If a supersonic jet flies at Mach 3.2, what will be the cone angle (to the nearest degree)?

The equations of parabolas, circles, ellipses, and hyperbolas are given. Graph the equation.

$$y^2/25-x^2/121=1$$

Find the second Taylor polynomial of $x(x+1)^{3 / 2}$ at x=0.

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?

Draw a cone with a height of 9 inches and a diameter of 4 inches. Find the volume.

Jodi says that if you double the radius of a right circular cone and divide the slant height by 2, then the surface area of the cone stays the same since the 2s cancel each other out. How do you respond?

A flask contains $\frac { 1 } { 3 }$ mole of $\mathrm { H } _ { 2 }$ and $\frac { 2 } { 3 }$ mole of He. Compare the force on the wall per impact of $\mathrm { H } _ { 2 }$ relative to that for He.

Give an example to illustrate each axiom of equality: a) Reflexive b) Symmetric c) Transitive d) Substitution

Suppose that a merchant buys a patio set from the wholesaler for $180. At what price should the merchant mark the patio set so that it may be offered at a discount of 25% but still give the merchant a 40% profit on his$180 investment.

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?

When an alternating current of frequency f and peak current

$$I_0$$

passes through a resistance R, then the power delivered to the resistance at time t seconds is

$$P = I _ { 0 } ^ { 2 } R \sin ^ { 2 } 2 \pi f t$$

Write an expression for the power in terms of

$$\csc ^ { 2 } 2 \pi \mathrm { ft }$$

Now suppose that instead of paying a dividend Good Values (from the previous problem) plans to repurchase $10,000 worth of stock.

a. What will be the stock price before and after the repurchase? b. Suppose an investor who holds 200 shares sells 20 of her shares back to the firm. If there are no taxes on dividends or capital gains, show that she should be indifferent between the repurchase and the dividend. c. Show that if dividends are taxed at 30% and capital gains are not taxed, the value of the firm is higher if it pursues the share repurchase instead of the dividend.

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

Two walkers start walking on different paths in the town park. Walker A starts at the 0.5m mark on his path and walks at a speed of lm/sec. Walker B starts at the 2m mark on her path and walks at a speed of 0.5m/sec. a) Make a table the keeps track of where each walker is over ten seconds of time. Walker A( , ) Walker B( , ) b) Where does it appear that the two walkers meet? c) Use the starting point and speed to write an equation for each walker: Walker A:_______________________ Walker B: ___________________________ d) Graph the two equations on the same set of axes.