Use your graphing calculator to solve the following system of equations. If there is no solution, state no solution if there is
more than one solution, state all solutions. Also, sketch the system of equation
y=x^2+3x-6
y=x^2+3x-6
1 answer:
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So we have three points A(4,3), B(4,4) and C(7,4).
We introduce a fourth point D(7,3).
We obtain a rectangle ABCD. By rotating the rectangle,
around the y axis, we get two cylinders. Denote the
first cylinder C1 and the inner cylinder with vertices AB by C2.
Computing the volume of C1:
Computing the volume of the cylinder C2:
In order to find the volume of the <span>hollow tube, simply compute the difference of the two obtained values like this:
</span>
Now, in order to find the <span>volume of the solid generated by revolving the region enclosed by the triangle, simply divide the previous </span>value over two like this:
Answer
We introduce a fourth point D(7,3).
We obtain a rectangle ABCD. By rotating the rectangle,
around the y axis, we get two cylinders. Denote the
first cylinder C1 and the inner cylinder with vertices AB by C2.
Computing the volume of C1:
Computing the volume of the cylinder C2:
In order to find the volume of the <span>hollow tube, simply compute the difference of the two obtained values like this:
</span>
Now, in order to find the <span>volume of the solid generated by revolving the region enclosed by the triangle, simply divide the previous </span>value over two like this:
Answer