13√3/2 = -1/(17√3) (x - 13/2)

y = -(x - 338)/(17√3)

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Read 2 more answers

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