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Math Knowledge

What is the circumference of a circle with a radius of 18?

36π

The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:

c = πd
c = π(2 * r)
c = π(2 * 18)
c = 36π

Math Knowledge

What is 7a³ + 7a³?

14a³

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a³ + 7a³ = 14a³

Automotive Information

A cylinders acts as a guide for a:

piston

Cylinders act as a guide for the pistons that translate the heat energy of combustion into the mechanical energy necessary to move a vehicle. Piston rings seal the piston to the cylinder to contain combustion gases and also regulate the oil distribution between the piston and cylinder wall. A cylinder head closes in the top of the cylinder forming the combustion chamber which is sealed by a head gasket (head). The head provides space for air and fuel intake valves, exhaust valves, and mounts for spark plugs and fuel injectors.

General Science

__________ is caused by a lack of iron in the diet.

anemia

Anemia, which may cause weakness, dizziness, and headaches is caused by a lack of iron in the diet.

Electronics Information

Silver and gold are among the most highly conductive elements. Why is copper used much more often as a conductor in electrical circuits?

all of these

All conductors have resistance and the amount of resistance varies with the element. But, resistance isn't the only consideration when choosing a conductor as the most highly conductive elements like silver and gold are also more expensive and more brittle than slightly less conductive elements like copper. A balance needs to be struck between the electrical qualities of a material and its cost and durability.

Mechanical Comprehension

A block and tackle with four pulleys would have a mechanical advantage of:

Two or more pulleys used together constitute a block and tackle which, unlike a fixed pulley, does impart mechanical advantage as a function of the number of pulleys that make up the arrangement. So, for example, a block and tackle with three pulleys would have a mechanical advantage of three.

Mechanical Comprehension

If 15 lbs. of force is applied 8 ft. from the fulcrum at the blue arrow and the green box is 7 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?

17.14 lbs.

To balance this lever the torques at the green box and the blue arrow 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 green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

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

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{15 lbs. \times 8 ft.}{7 ft.} \) = \( \frac{120 ft⋅lb}{7 ft.} \) = 17.14 lbs.

General Science

These clouds grow upward and can develop into cumulonimbus or thunderstorm clouds.

cumulus clouds

Cumulus clouds are large, puffy, mid-altitude clouds with a flat base and a rounded top. These clouds grow upward and can develop into a cumulonimbus or thunderstorm cloud.

General Science

Examples of secondary consumers include:

chickens

Secondary consumers (carnivores) subsist mainly on primary consumers. Omnivores are secondary consumers that also eat producers. Examples are rats, fish, and chickens.

General Science

What part of the nervous system is responsible for controlling involuntary actions like breathing, swallowing, and heartbeat?

medulla

Part of the brainstem, the medulla is the connection between the brain and the spinal cord. It controls involuntary actions like breathing, swallowing, and heartbeat.