Provide an appropriate response.The region bounded by the lines x = 2, x = 6, y = -2, and y = 1 is revolved about the y-axis to form a solid. Explain how you could use elementary geometry formulas to verify the volume of this solid.

What will be an ideal response?


The resulting solid is a cylindrical shell whose volume is given by V = ?h, where r1 is the outer radius, r2 is the inner radius, and h is the height. Since r1 = 6, r2 = 2 and h = 3, V = ?3 = 96?.

Mathematics

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Use synthetic division to find the function value.f(x) = 3x5 - 4x4 + 2x3 - x + 2; find f(3).

A. 458 B. 469 C. 459 D. 464

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Simplify completely.

A.
B.
C.
D.

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Explain how to obtain the graph of the given quadratic function from the graph of f(x) = (x - 7)2 + 9

A. Take the graph of y = x2 and shift it 7 units to the left and 9 units up. B. Take the graph of y = x2 and shift it 7 units to the right and 9 units up. C. Take the graph of y = x2 and shift it 7 units to the left and 9 units down. D. Take the graph of y = x2 and shift it 7 units to the right and 9 units down.

Mathematics

Write the number in expanded form.984

A. 984 hundreds = 984 B. 4 hundreds + 8 tens + 9 ones = 400 + 80 + 9 C. 9 thousands + 8 hundreds + 4 tens = 9000 + 800 + 40 D. 9 hundreds + 8 tens + 4 ones = 900 + 80 + 4

Mathematics