Five hundred gallons of 89-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane gasoline. How much of each type of gasoline is required to obtain the 500 gallons of 89-octane gasoline?

If the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept.

Vertical Motion Use $a(t)=-32$ feet per second per second as the acceleration due to gravity. (Neglect air resistance.)

A balloon, rising vertically with a velocity of $16$ feet per second, releases a sandbag at the instant it is $64$ feet above the ground.

(a) How many seconds after its release will the bag strike the ground?

Sketch the graph of the function in previous question. Show that the slope of the tangent can be found using the properties of circles.

What were the motives behind European exploration in the 1400s? Explain

$\odot Q$ and $\odot R$ both have a radius of $3 \mathrm{cm} .$ Therefore the circles are ____________. (concentric or congruent)

Use cylindrical or spherical coordinates, whichever seems more appropriate. A solid right circular cone with constant density has base radius a and height h. Find the moment of inertia of the cone about a diameter of its base.

Let A be an n × n symmetric negative definite matrix. Show that the leading principal submatrices of A are negative definite.

Thirty liters of a 40% acid solution is obtained by mixing a 25% solution with a 50% solution. (a) Write a system of equations in which one equation represents the amount of final mixture required and the other represents the percent of acid in the final mixture. Let x and y represent the amounts of the 25% and 50% solutions, respectively. (b) Use a graphing utility to graph the two equations in part (a) in the same viewing window. (c) As the amount of the 25% solution increases, how does the amount of the solution change? (d) How much of each solution is required to obtain the specified concentration of the final mixture?

Show that if u is a column vector in $R^{n}$, then $H=I_{n}-2 \mathbf{u} \mathbf{u}^{T}$ is symmetric.

Circles T and S intersect at points A and B. What is the relationship between

$$\overline{AB}\ and\ {\overleftrightarrow{TS}}?$$

Explain.

What were some of the effects of the CounterReformation on European society?

Find symmetric equations for the line of intersection of the planes. z = 2x - y - 5, z = 4x + 3y - 5

A circle has a radius of x. Another circle has a radius of 3x.

Write equations for the areas of both circles.