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An arch has the shape of a semi-ellipse. The arch has a height of [b] feet and a span of [a] feet. Find an equation for the ellipse, and use that to find the distance from the center to a point at which the height is [y] feet. Round to the nearest hundredth.

Write the following sum using sigma notation:

Determine the equation in standard form of the ellipse illustrated in the graph above.  

Given the equation of the hyperbola

The sides of a nuclear power plant cooling tower form a hyperbola.  The diameter of the bottom of the tower is [bottom] feet.  The smallest diameter of the tower is [center] feet which is [hc] feet above the ground.  The tower is [height] feet tall. Find the width of the tower at a height of [h] feet. Round to the nearest integer.

Find the first term and common difference of the arithmetic sequence whose term is

Write the following sum and difference of logarithms as a single log. Assume all variables are positive.

An exponential function passes through the points and . what are the values of a and b? [answera] [answerb]

Given two matrices and , find 4[] + 2[]. Please note the matrices are written as 3-by-3 tables. Matrix B Cols Rows -10 1 5 -6 -4 3 -8 6 2   Matrix A Cols Rows 4 -6 10 -7 -5 6 3 1 -2

Write an equation in factored-form for the function graphed below: