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2 years ago

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A cable is attached to the top of a 28-foot utility pole. The cable is fastened to the ground at a point 21 feet from the base o

f the pole. Find the length of the cable.

1 answer:

Elenna [48]2 years ago

4 0

Answer:

Length of the cable (H) = 35 foot

Step-by-step explanation:

Given:

Height of the pole (P) = 28 Foot

Distance from the pole (B) = 21 Foot

Find:

Length of the cable (H) = ?

Computation:

According to the Pythagoras theorem:

$H = \sqrt{P^2+B^2}$

$Length\ of\ the\ cable = \sqrt{(Height\ of\ the\ pole)^2+(Distance\ from\ the\ pole)^2}$

$Length\ of\ the\ cable =\sqrt{28^2+21^2}\\\\ Length\ of\ the\ cable =\sqrt{784+441}\\\\Length\ of\ the\ cable=\sqrt{1,225} \\\\Length\ of\ the\ cable = 35$

Length of the cable (H) = 35 foot

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For positive acute angles AA and B,B, it is known that \tan A=\frac{28}{45}tanA= 45 28 and \cos B=\frac{3}{5}.CosB= 5 3 . Fi

MrRa [10]

Answer:

$\cos(A + B) = \frac{23}{265}$

Step-by-step explanation:

Given

$\tan A=\frac{28}{45}$

$\cos B=\frac{3}{5}$

Required

$\cos(A+B)$

In trigonometry:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

We need to solve for cosA, sinA and sinB

Given that:

$\tan A=\frac{28}{45}$ and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),

So, we have:

$x =28$ and $y = 45$

For this angle A, we need t calculate its hypotenuse (z).

Using Pythagoras,

$z^2 = x^2 + y^2$

$z = \sqrt{x^2 + y^2$

$z = \sqrt{28^2 + 45^2$

$z = \sqrt{2809$

$z = 53$

From here, we can calculate sin and cos A

$\sin A= \frac{opposite}{hypotenuse}$ and $\cos A= \frac{adjacent}{hypotenuse}$

$\sin A= \frac{x}{z}$

$\sin A= \frac{28}{53}$

$\cos A= \frac{y}{z}$

$\cos A= \frac{45}{53}$

To angle B.

Give that

$\cos B=\frac{3}{5}$ and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),

So, we have:

$a = 3$ and $b = 5$

For this angle B, we need to calculate its opposite (b).

Using Pythagoras,

$c^2 = a^2 + b^2$

$5^2 = 3^2 + b^2$

$25 = 9 + b^2$

Collect like terms

$b^2 = 25 - 9$

$b^2 = 16$

$b = \sqrt{16$

$b = 4$

From here, we can calculate sin B

$\sin B= \frac{opposite}{hypotenuse}$

$\sin B = \frac{b}{c}$

$\sin B = \frac{4}{5}$

Recall that:

$\cos(A+B) = \cos\ A\ cosB - sinA\ sinB$

and

$\cos B=\frac{3}{5}$ $\sin B = \frac{4}{5}$ $\sin A= \frac{28}{53}$ $\cos A= \frac{45}{53}$

$\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}$

$\cos(A + B) = \frac{135}{265} - \frac{112}{265}$

$\cos(A + B) = \frac{135-112}{265}$

$\cos(A + B) = \frac{23}{265}$

7 0

2 years ago

A certain flight arrives on time 8484 percent of the time. Suppose 143143 flights are randomly selected. Use the normal approxim

Troyanec [42]

Answer:

a) P(x=108)=0.0020

b) P(x≥108)=0.9980

c) P(x<124)=0.7794

d) P(124≤x≤128)=0.1925

Step-by-step explanation:

We know the population proportion, that is p=0.84.

We take a sample of size n=143.

We will use the normal approximation to the binomial distribution to model this problem.

The mean and standard deviation of the normal approximation to the binomial distribution will be:

$\mu=np=143*0.84=120.12\\\\\sigma=\sqrt{np(1-p)}=\sqrt{143*0.84*0.16}=\sqrt{19.22}=4.38$

a) We have to calculate the probability that exactly 108 flights are on time.

As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.

In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):

$P(x=108)=P(107.5$

b) Now we have to calculate that at least 108 flights are on time.

As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:

$P(x\geq108)=P(x>107.5)=P(z>-2.88)=0.9980$

c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.

$P(x$

d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.

This interval corresponds to the probability P(123.5<x<128.5)

$P(123.5$

5 0

3 years ago

Jacob plans to work at his family's restaurant this summer to make some extra money. His parents have agreed to pay him $9.75 pe

san4es73 [151]

Answer:

There is a direct relationship between the amount of money that Jacob earns and the number of hours he works.

Step-by-step explanation:

In math, a direct relationship exists when a change in one variable causes another variable to change in the same manner. E.g. if variable X increases, then variable Y will increase. If variable X decreases, then variable Y will decrease.

In this case, if Jacob works 25 hours per week, he will earn $243.75. If he works 30 hours, he will earn $292.50. But if he only works 20 hours, he will earn $195.

4 0

2 years ago

Which ordered pairs are solutions to the equation?

neonofarm [45]

D.
y=2x+5
Sub in one pair (5,15)
15=2(5)+5
15=10+5
15=15 [Correct]
AND
9=2(2)+5
9=4+5
9=9 [Correct]

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3 years ago

What is the coefficient in this expression? <br> 2/5pq<br> A) p<br> B) 2/5<br> C)2<br> D)5

borishaifa [10]

Answer: 34+35

Step-by-step explanation: 35+33 bc that equals 69

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2 years ago

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