Question

1. using the information in the table, write and solve an equation to find the number of rentals it would take in order to pay the same amount for movie rental a and movie rental b.

rental a: membership fee: $20 and $1.50 per movie rental
rental b: membership fee: $50 with no rental fee per movie

(handwritten work: 20 + 1.50x = 50; -20 -20; 1.50x = 30; \frac{1.50x}{1.50} = \frac{30}{1.50}; x= )

1. the formula for determining the force (in newtons) needed to accelerate an object is determined by $f = ma$, where $m$ is the mass of an object (in kg), and $a$ is the acceleration rate (in m/sec²).

a. solve the formula for $m$.

b. if you needed 7500n of force for a racecar to accelerate at 3 m/sec², how much mass (kg) does the car have?

Explanation:

Question 17

Step1: Define variable

Let \( x \) be the number of movie rentals.

Step2: Cost for Rental A

Cost for Rental A: \( 20 + 1.50x \) (membership fee + per - movie cost)

Step3: Cost for Rental B

Cost for Rental B: \( 50 \) (only membership fee)

Step4: Set equations equal

To find when costs are equal: \( 20 + 1.50x=50 \)

Step5: Subtract 20 from both sides

\( 20 + 1.50x-20 = 50 - 20 \)
\( 1.50x=30 \)

Step6: Solve for x

Divide both sides by 1.50: \( x=\frac{30}{1.50}=20 \)

Step1: Start with formula

We have the formula \( f = ma \)

Step2: Solve for m

Divide both sides of the equation by \( a \) (assuming \( a
eq0 \)): \( m=\frac{f}{a} \)

Step1: Identify values

We know that \( f = 7500\space N \), \( a = 3\space m/sec^{2} \) and from part (a) \( m=\frac{f}{a} \)

Step2: Substitute values

Substitute \( f = 7500 \) and \( a = 3 \) into the formula for \( m \): \( m=\frac{7500}{3} \)

Step3: Calculate

\( m = 2500 \)

Answer:

The number of rentals is 20.

Question 18a