Math 116 Unit 3 Practice Test

250 feet This is a "find the missing hypotenuse" question, using the Pythagorean Theorem: a^2 + b^2 = c^2 150^2 + 200^2 = c^2 22,500 + 40,000 = c^2 c^2 = 62,500 c = 250 (or you may have realized that this was a 3-4-5 triangle with one leg that was 3 x 50 and one that was 4 x 50, so the hypotenuse had to be 5 x 50)

A 200-foot tower is secured by a guy wire that is attached to the ground 150 feet from the base of the tower. How long is the guy wire?

6/20 = x/80 480 = 20x x = 24 feet

A 6-foot person casts a 20-foot shadow at the same time a tree casts an 80-foot shadow. How tall is the tree?

13^2 + 8^2 = c^2 169 + 64 = c^2 c^2 = 233 c = 15.26 feet

A carpenter wants to build a diagonal brace for a wall that is 13 feet long and 8 feet high. How long should she make the brace?

CD: 36 - 20 = 16 AB: 54 - (20 + 16) = 18

Find the length of segments AB and CD.

For the given angle (60 degrees) you are given the side OPPOSITE the angle (10) and the side ADJACENT to the angle (x), so you can use TANGENT to solve for x: tan60 = 10/x ---> multiply both sides by x and simplify the x's on the right side xtan60 = 10 ---> divide both sides by tan60 and simplify the tan60's on the left side x = 10/tan60 x = 5.77

Find the length of side x.

You are given the ADJACENT side (23) and the HYPOTENUSE (x), so use cosine: cos55 = 23/x xcos55 = 23 x = 23/cos55 x = 40.1 cm

Find the length of the hypotenuse.

sin(180) = 0 cos(180) = -1 tan(180) = 0

Find the sine, cosine and tangent of a 180-degree angle.

sinA = 8/10 = 4/5 = 0.8 cosA = 6/10 = 3/5 = 0.6 tanA = 8/6 = 4/3 = 1.33...

Find the sine, cosine, and tangent of angle A.

sinC = 6/10 = 3/5 = 0.6 cosC = 8/10 = 4/5 = 0.8 tanC = 6/8 = 3/4 = 0.75

Find the sine, cosine, and tangent of angle C.

SA of a cylinder is the area of the circle on the top, plus the area of the circle on the bottom, plus the area of the rectangle wrapped around the center. The area of that rectangle is equal to the height of the cylinder times the circumference of one of the circles. SA = 2(πr^2) + h(2πr) SA = 2(π5^2) + 10(2)(π)(5) SA = 2(25π) + 10(10π) SA = 50π + 100π SA = 150π or 471.2 cm^2

Find the surface area.

V = lwh V = (11)(5)(6) V = 330 cm^3

Find the volume.

6/15 = x/17.5 15x = 105 x = 7 y/8 = 15/6 6y = 120 y = 20

Find x and y.

(3x - 4) + (3x - 4) = 64 6x - 8 = 62 6x = 72 x = 12 AB: 3(12) - 4 = 32 BC is equal to AB, so BC = 32 Check: 32 + 32 = 64

If AC = 64, find AB and BC.

INVALID Make a truth table for the two premises and the conclusion: p --> q T F T T ~p F F T T ~q F T F T Are there any rows where both premises are true but the conclusion is false? Yes: Row 3 So, it's invalid. http://www.math.fsu.edu/~wooland/argumentor/TruthTablesandArgs.html

Is the following argument valid? If you wear Axe body spray, you will offend people. You didn't wear Axe body spray. Therefore, you didn't offend people.

One-point perspective

This picture is an example of...

A = π(r^2) A = π(5^2) A = 25π cm^3 or 78.5 cm^3

What is the area of a circle with a 5 cm radius?

28°

What is the measure of angle x?

103°

What is the measure of angle y?

45° 90 - 45 = 45

What is the measure of the complement of a 45° angle?

150° 180 - 30 = 150

What is the supplement of a 30° angle?

V = π(r^2)(h) = π(5^2)(10) = 250π or 785.4 cm^3

What is the volume of this cylinder?