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Rearrange the formula F=ma

using m as the quantity of interest.(1 point)
Use the Division Property of Equality to rearrange the formula.

9 answers

To rearrange the formula \( F = ma \) using \( m \) as the quantity of interest, you can use the Division Property of Equality. Here’s how you can do it:

Starting with the formula: \[ F = ma \]

To solve for \( m \), divide both sides of the equation by \( a \): \[ m = \frac{F}{a} \]

So, the rearranged formula with \( m \) as the quantity of interest is: \[ m = \frac{F}{a} \]

The surface area of a square pyramid can be calculated using the equation S=12lp+B
. Rearrange the surface area equation for the quantity of interest B
.(1 point)
B=( )

To rearrange the surface area equation for a square pyramid, given by

\[ S = \frac{1}{2}lp + B \]

for \( B \), we can isolate \( B \) by subtracting \(\frac{1}{2}lp\) from both sides of the equation:

Starting with the equation:

\[ S = \frac{1}{2}lp + B \]

Subtract \(\frac{1}{2}lp\) from both sides:

\[ B = S - \frac{1}{2}lp \]

Thus, the rearranged equation for \( B \) is:

\[ B = S - \frac{1}{2}lp \]

Claudia’s family is buying a new cabinet for their home. The height of the cabinet is 5 ft., its length is 4 ft., and its volume is 60 ft.3
. They need to know the width of the cabinet to make sure that it will fit in the space where they want to put it. Using the volume formula, V=lwh
, rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V
in the formula.(1 point)

w=( )/( )

To find the width \( w \) of the cabinet using the volume formula \( V = lwh \), we will rearrange the formula to highlight \( w \).

Starting with the volume formula:

\[ V = lwh \]

We need to solve for \( w \). To do this, divide both sides by \( lh \):

\[ w = \frac{V}{lh} \]

Now, substituting the known values of length and height:

  • \( V = 60 , \text{ft}^3 \)
  • \( l = 4 , \text{ft} \)
  • \( h = 5 , \text{ft} \)

The rearranged formula to calculate \( w \) in terms of \( V \), \( l \), and \( h \) is:

\[ w = \frac{V}{lh} = \frac{60}{4 \cdot 5} \]

Thus, the final answer, in the requested format, is:

\[ w = \frac{60}{20} \]

This simplifies to:

\[ w = 3 , \text{ft} \]

In the format specified, it would be written as:

\[ w = \frac{V}{lh} \] with:

  • \( V = 60 \)
  • \( lh = 20 \)

So the final answer is:

\[ w = \frac{60}{20} \]

Amelia is traveling from Los Angeles, California, to Mesa, Arizona. The total distance she will drive is 388 miles. Amelia would like to get to Mesa in approximately 7 hours. She is wondering at what speed she will have to travel in order to make that happen. Using the formula d=vt
, rearrange the formula to highlight the quantity of interest

v=( )/( )

To find the speed \( v \) that Amelia must travel to reach Mesa in the desired time, we can start with the formula for distance:

\[ d = vt \]

where:

  • \( d \) is the distance,
  • \( v \) is the speed,
  • \( t \) is the time.

To rearrange the formula to solve for \( v \), we divide both sides by \( t \):

\[ v = \frac{d}{t} \]

Now, substituting the known values into the formula:

  • \( d = 388 , \text{miles} \)
  • \( t = 7 , \text{hours} \)

Thus, the formula for speed \( v \) becomes:

\[ v = \frac{388}{7} \]

In the requested format you asked for, it can be expressed as:

\[ v = \frac{d}{t} \]

where:

  • \( d = 388 \)
  • \( t = 7 \)

So the final answer is:

\[ v = \frac{388}{7} \]

A team of zoologists collected data on the velocity of falcons using a speedometer. The speedometer measured that a falcon was flying at 68 mph. The zoologists are interested in finding out how many hours it would take for the falcon to fly 52,800 feet if it continues to fly at a constant speed of 68 mph. In order to use units to verify your rearrangement of the formula, what process needs to be done? Enter the value that corresponds to your answer.

Option #1: miles

Option #2: yards

Option #3: hours

(1 point)
I would need to convert the units of distance from feet to Option #

To determine how many hours it would take for the falcon to fly 52,800 feet at a speed of 68 mph, we first need to ensure that the distance is in the same unit as the speed, which is in miles.

We know that:

  • 1 mile = 5,280 feet

To convert 52,800 feet to miles, we perform the following calculation:

\[ \text{Miles} = \frac{52,800 \text{ feet}}{5,280 \text{ feet/mile}} = 10 \text{ miles} \]

Since the speed is given in miles per hour (mph), it is necessary to convert the distance from feet to miles in order to correctly use the formula for calculating time.

So, the correct option is:

Option #1: miles

Therefore, the final statement is: "I would need to convert the units of distance from feet to miles."