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General Science

Which of the following would be found on a reflecting telescope?

concave mirror

A concave (or converging) mirror bulges inward and focuses reflected light on the mirror's focal point where the mirror's angles of incidence converge. In contrast, a convex (or diverging) mirror bulges outward and diffuses the light waves that strike it. A common use of a concave mirror is in a reflecting telescope, a common use of a convex mirror is in the side view mirror of a car.

Mechanical Comprehension

If a 25 lbs. weight is placed 3 ft. from the fulcrum at the blue arrow and the green box is 6 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?

12.5 lbs.

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.

Solving for R_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{25 lbs. \times 3 ft.}{6 ft.} \) = \( \frac{75 ft⋅lb}{6 ft.} \) = 12.5 lbs.

Math Knowledge

Simplify (y + 8)(y + 3)

y² + 11y + 24

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 8)(y + 3)
(y x y) + (y x 3) + (8 x y) + (8 x 3)
y² + 3y + 8y + 24
y² + 11y + 24

Math Knowledge

If side x = 12cm, side y = 9cm, and side z = 9cm what is the perimeter of this triangle?

30cm

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 12cm + 9cm + 9cm = 30cm

Automotive Information

Which of the following is a common firing order for four-cylinder engines?

1-3-4-2

The stroke cycle of an engine is governed by the crankshaft which serves to regulate the firing order of the cylinders. All cylinders are not on the same stroke at the same time and correct firing order is important to balance engine operation and minimize vibrations. A common firing order for four-cylinder engines is 1-3-4-2 which indicates that cylinders 1 and 3 fire (power stroke)together and cylinders 4 and 2 fire together.

Word Knowledge

Ramble most nearly means:

roam

To wander, physically or in language.

General Science

Veins carry blood __________ the heart.

back to

Veins carry blood back to the heart from the body. While arteries are thick-walled because they carry oxygenated blood at high pressure, veins are comparatively thin-walled as they carry low-pressure deoxygenated blood. Like the heart, veins contain valves to prevent blood backflow.

Shop Information

Which of the following saws would you use if you're cutting wood along the grain?

ripsaw

The ripsaw delivers maximum efficiency at cutting with or along the grain (ripping).

Word Knowledge

The drab winter scene made Keisha long for the vibrant colors of spring.

dreary

Dull, monotonous.

Arithmetic Reasoning

If \( \left|x + 9\right| \) - 3 = 7, which of these is a possible value for x?

-19

First, solve for \( \left|x + 9\right| \):

The value inside the absolute value brackets can be either positive or negative so (x + 9) must equal + 10 or -10 for \( \left|x + 9\right| \) to equal 10:

x + 9 = 10
x = 10 - 9
x = 1

x + 9 = -10
x = -10 - 9
x = -19

So, x = -19 or x = 1.