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Electronics Information

Use Ohm's Law to calculate the value of current in this circuit if voltage is 240 volts and resistance is 40 Ω.

6 A

Ohm's law specifies the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit: V = IR.

Solved for current, I = \( \frac{V}{R} \) = \( \frac{240}{40} \) = 6 A

Arithmetic Reasoning

How many hours does it take a car to travel 75 miles at an average speed of 25 miles per hour?

3 hours

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

speed = \( \frac{\text{distance}}{\text{time}} \)

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{75mi}{25mph} \)
3 hours

General Science

The ozone layer is in which of Earth's atmospheric layers?

stratosphere

The stratosphere is just above the troposphere and is stratified in temperature with warmer layers higher and cooler layers closer to Earth. This increase in temperature is a result of absorption of the Sun's radiation by the ozone layer.

Arithmetic Reasoning

What is \( 5 \)\( \sqrt{28} \) + \( 7 \)\( \sqrt{7} \)

17\( \sqrt{7} \)

To add these radicals together their radicands must be the same:

5\( \sqrt{28} \) + 7\( \sqrt{7} \)
5\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
5\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(5)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
10\( \sqrt{7} \) + 7\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

10\( \sqrt{7} \) + 7\( \sqrt{7} \)
(10 + 7)\( \sqrt{7} \)
17\( \sqrt{7} \)

General Science

What part of the food chain serves only as food for other organisms?

producers

Producers (autotrophs) serve as a food source for other organisms. Typical producers are plants that can make their own food through photosynthesis and certain bacteria that are capable of converting inorganic substances into food through chemosynthesis

General Science

Vector quantities are fully described by which of the following?

a magnitude and a direction

Velocity and displacement are vector quantities which means each is fully described by both a magnitude and a direction. In contrast, scalar quantities are quantities that are fully described by a magnitude only. A variable indicating a vector quantity will often be shown with an arrow symbol: \(\vec{v}\)

Math Knowledge

Solve 3a + 2a = 9a - 9x + 8 for a in terms of x.

1\(\frac{5}{6}\)x - 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

3a + 2x = 9a - 9x + 8
3a = 9a - 9x + 8 - 2x
3a - 9a = -9x + 8 - 2x
-6a = -11x + 8
a = \( \frac{-11x + 8}{-6} \)
a = \( \frac{-11x}{-6} \) + \( \frac{8}{-6} \)
a = 1\(\frac{5}{6}\)x - 1\(\frac{1}{3}\)

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

Electronics Information

Capacitors connected in series produce __________ capacitance compared to capacitors connected in parallel.

less

Capacitors store electricity and are used in circuits as temporary batteries. Capacitors are charged by DC current (AC current passes through a capacitor) and that stored charge can later be dissipated into the circuit as needed. Capacitors connected in series produce less capacitance than capacitors connected in parallel.

Automotive Information

What is the function of the head gasket?

to seal the engine block from the cylinders

A head gasket is a gasket that sits between the engine block and cylinder heads to seal the cylinders to ensure maximum compression and avoid leakage of coolant or engine oil into the cylinders.