Consider the circle of radius 5 centered at (0, 0). find an equation of the line tangent to the circle at the point (3, 4) in slope intercept form.

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Step-by-step explanation:

The equation of a circle of radius centered at is:

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Differentiate implicitly with respect to to find the slope of tangents to this circle.

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Apply the power rule and the chain rule. Treat as a function of , .

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That is:

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Solve this equation for :

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The slope of the tangent to this circle at point will thus equal

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Apply the slope-point of a line in a cartesian plane:

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For the tangent line in this question:

The equation of this tangent line will thus be:

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That simplifies to

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the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

open side up . . 1/50 . . 2%

closed side up . . 5/50 . . 10%

landed on side . . 44/50 . . 88%