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3 years ago

4. Elliott deposits $500 into a savings account

Mathematics

1 answer:

Len [333]3 years ago

7 0

Interest = 500 x .03 x 4

I = 60

Closing Balance = 500 (p) + 60 (1)

Closing Balance = 560

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3 years ago

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What is the perimeter of a square if the is a length of 4x and a width of 36-5x?

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3 years ago

The price of a television was reduced from $250 to $200. What was the percent of decrease?

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3 years ago

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5

zmey [24]

Differentiate both sides of the equation of the circle with respect to $x$ , treating $y=y(x)$ as a function of $x$ :

$x^2+y^2=5\implies2x+2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac xy$

This gives the slope of any line tangent to the circle at the point $(x,y)$ .

Rewriting the given line in slope-intercept form tells us its slope is

$x=2y+5\implies y=\dfrac12x-\dfrac52\implies\mathrm{slope}=\dfrac12$

In order for this line to be tangent to the circle, it must intersect the circle at the point $(x,y)$ such that

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In the equation of the circle, we have

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If $x=1$ , then $1=2y+5\implies y=-2$ , as expected. Therefore $x=2y+5$ is a tangent line to the circle $x^2+y^2=5$ at the point (1, -2).

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4 years ago

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