Find the time required, to the nearest 0.1 year, for the investment to reach the desired goal. $2,000 invested at 6.75%, compounded daily; goal:$3,000.

r(t) is the position vector of a moving particle. Graph the curve and the velocity and acceleration vectors at the indicated time. Find the speed at that time. $\mathbf{r}(t)=-\cosh 2 t \mathbf{i}+\sinh 2 t \mathbf{j} ; t=0$

A man owns two building supply stores, one on the east side and one on the west side of a city. Two customers order some $\frac{1}{2}$-inch plywood. Customer A needs 50 sheets, and customer B needs 70 sheets. The east-side store has 80 sheets, and the west-side store has 45 sheets of this plywood in stock. The east-side store’s delivery costs per sheet are $0.50 to customer A and$0.60 to customer B. The west-side store’s delivery costs per sheet are $0.40 to customer A and$0.55 to customer B. How many sheets should be shipped from each store to each customer to minimize delivery costs?

Use the properties of seawater to describe the characteristics of mixtures.

Solve the equation algebraically without using a calculator.

$$3x-4=6x+5$$

Give the name or condensed structural formula, as appropriate: 2,3-dimethylhexane

Explain how to cover your brake and when you should do it.

Determine the solution set to the system Ax = 0 for the given matrix A.

$$A = \left[ \begin{array} { r r r } { 1 } & { 2 } & { 3 } \\ { 2 } & { - 1 } & { 0 } \\ { 1 } & { 1 } & { 1 } \end{array} \right].$$

Explain the following observation. Ethyl 3-phenylpropanoate

$$\left( \mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 2 } \mathrm { CO } _ { 2 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 3 } \right)$$

reacts with electrophiles to afford orthoand para-disubstituted arenes, but ethyl 3-phenyl-2-propenoate

$$\left( \mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { CH } = \mathrm { CHCO } _ { 2 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 3 } \right)$$

reacts with electrophiles to afford meta-disubstituted arenes.

In which quadrant or on which axis of a coordinate plane does each point lie?

$$( 8 , - 6 )$$

Simplify: 7/5 + 8/5

Let

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

and g(x) = -2x - 1. Find the function value. g(-2)

Determine which relations are functions. a)

$$y=\sqrt[]{x+2}$$

b)

$$y=2-x$$

c)

$$3x^2-4y^2=12$$

d)

$$y=-3\left(x+2\right)^2-4$$

Verify the identity algebraically. Use a graphing utility to check your result graphically. $\sin \frac{\alpha}{3} \cos \frac{\alpha}{3}=\frac{1}{2} \sin \frac{2 \alpha}{3}$