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
Fynjy0 [20]
3 years ago
6

Two vertical poles, one 8 feet high and the other 10 feet high, stand 50 feet apart on a flat surface. We want to attach a suppo

rt wire to each poles by running wire from the ground to the top of each pole. If we are to stake both wires into the ground at the same point, where should the stake be placed to use the least amount of wire?
Mathematics
1 answer:
drek231 [11]3 years ago
4 0

Answer: amount of wire needed is 5.84 feet.

Step-by-step explanation:

given data:

height of the first pole = 8 feet

height of the second pole = 10 feet

distance between both poles = 50 feet

SOLUTION:

L1 = \sqrt{x^{2} + 8^{2} } \\

= \sqrt{x^{2} + 64}

L2 = \sqrt{(50-x)^{2} +10^{2} }

= \sqrt{(50-x)^{2}+100 }

total length of wire

L = L1 + L2

L =  \sqrt{x^{2} + 64}+\sqrt{(50-x)^{2}+100 }

\frac{dL}{dx}=\frac{2x}{2\sqrt x^{2} +64} + \frac{2(50-x(-1)}{2\sqrt{(50-x)^{2} +100} } =0  

\frac{x}{\sqrt x^{2} +64} = \frac{50-x}{\sqrt{(50-x)+100} }

x\sqrt{(50-x} )^{2}+100 = (50-x)\sqrt{x^{2} +64}

x^{2} ((50-x)+100)=(15-x)^{2} (x^{2} +64)

x^{2} (50-x)^{2} +100x^{2} =x^{2} (50-x)^{2} +64(50-x)^{2} \\\\100x^{2} = 64(50-x)^{2} \\100x^{2} =64((50-x)(50-x))\\100x^{2} = 64(2500-100x+x^{2} )\\\\100^{2} =160000 -6400x+64x^{2} \\\\36x^{2} +6400x-160000=0

36x^{2} + 64x-1600=0

18x^{2} +32x+800=0

using quadratic equation

a=18\\b=32\\c=800\\

refer to the attached image

x=\frac{-8}{9} +\frac{4}{9} \sqrt{229}   \\or   \\x=x=\frac{-8}{9} +\frac{-4}{9} \sqrt{229}

x = 5.84\\or\\x= -7.61

You might be interested in
0.2 with an exponent of 4
MakcuM [25]

Answer:

0.0016

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
A teacher wants to give 3 markers to
Novay_Z [31]
First, find out how many markers in total the teacher will need. 
25*3=75
Then, find out how many packages the teacher will need by dividing by 8 because that's how many are in each package.
\frac{75}{8}=9.375
Now because there is a remainder of .375 that tells us that there are not enough markers in 9 packages to give all students 3 each.

She will have to buy an additional package to give every student 3 markers each. 

10 Packages are needed.
8 0
3 years ago
Read 2 more answers
The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region? 2x2 4x2 6x2 8x2
Savatey [412]
The picture in the attached figure

we know that
area of the <span>the shaded region=area of rectangle -area of a kite

area of rectangle=(3x+x)*(x+x)----> 4x*2x---> 8x</span>²

area of a kite=(1/2)*[d1*d2]
where d1 and d2 are the diagonals
d1=4x
d2=2x
so
area of a kite=(1/2)*[4x*2x]----> 4x²

area of the the shaded region=8x²-4x²-----> 4x²

the answer is 
4x²

4 0
3 years ago
Read 2 more answers
Luther takes 45 bottles of water on a camping trip. If he drinks 80 % of them how many does he have left?
jeka94

Answer:

9

Step-by-step explanation:

80% of 45 is 36

45-36=9

3 0
3 years ago
If f(x) = 2x^2 - x, find f(-3).
ioda
F(-3)  = 2(-3)^2 - (-3) =  2(9)+3 = 18 + 3 = 21
4 0
4 years ago
Read 2 more answers
Other questions:
  • Which of the following can be determined about events A and C from the table.
    15·2 answers
  • In one settlement, there were 29 horses. There were 9 more brown horses than black horses. How many of each color were there?
    8·1 answer
  • Find measure a and b
    6·2 answers
  • A professor is trying to determine if her students guessed on a certain multiple choice question. She expects that if the studen
    14·1 answer
  • One fourth the sum of r and ten is identical to r minus 4
    11·1 answer
  • A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?**
    8·2 answers
  • Please help meh again...
    12·2 answers
  • Plzz help meee!
    13·2 answers
  • A line that includes the point (9, 10) has a slope of -1/9 what is its equation in point-slope
    8·1 answer
  • Help guy what is 57.3 - 4.32 =
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!