Given the following rectangle and circle, what appropriate value of x are the two areas equal? A: x= 3.4 B: x=5.8 C: x= 10.2 D:
the curves do not intersect, so there is no solution
1 answer:
The correct option is D:
the curves do not intersect, so there is no solution
<h3>For what values of x are the two areas equal?</h3>
The area of the rectangle is given by:
f(x) = (x + 7)*(5x - 3)
f(x) = 5x² -3x + 35x - 21
f(x) = 5x² + 32x - 21
For the circle, the area is:
g(x) = 2*pi*(x + 6)^2
g(x) = 2pi*x^2 + 12pi*x + 72pi
The solution is given g(x) = f(x).
By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.
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Solve the second equation for t, then substitute into the first.
.. y = 2t +3
.. y -3 = 2t
.. (y -3)/2 = t
.. x = t^2
.. x = ((y -3)/2)^2
.. x = (1/4)(y -3)^2 . . . . . . your rectangular equation, good for y in [-3, 3]
.. y = 2t +3
.. y -3 = 2t
.. (y -3)/2 = t
.. x = t^2
.. x = ((y -3)/2)^2
.. x = (1/4)(y -3)^2 . . . . . . your rectangular equation, good for y in [-3, 3]