Answered

Bonnie has a container in the shape of a rectangular pyramid. The formula for the surface area of the enclosed space is [tex]S = h w + 0.5 P h[/tex]. Solve for [tex]P[/tex].

A. [tex]P = S - h w = 0.5 h[/tex]
B. [tex]P = S + h w + 0.5 h[/tex]
C. [tex]P = \frac{S - h w}{0.5 h}[/tex]
D. [tex]P = \frac{S}{\sqrt{h w + 0.5 h}}[/tex]



Answer :

GinnyAnswer
To solve for [tex]\( P \)[/tex] from the given surface area formula [tex]\( S = h \cdot w + 0.5 \cdot P \cdot h \)[/tex], follow these steps:

1. Write the given equation:

[tex]\[ S = h \cdot w + 0.5 \cdot P \cdot h \][/tex]

2. Isolate the term involving [tex]\( P \)[/tex]:

Subtract [tex]\( h \cdot w \)[/tex] from both sides of the equation:

[tex]\[ S - h \cdot w = 0.5 \cdot P \cdot h \][/tex]

3. Eliminate the coefficient 0.5:

Multiply both sides of the equation by 2 to eliminate the 0.5 coefficient:

[tex]\[ 2 \cdot (S - h \cdot w) = P \cdot h \][/tex]

4. Solve for [tex]\( P \)[/tex]:

Divide both sides of the equation by [tex]\( h \)[/tex]:

[tex]\[ P = \frac{2 \cdot (S - h \cdot w)}{h} \][/tex]

5. Compare the derived formula with the given options:

- Option 1: [tex]\( P = S - I w = 0.5 h \)[/tex]
- Option 2: [tex]\( P = S + W + 0.5 h \)[/tex]
- Option 3: [tex]\( P = \frac{S - W}{0.5 h} \)[/tex]
- Option 4: [tex]\( P = \frac{S}{\sqrt{W + 0.5 h}} \)[/tex]

None of these provided options match our derived formula:

[tex]\[ P = \frac{2 \cdot (S - h \cdot w)}{h} \][/tex]

Conclusion:

None of the given choices are correct.

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