Find and draw an object (or part of an object) that can be modeled by a triangle and an exterior angle. Describe the relationship between the interior angles of the triangle and the exterior angle in terms of the object.

Speed is the magnitude of velocity. Is average speed the magnitude of average velocity? Explain.

determine whether the statement is true or false. Justify your answer. The equation

$$sin^2θ+cos^2θ=1+tan^2θ$$

is an identity because

$$sin^2(0)+cos^2(0)=1$$

and

$$1+tan^2(0)=1$$

Express

$$2 x ^ { 2 } + x y + 2 y ^ { 2 } = 1$$

in the x'y'-coordinate system obtained by rotating the xy-coordinate system through the angle

$$\theta = \pi / 4$$

The ratio of an object 's weight on Earth to its weight on the Moon is 6:1. The first person to walk on the Moon was Neil Armstrong. He weighed 165 pounds on Earth. How much did he weigh on the Moon?

Find each difference. −13 − (−8)

On an English test, Tito must write an essay for three of the five questions in Part 1 and four of the six questions in Part 2 in any order. How many different combinations of questions can be answer?

Solve and check. If an equation has no solution, say so.

$$\frac { 1 } { y - 2 } + \frac { 1 } { y + 2 } = \frac { 4 } { y ^ { 2 } - 4 } n$$

According to Newton’s law of cooling (see Problem 23 of Section 1.1), the temperature u(t) of an object satisfies the differential equation dudt=−k(u−T), where T is the constant ambient temperature and k is a positive constant. Suppose that the initial temperature of the object is u(0)=u0. (a) Find the temperature of the object at any time. (b) Letτbe the time at which the initial temperature difference u0−T has been reduced by half. Find the relation between k and τ.

Factor the polynomial.

$$x ^ { 2 } - 22 x + 121$$

The measure of an exterior angle of an isosceles triangle is x°. Write expressions representing the possible angle measures of the triangle in terms of x.

Susan B. Anthony did not only promote women's rights. She also fought in the temperance (anti-alcohol) and abolition (anti -slavery) movements. How did she try to get those reforms passed? Learn about Anthony's efforts to promote temperance or abolition. Share your findings in class.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Without writing the expansion of

$$( x - 1 ) ^ { 6 },$$

I can see that the terms have alternating positive and negative signs.

What is the approximate value of x in this equation? $\ln (5 x-1)+6=15$ A. 7.39 B. 1620.82 C. 4405.29 D. 653,802.47