Find the vertex, focus, and directrix of the parabola. Sketch its graph, showing the focus and the directrix.

1. 20x=y2 2. (x-3)squared =1/2(y+1) 3. y2+14y+4x+45=0 Find an equation of the parabola that satisfies the given conditions Focus F(0-4), directrix y=4 Find the vertices, the foci and the equations of the asymptotes of the hyperbola. 1.y2divided by 49 minus x2 divided by sixteen =1 2.x2-2y2=8 Find an equat ...continues

Integration of indefinite integrals

Evaluate the following indefinite integrals: See attached file.

vertex, focus, and directrix of a parabola.

1. 20x=y^2 2. (x-3)^2 =1/2(y+1) 3. y2+14y+4x+45=0 Find the vertex, focus, and directrix of the parabola described by the above equations.

Volume maximization : Finding the dimensions of a cylinder given the surface area.

Find the dimensions of a cylinder with a surface area of 300 cm^2 with a maximum volume.

Arc length of a Curve

How does the length of the curve x=t^2, y=t^3, [0,2] come out to be 3/4 + (ln2)/2?

Surface area of revolution

How do I find the surface area obtained by revolving the curve y=x-1 from x=1 to x=4 about the line x= -1?

Calculus: Integration by Parts

I need to find the integral of x^2 sin 3x dx. My text says that the answer should be 1/27[6x sin 3x -(9x^2-2) cos 3x] + c I'm hoping that someone can show me how to get to this answer, and would appreciate any advice for integration by parts.

Volume of water poured in to bowl with iron ball.

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

A problem dealing with volume of revolution

A bowl is shaped like a hemisphere with radius R centimeters. An iron ball with radius R/2 centimeters is placed in the bowl and water is poured in to a depth of 2R/3 centimeters. How much water was poured in?

Calculus: Double Integration

Please see the attached file for the fully formatted problem.