High School

Find the value of [tex]c[/tex] with the correct number of significant figures from the equation [tex]a - b - c = 401[/tex], if [tex]a = 1387.11[/tex] and [tex]b = 928.321[/tex].

A. 57.789
B. 57
C. 58
D. 57.9
E. 57.8
F. 58.789

Answer :

Sure! Let's find the value of [tex]\( c \)[/tex] from the equation [tex]\( a - b - c = 401 \)[/tex] given [tex]\( a = 1387.11 \)[/tex] and [tex]\( b = 928.321 \)[/tex].

Here's the step-by-step solution:

1. Write down the given equation:
[tex]\[
a - b - c = 401
\][/tex]

2. Substitute the known values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[
1387.11 - 928.321 - c = 401
\][/tex]

3. Combine the constants on the left-hand side:
[tex]\[
1387.11 - 928.321 = 458.789
\][/tex]

4. Simplify the equation:
[tex]\[
458.789 - c = 401
\][/tex]

5. Solve for [tex]\( c \)[/tex]:
[tex]\[
c = 458.789 - 401
\][/tex]

6. Subtract the numbers:
[tex]\[
c = 57.789
\][/tex]

7. Round [tex]\( c \)[/tex] to the correct number of significant figures. Since the answer needs to have 4 significant figures (as per the given options and where the number of decimal places in the given inputs guides this):
[tex]\[
c \approx 57.8
\][/tex]

Hence, the correct value of [tex]\( c \)[/tex] is approximately 57.8, which corresponds to option (e).

So, the value of [tex]\( c \)[/tex] is:

(e) 57.8