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
viktelen [127]
3 years ago
14

Two vertical poles of lengths 11 ft and 14 ft stand 16 ft apart. A cable reaches from the top of one pole to some point on the g

round between the poles and then to the top of the other pole. Where should this point be located to use 30 ft of cable?

Mathematics
1 answer:
Alex17521 [72]3 years ago
6 0

We are given

total length of cable is 30 feet

and this cable is on hypotenuse sides of the triangles

so, we can draw triangle as

Let's assume those hypotenuse as 'a' and 'b'

so, we will have

a+b=30

now, we can find 'a' and 'b' from triangle

Smaller triangle:

a=\sqrt{x^2+11^2}

Larger triangle:

b=\sqrt{(16-x)^2+14^2}

we know that

a+b=30

so, we can plug this value

and we get

\sqrt{x^2+11^2}+\sqrt{(16-x)^2+14^2} =30

now, we can solve for x

\left(\sqrt{x^2+11^2}\right)^2=\left(30-\sqrt{\left(16-x\right)^2+14^2}\right)^2

32x-1231=-60\sqrt{x^2-32x+452}

1024x^2-78784x+1515361=3600x^2-115200x+1627200

now, we can use quadratic formula

we get

x=\frac{-\sqrt{36416^2-1152389056}+36416}{5152},\:x=\frac{\sqrt{36416^2-1152389056}+36416}{5152}

x=4.510,x=9.627

so,

The point should be located 4.510 feet , 9.627 feet from the smaller pole to use 30 feet cable............Answer

You might be interested in
16 to the power of x=64<br> What is x?
mina [271]

Answer:

the answer is 32 to the 3rd power

Step-by-step explanation:

5 0
3 years ago
Please answer There is a bag filled with 3 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted
Misha Larkins [42]

Answer:

\frac{15}{28}  is the required probability.

Step-by-step explanation:

Total number of Marbles = Blue + Red = 3 + 5 = 8

Probability of getting blue = \frac{3}{8}

Probability of not getting a blue =\frac{5}{8}

To get exactly one blue in two draws, we either get a blue, not blue, or a not blue, blue.

<u>First Draw Blue, Second Draw Not Blue:</u>

1st Draw: P(Blue) = \frac{3}{8}

2nd Draw: P(Not\:Blue)=\frac{5}{7}  (since we did not replace the first marble)

To get the probability of the event, since each draw is independent, we multiply both probabilities.

P(Event)=\frac{3}{8}\cdot \frac{5}{7}=\frac{15}{56}

<u>First Draw Not Blue, Second Draw Not Blue:</u>

1st Draw: P(Not\:Blue)=\frac{5}{8}

2nd Draw: P(Not\:Blue)=\frac{3}{7}  (since we did not replace the first marble)

To get the probability of the event, since each draw is independent, we multiply both probabilities.

P(Event)=\frac{5}{8}\cdot \frac{3}{7}=\frac{15}{56}

To get the probability of exactly one blue, we add both of the events:

\frac{15}{56}+\frac{15}{56}=\frac{15}{28}

4 0
3 years ago
Please help me asap!!!
blondinia [14]

Answer:

the answer is 120.6                     (:

Step-by-step explanation:

3 0
3 years ago
Se desea constrir una barda utilizando block . las dimensiones de la barda son 25 m de largo y 2 m de altura . si se requieren 1
Andrew [12]

Answer:

I don't understand the language

Step-by-step explanation:

am not form Paris

3 0
3 years ago
A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)= at² + bt + c, where t is the
frutty [35]

Answer:

<h2>a) a = -3, b = 18, c = 48; </h2><h2>s(t) = -3t²+18t+48</h2><h2>b) 48m</h2><h2>c) 8secs</h2>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'

Given the equation of the distance modelled as s(t)=at²+bt+c

If after 1 second the rock was 63 m, then 63 = a+b+c

If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c

Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c

i) Solving the 3 equations simultaneously to get a, b and c we have;

a+b+c = 63 ... 1

4a+2b+c = 72 ...2

49a+7b+c = 27 ...3

Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;

eqn 2- eqn1: 3a + b = 9...4

eqn 3- eqn 2: 45a + 5b = -45

eqn 3- eqn 2: 9a+b = -9 ... 5

solving 4 and 5 simultaneously

3a + b = 9 ...4

9a+b = -9 ... 5  

Taking the difference of 4 and 5 we have

6a - -9-9

6a = -18

a = -3

substituting a = -3 into equation 4 to get b we have;

3(-3)+b = 9

-9 + b = 9

b = 9+9

b = 18

substituting a = -3 and b = 18 into equation 1 to get c we have;

-3+18+c = 63

15+c = 63

c = 48

a = -3, b= 18 and c = 48

The distance function will be s(t) = -3t²+18t+48

ii) If the height of the cliff is modelled by the equation  s(t)=at²+bt+c

The height of the cliff is at when t = 0

s(0) = -3(0)²+18(0)+48

s(0) = 48m

The height of the cliff is 48m

iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;

s(t)=at²+bt+c

0 = -3t²+18t+48

3t²-18t-48 = 0

t² - 6t - 16 =0

t² - 8t+2t - 16 = 0

t(t-8)+2(t-8) = 0

(t+2)(t-8) = 0

t = -2 or 8

Taking the positive value of the time, t = 8secs

Time taken for the rock to reach sea level is 8secs

7 0
3 years ago
Other questions:
  • The proportion of households in a region that do some or all of their banking on the Internet is 0.31. In a random sample of 100
    12·1 answer
  • It takes 2 1/2 poster boards to display half of your project. How many poster boards will you need for your entire project?
    9·1 answer
  • Pls help!! if f(x) = 2x^2-4x and g(x)=5-2x, evaluate f(x) - g(x) for x=5
    8·1 answer
  • On september 8, 2004, the genesis spacecraft crashed in the utah desert because its parachute did not open. the 210-kg capsule h
    9·1 answer
  • Which is the solution to the inequality?1/4+x&lt;5/6​
    10·1 answer
  • Double the quotient of 3 and 6​
    10·1 answer
  • Lainey bought a set of 20 markers for $6. <br> What is the cost of one marker?
    12·2 answers
  • Two supplementary angles differ by 34. find the angles..​
    6·1 answer
  • Name a plane parallel to QRZ
    12·2 answers
  • Alex saved x dollars.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!