Question

Solve D\left(h\right)=440-65h if \:h=3\frac{1}{2}

Answer 1

To solve the equation \( D(h) = 440 - 65h \) for \( h = 3\frac{1}{2} \), we first convert \( 3\frac{1}{2} \) to an improper fraction.

\[
3\frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}
\]

Now, we can substitute \( h = \frac{7}{2} \) into the equation:

\[
D\left(\frac{7}{2}\right) = 440 - 65\left(\frac{7}{2}\right)
\]

Next, we calculate \( 65 \times \frac{7}{2} \):

\[
65 \times \frac{7}{2} = \frac{65 \times 7}{2} = \frac{455}{2}
\]

Now substituting this back into the equation:

\[
D\left(\frac{7}{2}\right) = 440 - \frac{455}{2}
\]

To perform the subtraction, we first convert 440 into a fraction with a denominator of 2:

\[
440 = \frac{440 \times 2}{2} = \frac{880}{2}
\]

Now we can subtract:

\[
D\left(\frac{7}{2}\right) = \frac{880}{2} - \frac{455}{2} = \frac{880 - 455}{2} = \frac{425}{2}
\]

Thus,

\[
D\left(3\frac{1}{2}\right) = \frac{425}{2} = 212.5
\]

Therefore, the solution is:

\[
D\left(3\frac{1}{2}\right) = 212.5
\]