Let

$$Q \left( x ^ { \prime } , y ^ { \prime } \right)$$

be any point of L' different from

$$P \left( x _ { 1 } , y _ { 1 } \right)$$

Explain why

$$\frac { y ^ { \prime } - y _ { 1 } } { x ^ { \prime } - x _ { 1 } } = m$$

.

A baseball with mass 0.15 kg and speed 45 m/s is struck by a baseball bat of mass m kg and speed 40 m/s (in the opposite direction of the ball’s motion). After the collision, the ball has initial speed $u(m)=\frac{82.5 m-6.75}{m+0.15} \mathrm{m} / \mathrm{s}$. Show that u'(m)>0 and interpret this in baseball terms. Compare a'(1) and u'(1.2).

Using electromagnetic waves, you generally cannot resolve any structures that are smaller than the wavelength you are using. CD, DVD, and Blu-ray players use small “pits” that encode the 0s and 1s of the digital information stored on them—the smaller the pits, the more information you can store. A DVD can store 4.7 GB, and a Blu-ray can store 25 GB. If a DVD player typically uses lasers that emit red light in the wavelength range from 640 nm to 660 nm, what do you expect the wavelength and color of a Blu-ray laser to be?

Find the antiderivative $F(x)$ of the function $f(x)$

$$f(x)=\sin ^{2}(x) \cos (x)$$

Involve trigonometric equations quadratic in form. Solve each equation on the interval

$$[ 0.2 \pi )$$

$$4 \sec ^ { 2 } x - 2 = 0$$

Of the students in a class playing musical instruments, 60% are female. 20% of the females and 30% of the males play the violin. Copy and complete the tree diagram.

Find the y-intercept.

$$f ( x ) = - 2 x ^ { 4 } + 2 x ^ { 3 }$$

Find the determinants by row reduction to echelon form.

$$\left| \begin{array}{rrrrr}{1} & {3} & {-1} & {0} & {-2} \\ {0} & {2} & {-4} & {-2} & {-6} \\ {-2} & {-6} & {2} & {3} & {10} \\ {1} & {5} & {-6} & {2} & {-3} \\ {0} & {2} & {-4} & {5} & {9}\end{array}\right|$$

How were economic competition and imperialism causes of World War I?

Count the possible combinations of r letters chosen from the given list. U, V, W, X, Y, Z; r = 3

Solve each rational inequality. $\frac { 3 x + 1 } { 3 } - \frac { x } { 2 } \leq \frac { x + 2 } { 2 }$

Use Simpson's rule with n = 6 to estimate the volume of the solid generated by rotating the region under the curve y = ln x between x = 1 and x = 2 about the x axis.

Simplify and rationalize the denominator, if necessary. $\frac{8}{\sqrt[7]{x}}$

A hollow circular shaft for use in a pumping station is being designed with an inside diameter equal to 0.75 times the outside diameter. The shaft must transmit 400 hp at 400 rpm without exceeding the allowable shear stress of 6000 psi. Determine the minimum required outside diameter d.