Describe and correct the error in finding the measure of one exterior angle of a regular pentagon. (n - 2) · 180° = (5 - 2) · 180° = 3 · 180° = 540°. The sum of the measures of the angles is 540°. There are five angles, so the measure of one exterior angle is 540°/5 = 108°.

The base of jewelry box is shaped like a regular hexagon. What is the measure of each interior angle of the jewelry box base?

Which sum does not belong to the other three? Explain. →The sum of measure of the interior angles of a quadrilateral. →The sum of the measures of the interior angles of a pentagon. → The sum of measures of the exterior angles of a quadrilateral. →The sum of the measure of the exterior angles of a pentagon.

A zip line is constructed across a valley, as shown in the diagram. What is the width w of the valley?

Estimate each value.

$$6.43 - 4.079$$

The outside of an ideal solenoid ($N_1$ turns, length L radius r) is wound with a coil of wire with $N_2$ turns. If the current in the solenoid is changing at a rate $\Delta I _ { 1 } / \Delta t$ what is the magnitude of the induced emf in the coil?

Find the exact value of each of the following.

$$2 \sin 165 ^ { \circ } \cos 165 ^ { \circ }$$

Suppose you examine a tree stump and notice that the annual rings are thinner and closer together 50 rings in from the edge. What would you conclude about the climate in the area 50 years ago?

A student was asked to find the value of x. What error did the student make? By the Linear Pairs Theorem, w+56=180, so w=124. By the Triangle Exterior Angle Theorem, w=x+31, or 124=x+31, so x=93.

You have two capacitors and want to connect them across a voltage source (battery) to store the maximum amount of energy. Should they be connected in series or in parallel?

Find the Maclaurin series for the given function. $f(x)=\ln (x+1)$

find all real zeros of the function. f(x) = 4x^3 - 3x - 1

A copper wire, whose cross-sectional area is

$$1.1 \times 10 ^ { - 6 } \mathrm { m } ^ { 2 }$$

has a linear density of

$$7.0 \times 10 ^ { - 3 } \mathrm { kg } / \mathrm { m }$$

and is strung between two walls. At the ambient temperature, a transverse wave travels with a speed of 46 m/s on this wire. The coefficient of linear expansion for copper is

$$17 \times 10 ^ { - 6 } \left( C ^ { \circ } \right) ^ { - 1 }$$

and Young's modulus for copper is

$$1.1 \times 10 ^ { 11 } \mathrm { N } / \mathrm { m } ^ { 2 }$$

What will be the speed of the wave when the temperature is lowered by

$$14 C^\circ?$$

Ignore any change in the linear density caused by the change in temperature.

Using verbal or written explanations. Briefly describe Polya's four steps in problem solving.