1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
REY [17]
3 years ago
9

Two vertical poles of length 10 and 12 ​feet, respectively, stand 17 feet apart. A cable reaches from the top of one pole to the

some point on the ground between the poles and then to the top of the other pole. Express the amount of cable​ used, L, as a function of the distance of the cable from the 10​-foot ​pole, x.

Mathematics
1 answer:
Marat540 [252]3 years ago
3 0

Answer:

L=\sqrt{x^{2}+100}+\sqrt{x^{2}-34x+433} ft

Step-by-step explanation:

let length of calble = L

distance from 10-foot pole = x ft

Moving from the top of the 10-foot pole to point x, we have

From the diagram that

x^{2} +10^{2}=L_{1} ^{2}  \\x^{2} + 100 = L_{1} ^{2}

Take the square root of both sides

\sqrt{x^{2}+100}=\sqrt{L_{1} ^{2}}\\  \sqrt{x^{2}+100}= L_{1}

Moving from point x to the top of the 12-foot pole, we have

From the diagram that

(17-x)^{2}+12^{2}=L_{2} ^{2}   \\289-34x+x^{2} +144=L_{2} ^{2}\\x^{2} -34x+433=L_{2} ^{2}

Take the square root of both sides

\sqrt{x^{2}-34x+433}=\sqrt{L_{2} ^{2}}  \\\sqrt{x^{2}-34x+433}=L_{2}

Amount of cable used, L = L1 + L2

L=\sqrt{x^{2}+100}+\sqrt{x^{2}-34x+433}

You might be interested in
Which two integers are 7 units away from the number 5 on a number line? A-2 and 2 O B-2 and c. -- and D. -2 and​
Sloan [31]

Answer:

-2 and 12

Step-by-step explanation:

To find the two numbers which are 7 units away from 5, add 7 to 5 and subtract 7 from 5

5+7 = 12

5-7 = -2

5 0
2 years ago
–5(3 – q) + 4 = 5q – 11
mrs_skeptik [129]

Answer:

0

Step-by-step explanation:

–5(3 – q) + 4 = 5q – 11

-15 +5q + 4 = 5q -11

-11 + 5q = 5q - 11

+5q - 5q = -11 + 11

0=0

6 0
3 years ago
which cost more. 8 printers priced at $145 per printer or 3 laptop computer priced at $439 per computer? explain.
Elodia [21]
8 printers for $145 each is a total of $1160.

3 laptops for $439 is a total of $1317.

Therefore, the price of 3 laptops for $439 each cost more than 8 printers for $145 each.
8 0
3 years ago
Read 2 more answers
Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twe
alina1380 [7]
Just to remove ambiguities, the bar over the expression means it's repeating itself to infinity.

\bf 2.888\overline{8}\impliedby \textit{now say, let's make }x=2.888\overline{8}
\\\\\\
\textit{and multiply it by 10, to move over the 8 to the left}
\\\\\\
\begin{array}{llll}
10x&=&10\cdot 2.888\overline{8}\\
&&28.88\overline{8}\\
&&26+2.888\overline{8}\\
&&26+x
\end{array}\implies 10x=26+x
\\\\\\
9x=26\implies x=\cfrac{26}{9}

notice, the idea being, you multiply it by 10 at some power, so that you move the "recurring decimal" to the other side of the point, and then split it with a digit and "x".

now, you can plug that in your calculator, to check what you get.
4 0
3 years ago
Read 2 more answers
Find the cost of 20cm at 75 per m
zheka24 [161]

Answer:

20cm = 0.2 m

The cost

= 0.2 x 75

= $15

7 0
2 years ago
Read 2 more answers
Other questions:
  • A researcher has noted that the repair times of a sample of 15 new lawn mowers has a standard deviation of 4 minutes. A 95% conf
    8·1 answer
  • What is the equation of this circle in standard form?
    7·2 answers
  • Calculate the area of the shaded region
    12·1 answer
  • a slab or ribs at the butcher costs $4.55 per pound how much will it cost if you buy 3.5 pounds of ribs round to the nearest pen
    12·1 answer
  • Write 3 different equivalent expression of 6(3x plus 8) plus 32 plus 12x
    8·2 answers
  • Simplify. <br><br> 3^2 · 3^4 · 3^6 <br><br> A) 3^0 <br> B) 3^10 <br> C) 3^12 <br> D) 3^48
    7·1 answer
  • Give one example of when you would make a frequency table to solve a problem
    8·1 answer
  • What is the result of subtracting a number greater than -3 and less than -2 from a number greater than 1 and less than 6
    5·1 answer
  • Plzzzzzzzzzzzzzzzzzzzzzz
    6·1 answer
  • 5 mins on the clock on correct answers
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!