Find $\mathbf{v} \times \mathbf{w}$ for the vectors given.

$$\mathbf{v}=\mathbf{k} ; \mathbf{w}=\mathbf{k}$$

Select the letter of the choice that best completes the statement. A decrease in the production of insulin causes: (a.) diabetes mellitus (b.) diabetes insipidus (c.) cretinism (d.) exophthalmos

Now that you have analyzed some number tricks with algebraic reasoning, you can adapt those arguments to design your own trick. a. Create a similar number trick. Test it with other students to see if it works as intended. b. Develop an algebraic argument to prove the trick that you created will work in every case.

Use the method to calculate the step response of the system with transfer function $\frac{z}{z-\frac{1}{2}}$ Verify the result by direct calculation.

Find the tangential and normal components of acceleration for the given position functions at the given points. $\mathbf{r}(t)=\langle\cos 2 t, \sin 2 t\rangle$ at t=0, $t=\frac{\pi}{2}$

You are given the price p(q) at which q units of a particular commodity can be sold and the total cost C(q) of producing the q units. (a) Find the revenue function R(q), the profit function P(q), the marginal revenue R'(q), and marginal cost C'(q). Sketch the graphs of P(q), R'(q), and C'(q) on the same coordinate axes and determine the level of production q where P(q) is maximized. (b) Find the average cost $A(q)=\frac{C(q)}{q},$ and sketch the graphs of A(q), and the marginal cost C'(q) on the same axes. Determine the level of production q at which A(q) is minimized. p(q) = 180 - 2q; $C(q)=q^{3}+5 q+162$

Identify the major effects of new technology and transportation on industry during the Industrial Revolution.

The magnitudes of the radii of curvature are 32.5 cm and 42.5 cm for the two faces of a biconcave lens. The glass has index of refraction 1.53 for violet light and 1.51 for red light. For a very distant object, locate the image formed by violet light.

For the two given intercepts, use the factored form to generate a quadratic function for each given constant k. Write the function in standard form. x-intercepts: -5 and 3; k = 1, k = -2, k = 5

Solve each equation. Choose the method you prefer to use. Check your answer.

$$5 y - \frac { 3 } { 5 } = \frac { 4 } { 5 }$$

Simplify each fraction.

$$\frac { 24 } { 40 }$$

Find the area of each SAS triangle A B C. Round your answers to the nearest tenth. $B = 112.5 ^ { \circ } , a = 151.6 \mathrm { ft } , c = 221.8 \mathrm { ft }$

Find the position function x(t) for forced mass-spring system $m=1, b=2, k=1, F=6\cos t$. Find the amplitude and phase shift for $x_{ss}$, the steady-state solution.

Subtract. 2.64 – 1.52