Circle A is shown on the coordinates plane shown above
1 answer:
The center of the circle is at (-2, 0). The radius is 5 units. The equation for a circle, in standard form is
.
We have our h and k from the center. h is the x coordinate and k is the y coordinate. The radius is 5. That means that the circle's equation, before simplifying, is
. After simplifying it is
. That's A and B. For C, we will simply pick points on the axes. One point on the circle is at (3, 0); another point is at (-2, 5); a third point is at (-7, 0). For D, the area of a circle is
.
For us that looks like this
. In terms of pi the answer is 25 pi, but in decimal form to the nearest square unit, it's 79 units squared.
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well, about A and D, I just plugged the values on the slope formula of
for A the values are 8.01 and 8.0, so indeed those "slopes" are close.
for D the values are -2.25 and 8.0, so no dice on that one.
for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.
checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice.
for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.
for E, do they intercept at (2,1)? well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent.
for F, we know the slope of the line L(x) is 8, is g'(2) = 8? let's check
recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice.
Answer:
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