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Math Knowledge

If angle a = 53° and angle b = 27° what is the length of angle d?

127°

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 53° - 27° = 100°

So, d° = 27° + 100° = 127°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 53° = 127°

Mechanical Comprehension

Which of the following is the formula for torque?

τ = rF

Torque measures force applied during rotation: τ = rF. Torque (τ, the Greek letter tau) = the radius of the lever arm (r) multiplied by the force (F) applied. Radius is measured from the center of rotation or fulcrum to the point at which the perpendicular force is being applied. The resulting unit for torque is newton-meter (N-m) or foot-pound (ft-lb).

General Science

Herbivores are __________ that subsist on producers like plants and fungus.

primary consumers

Primary consumers (herbivores) subsist on producers like plants and fungus. Examples are grasshoppers, cows, and plankton.

Word Knowledge

Heinous most nearly means:

odious

Shockingly evil.

Word Knowledge

Gravity most nearly means:

seriousness

Importance, significance.

General Science

What is the body's largest artery?

aorta

The aorta is the body's largest artery and receives blood from the pulmonary vein via the left ventricle. From there, blood is circulated through the rest of the body through smaller arteries called arterioles that branch out from the heart. Finally, blood is delivered to bodily tissues through capillaries.

Mechanical Comprehension

If the handles of a wheelbarrow are 1.5 ft. from the wheel axle, how many pounds of force must you exert to lift the handles if it's carrying a 130 lbs. load concentrated at a point 0.5 ft. from the axle?

43.3

This problem describes a second-class lever and, for a second class lever, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance: F_ed_e = F_rd_r. In this problem we're looking for effort force:
\( F_e = \frac{F_r d_r}{d_e} \)
\( F_e = \frac{130 \times 0.5}{1.5} \)
\( F_e = \frac{65.0}{1.5} \)
\( F_e = 43.3 \)

Mechanical Comprehension

If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how much weight would need to be placed at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 8 ft.?

2.5 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_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{20 lbs. \times 1 ft.}{8 ft.} \) = \( \frac{20 ft⋅lb}{8 ft.} \) = 2.5 lbs.

Electronics Information

This circuit component symbol represents a(n):

fuse

Fuses are thin wires that melt when the current in a circuit exceeds a preset amount. They help prevent short circuits from damaging circuit components when an unusually large current is applied to the circuit, either through component failure or spikes in applied voltage.

Shop Information

What is a framing square used for?

marking lines at a right angle

Rulers are used to both measure distance and to draw straight lines. Tape measures are flexible rulers made from cloth or metal and are useful for measuring longer distances and in tighter spaces. Both rulers and tape measures provide similar accuracy, commonly down to \({1 \over 16}\) or \({1 \over 32}\) inch. A steel framing square is made up of a shorter ruler (tongue) and a longer ruler (blade) that meet at a 90° (right) angle. A framing square is often used by carpenters when framing stairs and roofs.