Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Sure, let's determine the height at which the cable will be anchored on the first vertical tower using the given function and [tex]\(x\)[/tex] value.
Given:
[tex]\[ f(x) = \frac{1}{8}x^2 - 5x + 52 \][/tex]
We need to find the height when [tex]\( x = 10 \)[/tex] meters. Here's the detailed solution:
1. Substitute [tex]\( x = 10 \)[/tex] into the function:
[tex]\[ f(10) = \frac{1}{8}(10)^2 - 5(10) + 52 \][/tex]
2. Calculate [tex]\( (10)^2 \)[/tex]:
[tex]\[ (10)^2 = 100 \][/tex]
3. Multiply by [tex]\( \frac{1}{8} \)[/tex]:
[tex]\[ \frac{1}{8} \times 100 = 12.5 \][/tex]
4. Multiply [tex]\( -5 \)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\[ -5 \times 10 = -50 \][/tex]
5. Add the results to the constant term [tex]\( 52 \)[/tex]:
[tex]\[ 12.5 - 50 + 52 \][/tex]
6. Simplify step-by-step:
- First, add [tex]\( 12.5 \)[/tex] and [tex]\( 52 \)[/tex]:
[tex]\[ 12.5 + 52 = 64.5 \][/tex]
- Then subtract [tex]\( 50 \)[/tex]:
[tex]\[ 64.5 - 50 = 14.5 \][/tex]
Thus, when [tex]\( x = 10 \)[/tex] meters, the height at which the cable will be anchored on the first vertical tower is [tex]\(\boxed{14.5}\)[/tex] meters.
Given:
[tex]\[ f(x) = \frac{1}{8}x^2 - 5x + 52 \][/tex]
We need to find the height when [tex]\( x = 10 \)[/tex] meters. Here's the detailed solution:
1. Substitute [tex]\( x = 10 \)[/tex] into the function:
[tex]\[ f(10) = \frac{1}{8}(10)^2 - 5(10) + 52 \][/tex]
2. Calculate [tex]\( (10)^2 \)[/tex]:
[tex]\[ (10)^2 = 100 \][/tex]
3. Multiply by [tex]\( \frac{1}{8} \)[/tex]:
[tex]\[ \frac{1}{8} \times 100 = 12.5 \][/tex]
4. Multiply [tex]\( -5 \)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\[ -5 \times 10 = -50 \][/tex]
5. Add the results to the constant term [tex]\( 52 \)[/tex]:
[tex]\[ 12.5 - 50 + 52 \][/tex]
6. Simplify step-by-step:
- First, add [tex]\( 12.5 \)[/tex] and [tex]\( 52 \)[/tex]:
[tex]\[ 12.5 + 52 = 64.5 \][/tex]
- Then subtract [tex]\( 50 \)[/tex]:
[tex]\[ 64.5 - 50 = 14.5 \][/tex]
Thus, when [tex]\( x = 10 \)[/tex] meters, the height at which the cable will be anchored on the first vertical tower is [tex]\(\boxed{14.5}\)[/tex] meters.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.