The volume of a right circular cone of radius r and height h is Suppose that the radius and height of the cone are changing with respect to time t.

a. Find a relationship between

b. At a certain instant of time, the radius and height of the cone are 12 in. and 13 in. and are increasing at the rate of 0.2 in./sec and 0.5 in./sec, respectively. How fast is the volume of the cone increasing?


a.

b.

Mathematics

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Solve the system of equations by elimination, if a solution exists.

A. x = 1, y = 1 B. No solution C. x = 0, y = 1 D. x = 1, y = 0

Mathematics

Sketch the graph of the quadratic function. Identify the vertex and axis of symmetry.f(x) = (x + 1)2 - 9

A. vertex: (1, - 9)
axis of symmetry: x = 1


B. vertex: (1, - 9)
axis of symmetry: x = 1


C. vertex: (- 1, - 9)
axis of symmetry: x = - 1


D. vertex: (- 1, - 9)
axis of symmetry: x = - 1


Mathematics

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

A. y = 55.3 B. y = 3x + 50 C. y = 54 D. y = 2.5x + 50.4

Mathematics

A cone sliced by a plane results in a type of curve called a conic section. Use the given information and figure to identify the conic section produced in the plane.  The plane is perpendicular to the axis of the cone. 

A. parabola B. hyperbola C. ellipse D. circle

Mathematics