Find the future value of an income stream of $2000 per year, deposited into an account paying 2% interest per year, compounded continuously, over a 15-year period.

Find the value of the constant k such that

$$\lim _ { x \rightarrow 5 } ( k x + 10 ) = 20$$

Simplify:

$$\dfrac{x^{5t} \left( x^t\right)^2 }{\left( x^{3t}\right)^2 }$$

Explain how you know whether the diver is moving in a positive or a negative direction before you solve the equation.

Use your calculator to find the value of the following, recording the entire display: a.

$$2 ^ { 9 }$$

b.

$$( - 5 ) ^ { 5 }$$

c.

$$- 3 ^ { 5 }$$

d.

$$7 ^ { 5 }$$

e.

$$8 ^ { 3 }$$

f.

$$( - 9 ) ^ { 4 }$$

g.

$$- 9 ^ { 4 }$$

h.

$$1.16 ^ { 11 }$$

i.

$$- 0.981 ^ { 14 }$$

j.

$$( - 1.14 ) ^ { 23 }$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality

$$\frac { x - 2 } { x + 3 } < 2$$

can be solved by multiplying both sides by x + 3 resulting in the equivalent inequality

$$x - 2 < 2 ( x + 3 ).$$

The maximum grade (slope) allowed for highways in Ontario is 12%. a) Predict the angle

$$\theta$$

, to the nearest degree, associated with this slope. b) Calculate the value of

$$\theta$$

to the nearest degree. c) Determine the six trigonometric ratios for angle

$$\theta$$

.

find the slope and y-intercept (if possible) of the equation of the line. Sketch the line. y - 3 = 0

Evaluate the expression.

$$8 ^ { - 4 / 3 }$$

The concentration, C, in ng/ml of a drug in the blood as a function of the time, t, in hours since the drug was administered is given by $C = 15 t e ^ { - 0.2 t }.$ The area under the concentration curve is a measure of the overall effect of the drug on the body, called the bioavailability. Find the bioavailability of the drug between t = 0 and t = 3.

a. What is the major product obtained from the reaction of propene and

$$Br_2$$

plus excess

$$Cl^-$$

? b. Indicate the relative amounts of the stereoisomers that are obtained.

Write <, =, or > to make a true sentence. -6 + 5 $\underline{?}$ -5 + 7

Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. You do not need to use the definition of the Taylor series coefficients.

What is the purpose of the AC adapter on the end of the cord used for mobile phones?