An auditorium measures 35.0 m multiplied by 20.0 m multiplied by 11.0 m. The density of air is 1.20 kg/m3.

An auditorium measures 35.0 m 20.0 m 11.0 m. The density of air is 1.20 kg/m³.

(a) What is the volume of the room in cubic feet?


(b) What is the weight of air in the room in pounds?

Assumptions: 1 m = 3.28 ft and 1 m³= 35.31 ft³

Logic (a): 35.0 m x 20.0 m x 11.0 m = 7700 m³, 7700 m³ x 35.31 = 271887 ft³

The price of gasoline at a particular station is 1.3 euros per liter. An American student can use 41 euros to buy gasoline. Knowing that 4 quarts make a gallon and that 1 liter is close to 1 quart, she quickly reasons that she can buy which of the following?

The price of gasoline at a particular station is 1.3 euros per liter. An American student can use 41 euros to buy gasoline. Knowing that 4 quarts make a gallon and that 1 liter is close to 1 quart, she quickly reasons that she can buy which of the following?

Given: 1L of gasoline cost 1.3 euros per liter, 41 euros to buy gasoline, 4 quarts make a gallon, and 1L is close to 1 quart.

Logic: 41 euro / 1.3 euro = 31.54L that could be bought with the euros, 31.54L equals approximately 31.54 quarts, and 31.54 quarts / 4 quarts = 7.89 gallons.

Answer: About 8 gallons of gasoline

A motorist drives south at 30.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.60 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.60 min trip, find the following values.

A motorist drives south at 30.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.60 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.60 min trip, find the following values. 

Find (a) total vector displacement in m (magnitude) and ° south of west, (b) average speed in m/s, and (c) average velocity in m/s (magnitude) and ° south of west.

Logic:  A motorist drives a car for 6.6 minutes, of which he drives at various speeds during each turns, the question ask you to find the total displacement, degree of it's origin, the average speed, and average velocity with it's degree south of the origin.

Units: m is for meter, s is for second, min is for minute, and hr is for hour.

b) using the formula avg speed = m1 + m2 + ... + mn / t1 + t2 + ... + tn we get 30 + 25 + 30 / 3 + 2.6 + 1 = 28.03.

The polar coordinates of a point are r = 5.10 m and θ = 270°. What are the Cartesian coordinates of this point?

The polar coordinates of a point are r = 5.10 m and θ = 270°. What are the Cartesian coordinates of this point? Find x and y.

1) Given r = 5.10 and θ = 270°, we can find x using the formula x = rcosθ and y using the formula y = rsinθ

2) x = (5.10)cos(270) = 0

3) y = (5.10)sin(270) = -5.1

Therefore, x = 0 and y = -5.1

What is Mass?

Mass is a characteristic (property) of an object, which is quantified in kilogram, the SI unit for mass. It also specifies the resistance in relation to the change of velocity.

Newton's Law of Cooling/Warming

dT/dt = k(T-Tm)

k is the constant of proportionality
T(t) is the temperature of the object where t > 0
Tm is the ambient temperature