A steep mountain is inclined 72 degree to the horizontal and rises 4500 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 900 ft from the base of the mountain. Find the shortest length of cable needed.

Answers

Answer 1

Answer:

[tex]l_c=5078.27ft[/tex]

Step-by-step explanation:

From the question we are told that:

Angle of inclination [tex]\angle=72 \textdegree[/tex]

Height [tex]h=4500ft[/tex]

Distance b\w cable base and mountain base [tex]d_{cm}=900ft[/tex]

Generally the equation for length of mountain base [tex]d_{mb}[/tex] is mathematically given by

 [tex]Tan\theta=\frac{h}{d_{mb}}[/tex]

 [tex]d_{mb}=\frac{h}{Tan\theta}[/tex]

 [tex]d_{mb}=\frac{4500}{Tan 72 \textdegree}[/tex]

 [tex]d_{mb}=1462.11ft[/tex]

Generally the Pythagoras equation for length of the cable [tex]l_c[/tex] is mathematically given by

[tex]l_c^2=h^2+(d_{mb}+d_{cm}^2)[/tex]

[tex]l_c^2=4500^2+(1462.11}+900}^2)[/tex]

[tex]l_c=5078.27ft[/tex]


Related Questions

The table shows the relationship between the number of cups and total volume of lemonade served.
Cups of Total. Volume Lemonade Served
2 (ounces)
3 16
4 24
32
How many ounces is served per cup of lemonade?
Enter the answer in the box.
ounces per cup=​

Answers

Answer: 8

Step-by-step explanation:

2 cups = 16

Half of the 16 is 8

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Answers

Answer:

Option 4

Step-by-step explanation:

The circle is filled so it must be either :less then or equal to: or :greater then or equal to: and since it is going to the left that means it is on the less then or equal to.

Answer:

option 4

Step-by-step explanation:

the circle is filled so it can be equal

it shows n is everything lower then -1 so

n<=-1

What is ;

i^82

(Show work) ​

Answers

Answer:

-1

Step-by-step explanation:

We know that i^4 is equal to one so what you do is divide by 4 and the remainder is your simplified version

In this case the remainder is two which means taht i^82 = i^2 = -1

The cadets had to complete a 12 mile hike in 3 hours. How many miles an hour did they have to walk?

Answers

4 mph, 12/3=4
Hope this helps!

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Answers

Answer:

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Explanation:

Which expression is equivalent to 9s + 3 x 5 -2s?
A. 7s + 15
B. 2s + 22
C. 22s
D. 15s

Answers

The answer is A. When you take the 9s and the -2s, you get 7s. Then you add the 3x5 and end up with 15. Giving you the answer 7s+15
Answer is A hope this helps

Which holds more, a cylinder with a height of 10.0 cm and a diameter of 7.0 cm or a cylinder with a height of 7.0 cm and a diameter of 10.0 cm? Explain your answer using calculations. *

Answers

Answer:

The cylinder with a height of 7.0 cm and a diameter of 10.0 cm

Step-by-step explanation:

v = πr²h

---------------------

cylinder with a height of 10.0 cm and a diameter of 7.0 cm

v = π(3.5²)10

v = 384.65 cm³

cylinder with a height of 7.0 cm and a diameter of 10.0 cm

v = π(5²)7

v = 549.5 cm²

549.5 > 384.65

The second cylinder holds more

PLS HELP NO FAST LINKS!!!

Answers

All of them but A because hexagon as no acute angel

Given that A = (9,9,2), B = (1,3,5) and C = (5,6,4), find the vector equation of the line through A and B

Answers

Answer:

Equation = 9i + 9j + 2k - λ ( 8i + 6j - 3k)

Step-by-step explanation:

Vector equation of a line passing through two points A & B is : r = a + λ(b - a)

Given A = (9,9,2) ; B = (1,3,5)

Equation of line : r = 9i + 9j + 2k + λ [ (1-9) i + (3-9) j + (5-2) k ]

= 9i + 9j + 2k + λ ( -8i + -6j + 3k)

= 9i + 9j + 2k - λ ( 8i + 6j - 3k)

1. Is x + 8 a factor of b(x) = x3 + 18x2 + 80x? Determine using synthetic
division. Explain how you know it is or isn't.

Answers

Answer:

If x+8 is a factor, divide by -8.

-8      1   18   80

             -8  -80

_______________

       1     10      0

It is a factor because there is no remainder.

Step-by-step explanation:

What is the volume of a sphere with a diameter of 49.3cm, rounded to the nearest tenth of a cubic centimeter?

Answers

The answer is V≈62739.26cm³

The slope of the line below is -3. Which of the following is the point-slope
form of the line?
10
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10
(2.-6)
- 10

Answers

A
Below is the method I used and the formula

Miss David's birthday is in April, and she is going to have a party. She is looking to buy a bag of decorations. Each bag has two different types of decorations: balloons and streamers. The first bag has 11 balloons and 6 streamers. The second bag has 15 balloons and 4 streamers. The last bag has 6 balloons and 12 streamers. Bag 1 costs $91, bag 2 costs $99, and bag 3 costs $102. How much does each type of decoration cost?

Answers

Answer:

b = $5

s = $6

Step-by-step explanation:

this can be solved using simultaneous equation

s = streamers

b = balloons

either of the 3 equations can be used to determine the price of the items

11b + 6s = 91 equation 1

15b + 4s = 99 equation 2

multiply equation 1 by 4 and equation 2 by 6

44b + 24s = 364 eqn 3

90b + 24s = 594 eqn 4

subtract equation 3 from 4

230 = 46b

b = 5

substitute for b in eqn 1

55 + 6s = 91

s = 6

Anyone know this?? I’m confused..

Answers

Answer:

jgh

side side side axioms

not sure

Answer:

[tex]\triangle CAB\cong \triangle ONP[/tex]

Step-by-step explanation:

Triangles [tex]\triangle CAB[/tex] and [tex]\triangle ONP[/tex] share two corresponding angles and the inclusive side between them. This is known as ASA (angle-side-angle) and does prove congruence. Therefore, [tex]\triangle CAB\cong \triangle ONP[/tex].

The four proofs of congruence include SSS (side-side-side), SAS(side-angle-side), ASA (angle-side-angle) and AAS (angle-angle-side). No other pair of triangles demonstrate any of these.

This pattern repeats every 4 terms. The pattern is square, hexagon, pentagon, triangle. What is the shape in the 13th term of this pattern? sorry if it looks weird i dont know why it does

Answers

Answer:

the answer is square

Square (first one) :)

Just count up to 13 while moving to the right and you get your answer :)

Is 511Q bad on a test :((

Answers

Answer:

big brain

Step-by-step explanation:

State six ordered pairs for this function.
F(x) = x2 +14x+45

Answers

i only could look up three but here:
(
0
,
45
)
,
(
1
,
60
)
,
(
2
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Rewrite the following polynomial in standard form
-x2 + 1 + 2x

Answers

Answer:

Simplify terms.

Tap for more steps...

2 x ^3 − 9 x^ 2 + 7 x + 6

Step-by-step explanation:

HELP ME ASAP!!! On a scale used on a map, 3/4 inch represents 8 feet. On the map, what is the length of a room with an actual length of 24 feet?



A
4 in.

B[tex]1 \frac{3}{4} [/tex]

C
[tex]4 \ \frac{1}{2} [/tex]

D
[tex]2 \ \frac{1}{4} [/tex]

Answers

Answer:

D. 2 1/4

Step-by-step explanation:

3/4 inch = 8 feet

24 divided by 8 = 3

(meaning you would multiply eight three times in order to get to 24)

So....

3/4 x 3 = 2 1/4

Answer: 2 1/4

Hope this helps :)

Answer: D - 2 1/4”

Step-by-step explanation:

8 feet goes into 24 feet 3 times

Eg. 24/8 = 3

If 3/4” = 8 feet, then 3 x 3/4” = 24 feet

3 x 3/4” = 2 1/4”

Katy put $3000 into his bank account. If the account pays 9% interest compounded continuously, when will it be worth $12000?

Answers

Answer:

33 years and 4 months.

Step-by-step explanation:

Assuming it is a flat rate

3000 x 0.09 = $270 per year

12000-3000=9000

9000/270 = 33 years, 4 months

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Answers

The area of the rectangle is 40 cm.
To find this, just multiply 8 and 5.
Area: length times width
Area: 8 times 5
Area: 40 cm

The perimeter of the rectangle is 26 cm.
Perimeter: 2L + 2W
Perimeter: 2(8) + 2(5)
Perimeter: 16 + 10
Perimeter: 26
Hope this helps!

Answer:

Area is 40

perimeter is 26

Step-by-step explanation:

area = l×w

[tex]8 \times 5 = 40[/tex]

Perimeter = 2L +2W

[tex]2 \times 8 + 2 \times 5 \\ 16 + 10 \\ 26[/tex]

- 7th Grade Work -

A bagel shop offers a mug filled with coffee for $7.75, with each refill costing $1.25. Kendra spent $31.50 on the mug and refills last month. How many refills did Kendra buy?

Answers

Answer:

19

Step-by-step explanation:

hope this helps with the problem

ace please help

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Answers

Answer: C $25

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if sarah went to the shop and there was a 10% sale. she was going to buy 7 CDs for $60

Answers

Answer:

10 % of 60$ => 10/100 × 60$ => 6$

6$ for 7 cds => 42 $

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Answers

Answer:

AC ≈ 5.5

Step-by-step explanation:

Angle bisector theorem states that "angle bisector of an angle divides the opposite side into two segments which are proportional to the other two sides of the triangle."

By applying this theorem in the given ΔABC,

AD is the angle bisector of ∠CAB which divides the opposite side of the angle into two segments BD and CD.

Therefore, [tex]\frac{AB}{BD}=\frac{AC}{CD}[/tex]

[tex]\frac{5.1}{4}=\frac{AC}{4.3}[/tex]

[tex]AC=\frac{5.1\times 4.3}{4}[/tex]

AC = 5.4825

AC ≈ 5.5 units

Evelyn bought 1 pound of pecans and 0.36 pounds of almonds from the shop. How many pounds of nuts did she buy altogether? А. 0.46 pounds 1.36 pounds С 0.64 pounds D 4.6 pounds​

Answers

Answer: I think it is B: 1.36

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What is the measurement of 40°

Answers

Answer:

80

Step-by-step explanation:

x by 2

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Answers

Answer:

We are learning this in 7th grade lol how did you get 7th grade math to 6th grade math

The school library has 300 books on the topic of
sports. Students have checked out seventy-four
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of sports still remain in the library?

Answers

226 Sports Books! Hope you have an amazing day!

Step-by-step explanation:

226 sports book have a good day

In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked. If the store has 3,000 eggs for sale, how many can expect to be cracked. (Prediction = Proportion)




Group of answer choices

90

60

600

900

Answers

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}[/tex]

In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.

In 200 eggs cracked =6

in 1 egg cracked =[tex]\dfrac{6}{200}[/tex]

According to the question,

If the store has 3,000 eggs for sale, how many can expect to be cracked.

In 3000 eggs cracked=[tex]\dfrac{6}{200}×3000[/tex]

90 eggs

Therefore:-

If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked

If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked.

What is Proportion?

A proportion is an equation in which two ratios are set equal to each other.

For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)

Given that :

In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.

In 200 eggs cracked = 6 / 200 in 1 egg cracked

According to the question,

If the store has 3,000 eggs for sale, how many can expect to be cracked.

In 3000 eggs cracked = 6 / 200 x 3000

= 90 eggs

Hence, If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked.

Learned more about Proportion, click;

https://brainly.com/question/30657439

#SPJ3

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