Basic Math and Basic Engineering

A machine consumes 3000 kilojoules of energy in 2 minutes. What is the power output in watts?

25,000 W

An object has a mass of 5 pounds and is raised to a height of 12 feet. What is its potential energy?

81.3 joules

A car with a weight of 18,000 N is moving at a velocity of 10 m/s. What is its kinetic energy?

917.6 kJ

For a 5- year period, determine the compound interest rate per year that is equivalent to a simple interest rate of 15%.

11.84%

The measure of 2.25 revolutions counterclockwise is:

810 degrees

How many centimeters if water is equivalent to 200,000 Pa?

2039 cm

A rectangular fish tank 60 centimeters by 15 centimeters by 34 centimeters is a 1/3 full of water. Find the volume in cubic meter of water needed to fill the tank completely.

0.0204 m³

A fluid has a specific weight of 15,500 N per cubic meter. Find its density in SI unit.

1,579.0 kg/m³

A tractor weighs 5600 Newtons. What is its equivalent weight in pounds?

1259lbf

A square prism of height 11 inches has a volume of 539 cubic inches. Find the surface area of the prism

406in²

A ball has a diameter of 10 meters. Calculate the volume of the hemisphere.

261.8m³

Car A drives east at 20 kph at half an hour earlier than Car B that started at the same point and the same direction at 50 kph. How far are the two cars 10 minutes after Car B.

5 KM

What is the peak storage capacity (𝑚3) of a 5-m diameter grain storage bin with an eave height and a minimum angle of fill of 6 m and 28 deg., respectively?

126.5 𝒎³

What is the sum of the smallest prime and largest 2-digit prime number?

99

Find the sum of all odd integers from -100 to 110?

525

During a survey, the following data were gathered: 60 students like algebra, 50 students like calculus, and 45 likes physics. Thirty students like both algebra and calculus; 25 students like both calculus and physics; and 20 students like algebra and physics. Only 15 students like all the three subjects. How many students were surveyed?

95 students

If 𝑥2+𝑦2 =22 and 𝑥𝑦 =9, find the value of (𝑥 − 𝑦)2.

4

A student in a chemistry laboratory wants to form a 32 ml mixture of 2 solutions to contain 30% acid. Solution A contains 42% acid and solution B contains18% acid. How many ml of each solution must be used?

X= 16, Y=16

The number of centimeters in the perimeter of a certain square is equal to the number of square centimeter in its area. Find the length of the sides of the square.

4 cm

A certain angle has a supplement five times its complement. Find the angle.

67.5 degrees

Lexi can do a piece of work in 15 days while Lore can do it in 10 days. How long will they take together to do it?

6 days

One pipe can fill a tank in 45 minutes and another pipe can fill it in 30 minutes. If these two pipes are open while a 3rd pipe is drawing water from the tank, it takes 27 minutes to fill the tank. How long will it take the 3rd pipe alone to empty a full tank?

54 minutes

Convert 55 degrees to radian.

𝟏𝟏/𝟑𝟔 π rad

What is the domain of this function, {(1,2) , (2,4) , (4,5) , (5,8) }.

{1,2,4,5}

Find the domain:

Any real number except 4 and 2.

Find the domain:

x ≤ 5/3

Determine if the following function is odd, even or neither: 𝑓(𝑥) = 4𝑥³ − 2𝑥.

ODD

Determine if the following function is odd, even or neither: 𝑓(𝑥) = 4𝑥⁴ − 2𝑥² − 5

EVEN

Find the intercepts of y=3x+2.

(0,2) and (-2/3,0)

Find the equation of the line that contains the following points: (3,4) and (5,8).

y= 2x-2

What is the equation of the line through (2,4) and parallel to y=3x+5.

y=3x-2

What is the equation of the line through (2,4) and perpendicular to y=3x+5

𝒚 = (-x+14)/3

A specific radioactive isotope has a half life of 12,000 years.

(a) What is the decay constant?

(b) How long will it take 5 grams to decay to 1 gram?

K= 0.000058

t= 27,749 years

Find the three arithmetic means of 3 and 48.

14.25, 25.5, 36.75

Find the sum of numbers 1 to 100.

5050

Find the three geometric means of 3 and 48.

6, 12, 24

What is the general equation of a circle having a diameter with endpoints at (4,5) and (-2,3).

(𝒙 −𝟏)² + (𝒚−𝟒)² =𝟏𝟎

A triangle has sides of lengths 2.8 inches, 3.2 inches and 4.1 inches. Find the area of the triangle.

4.47 sq. in

In a 90°-60°-30° triangle, if the shortest side is 6 cm, what is the length of the hypotenuse?

12 cm

In △ ABC, A=74 degrees, B=50 degrees, and c=75 cm. Solve for b.

69.3 cm

A triangular plot of land is to be used as a vegetable garden. The measures of the plot are AB = 8 meters, BC = 12 meters and AC = 18 meters. Find the measure of angle B.

127.2 deg

A ladder 16 feet long leans against the side of a building. Find the height from the top of the ladder to the ground if the angle of elevation of the ladder is 74°.

15.4 ft

Two vertical poles 20 m and 80 m high, stand apart on a horizontal plane. What is the height, in meters, of the point of intersection of the lines joining the top of each pole to the foot of the other?

16 m

A ball is released from the rest and drops straight down starting at a height of 800m. How long will it take to hit the ground?

12.8 sec

A ball is released from a height of 800m. How long will it take to reach the ground if the ball was thrown down with an initial speed of 30 m/s.

10.1 sec

Convert 110402 decimal to base 9.

177,488

Convert 717314 decimal to base 12.

2A7142

Convert 110402 base 7 to decimal.

19,406

Convert 12826307 base 9 to decimal.

6, 335, 989

Find the two numbers whose sum is 20, if the product of one by the cube of the other is to be a maximum.

5 and 15

The highway department is planning to build a picnic area for motorist along a major highway. It is to be a rectangle with an area of 5000 sq. m to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing that will be needed to complete the job?

200 m

A spherical balloon is being inflated, and its radius increases at a rate of 0.5 cm/s. At the instant when the radius is 10 cm, how fast is the volume of the balloon increasing?

200 π 𝒄𝒎³/s

A ladder is resting against a wall. The ladder is 10 ft long, and it is sliding away from the wall at a rate of 1 foot per second. How fast is the ladder sliding down the wall when the bottom of the ladder is 6 ft away from the wall?

0.75 ft/sec

Find the area bounded by the curve y=x2 and the x-axis from x=0 to x=2.

8/3 sq units

Calculate the area of the region bounded by the lines y=x and y=𝑥².

1/6 sq. units