Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 430 miles on 10 gallons of gas. How far could you drive on 55 gallons of gas? What is the car's gas mileage?

With 55 gallons of gass the car is able to travel 2,365 miles. Its mileage is 43 miles per gallon.

Step-by-step explanation:

Since the car ran 430 miles on 10 gallons of gas, we can calculate its mileage by dividing the distance traveled by the amount of gas used, so:

If he had 55 gallons of gas on the tank, then he'll be able to travel:

With 55 gallons of gass the car is able to travel 2,365 miles. Its mileage is 43 miles per gallon.

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

(1)

And this formula is expanded by definition of vectors in rectangular and polar form:

(1b)

Where:

- Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

- Length of each vector, in kilometers.

- Bearing of each vector in standard position, in sexagesimal degrees.

If we know that , , and , then the resulting coordinates of the final position of the surveyor is:

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

And the distance from the camp is calculated by the Pythagorean Theorem:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).