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
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
