Acid or subtract. $\frac { 6 r s } { r ^ { 2 } s ^ { 2 } } + \frac { 18 r } { r ^ { 2 } s ^ { 2 } }$

What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?

Make the following conversions:

$$2500 ^ { \circ } \mathrm { F }$$

to K

For the function, give the new function rule after the given transformation.

$$f ( x ) = \left\{ \begin{array} { l l } { 3 x ^ { 2 } } & { \text { if } x < 1 } \\ { - 2 x + 4 } & { \text { if } x \geq 1 } \end{array} \right.$$

after a vertical stretch by a factor of 5

use a graphing utility to graph the quadratic function. Find the x-intercept(s) of the graph and compare them with the solutions of the corresponding quadratic equation when f(x) = 0. f(x) = x^2 - 4x

Solve the inequality and graph the solution. $\frac{3}{8}+x \leq \frac{5}{16}$

Arrange these numbers in order from least to greatest: -1, 1, 0.1, -0.1, 0

Let

$$g ( x ) = \frac { 1 } { 3 } | x - 1 | - 2$$

. (a) Describe the transformations from the graph of

$$f ( x ) = | x |$$

to the graph of g. (b) Graph g.

At t = t0 the voltage across a certain capacitance C is zero. A pulse of current flows through the capacitance between $t_0$ and $t_0 + \Delta t$, and the voltage across the capacitance increases to $V_f$ . What can you say about the peak amplitude $I_m$ and area under the pulse waveform (i.e., current versus time)? What are the units and physical significance of the area under the pulse?What must happen to the peak amplitude and area under the pulse as $\Delta t$ approaches zero, assuming that $V_f$ remains the same?

Which pairs of puzzle pieces can fit together to form rectangles? Make sketches to show how they fit.

An amusement park has a marginal cost function $C(x)=1000 e^{-x}+5$ where x represents the number of tickets sold, and a marginal revenue function given by R(x) = 60 − 0.1x. Find the total profit generated when selling 550 tickets. Use a calculator to determine intersection points, if necessary, to two decimal places.

There are 15 black mice in a cage. The ratio of all mice to black mice is 5:1. How many mice are in the cage?

At the beginning of year 1, Julie Ripe has D dollars (this includes year 1 income). During each year, Julie earns i dollars and must determine how much money she should consume and how much she should invest in Treasury bills. During a year in which Julie consumes d dollars, she earns a utility of In d. Each dollar invested in Treasury bills yields $1.10 in cash at the beginning of the next year. Julie’s goal is to maximize the total utility she earns during the next 10 years. a. Why might ln d be a better indicator of Julie’s utility than a function such as d2? b. Formulate a dynamic programming recursion that will enable Julie to maximize the total utility she receives during the next 10 years. Assume that year t revenue is received at the beginning of year t.

The cost function C of rent at an apartment complex increased $50 last year and another$60 this year. Which function accurately reflects these changes? A. 60(C + 50) B. 60(50C) C. (C + 50) + 60 D. 50C + 60