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The surface area of a square pyramid can be calculated using the equation S=1/2lp+B . Rearrange the surface area equation for the quantity of interest B .(1 point)

B=()

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
20 days ago

To rearrange the surface area equation \( S = \frac{1}{2}lp + B \) for the quantity of interest \( B \), follow these steps:

1. Start with the original equation:
\[
S = \frac{1}{2}lp + B
\]

2. Subtract \( \frac{1}{2}lp \) from both sides:
\[
S - \frac{1}{2}lp = B
\]

3. Therefore, the rearranged equation is:
\[
B = S - \frac{1}{2}lp
\]

So, the final answer is:
\[
B = S - \frac{1}{2}lp
\]

User Icon for Finally Some Answers Finally Some Answers answered
20 days ago

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= ()/()

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
20 days ago

To rearrange the volume formula \( V = lwh \) to solve for the width \( w \), follow these steps:

1. Start with the original volume formula:
\[
V = lwh
\]

2. To isolate \( w \), divide both sides by \( lh \):
\[
w = \frac{V}{lh}
\]

Given Claudia’s family's cabinet dimensions:
- Height \( h = 5 \) ft
- Length \( l = 4 \) ft
- Volume \( V = 60 \) ft³

Substituting these values into our rearranged equation for \( w \):

\[
w = \frac{60 \, \text{ft}^3}{4 \, \text{ft} \times 5 \, \text{ft}}
\]

Hence, the formula for \( w \) is:

\[
w = \frac{60}{4 \times 5}
\]

So, the final answer is:

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

Thus, you can write it as:

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