Question

Which of the following shows the equation A=1/2(b1+b2)h correctly rearranged for the quantity of interest b1 ?(1 point)
b1 = 2A-b2/H
B1 = H/2A - B2
B1 = 2A/H - B2
BY = H-B2/2A

Answer 1

To rearrange the equation \( A = \frac{1}{2}(b_1 + b_2)h \) for \( b_1 \), follow these steps:

1. Start with the original equation:
\[
A = \frac{1}{2}(b_1 + b_2)h
\]

2. Multiply both sides by \( 2 \):
\[
2A = (b_1 + b_2)h
\]

3. Divide both sides by \( h \):
\[
\frac{2A}{h} = b_1 + b_2
\]

4. Subtract \( b_2 \) from both sides to isolate \( b_1 \):
\[
b_1 = \frac{2A}{h} - b_2
\]

Now let's compare this final expression to the options provided:

1. \( b1 = \frac{2A - b2}{h} \) - Incorrect
2. \( B1 = \frac{h}{2A} - B2 \) - Incorrect
3. \( B1 = \frac{2A}{h} - B2 \) - Correct
4. \( BY = \frac{h - B2}{2A} \) - Incorrect

The correct rearranged equation for \( b_1 \) is:
\[
b1 = \frac{2A}{h} - b2
\]

Thus, the third option \( B1 = \frac{2A}{h} - B2 \) is the correct answer.