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Nataly_w [17]
3 years ago
10

A cell phone tower that is 150 ft tall sits on a mountain that

Mathematics
1 answer:
aliina [53]3 years ago
5 0

Answer:

angle of elevation will be 2.14^o.

Step-by-step explanation:

Given,

height of tower = 150 ft

height of tower = 1200 ft

So, total height of peak of tower = 1200 + 150

                                                       = 1350 ft

distance of user from cell tower = 5 miles

                                                     = 5 x 5280 feet

                                                     = 26,400 feet

Since the height of user from sea level = 400 ft

so, height of peak of tower with respect to user = 1350 - 400 ft

                                                                                = 950 ft

If the angle of depression is assumed as \theta, then we can write

tan\theta\ =\ \dfrac{\textrm{height of peak of tower w.r.t user}}{\textrm{distance of user from tower}}

=>\ tan\theta\ =\ \dfrac{950}{26400}

=>\ tan\theta\ =\ 0.374

 =>\ \theta\ =\ 2.14^o

So, the angle of elevation will be 2.14^o.

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3 years ago
Arjun and Jessica each improved their yards by planting daylilies and shrubs. They bought their
Anvisha [2.4K]

Hi there! Let me know if you have questions about my answer:

One shrub is $11.

One daylily is $4.

Step-by-step explanation:

To find the cost of each item, write a system of equations, one equation for what each person bought, and solve for each variable.

<u>Define your variables.</u>

let 'd' be the cost of one daylily

let 'r' be the cost of one shrub

<u>Create a system using the variables and information from the question.</u>

Write an equation for what Arjun bought:

5d + 7r = 97            5 daylilies, 7 shrubs, totaling $97

Write an equation for what Jessica bought:

2d + 11r = 129          2 daylilies, 11 shrubs, totaling $129

<u>Solve the system.</u>

I will solve the system algebraically, using the substitution method. Isolate one variable in one of the equations.

I will isolate 'd' in Jessica's equation:

2d + 11r = 129              Start with Jessica's equation

\frac{2d + 11r}{2} = \frac{129}{2}                  Divide everything in the equation by 2

d + \frac{11r}{2} = \frac{129}{2}                 Simplify

d = \frac{129}{2} - \frac{11r}{2}                 Isolate 'd' by subtracting \frac{11r}{2} from both sides.

Now you have an expression for 'd'.

Substitute Arjun's equation with the expression for 'd'. Solve for 'r' to find the cost of one shrub.

5d + 7r = 97                      Start with Arjun's equation

5(\frac{129}{2} - \frac{11r}{2}) + 7r = 97       Substitute 'd' for  d = \frac{129}{2} - \frac{11r}{2}

\frac{5*129}{2} - \frac{5*11r}{2} + 7r = 97      Distribute the 5

\frac{645}{2} - \frac{55r}{2} + 7r = 97            Simplify the numerators

\frac{645}{2} - \frac{55r}{2} + \frac{14r}{2} = 97          Change 7r to a fraction over 2

\frac{645}{2} - \frac{41r}{2} = 97                    Combine like terms, the terms with 'r'

\frac{645-41r}{2} = 97                       Simplify

645-41r = 194                 Multiply both sides by 2

-41r = 194-645              Subtract 645 from both sides

-41r = -451                     Divide both sides by –41

r = 11                                Solved for cost of one shrub

Substitute 'r' for 11 using either Arjun's or Jessica's equation. Then, isolate 'd' to solve for the cost of one daylily.

I will use Arjun's equation.

5d + 7r = 97                   Start with Arjun's equation

5d + 7(11) = 97              Substitute 'r' for r = 11

5d + 77 = 97                   Simplify. Subtract 77 from both sides.

5d = 20                           Divide both sides by 5.

d = 4                              Solved for the cost of one daylily

I hope this helped! Check out a similar problem about solving systems here to learn more:

brainly.com/question/11103098

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2 years ago
You estimate that there are 75 marbles in a jar. The actual amount is 82 marbles. Find the percent error
Vikentia [17]

Answer:

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Step-by-step explanation:

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3 years ago
Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and rem
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Answer:

3/5

Step-by-step explanation:

We want to find the fraction of the original branch that remains, so we will assume a length of the branch in order to make our calculation easier.

Since Kim marks it off in thirds and fifths, let's find the least common multiple of 3 & 5.

Least common multiple of 3 & 5 is 15.

Thus,let's make the length of the branch to be 15-meter long.

Now, if the branch is 15 m long, considering the markings of thirds and fifths, the branch would be cut at:

3, 5, 6, 9, 10, 12 meters.

We are told that She then breaks the branch along all the markings and removes one piece of every distinct length. Thus;

Distinct lengths are;

3 metres

5 - 3 = 2 metres

10 - 9 = 1 meter

Total she removes = 3 + 2 + 1 = 6 meters.

Total remaining is;

15 - 6 = 9 meters

Expressing this as a fraction of the original branch gives:

9/15

Divide both numerator and denominator by 3 to get; 3/5

7 0
2 years ago
ABC is dilated by a scale factor of 3 with the origin as the center of dilation, resulting in the image A'B'C'. If the slope of
uysha [10]

Answer:

The slope of A'B' = -1.2 ⇒ answer A

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

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- The scale factor, measures how much larger or smaller  

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- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- If the center of the dilation is the origin then multiply each coordinate

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* In the problem

∵ Δ ABC is dilated by a scale factor of 3 with the origin as the center

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∴ The slope of AB = (d - b)/(c - a) = -1.2

∵ Point A' is (3a , 3b) and point B' is (3c , 3d)

∴ The slope of A'B' = (3d - 3b)/(3c - 3a)

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∴ The slope of A'B' = 3(d - b)/3(c - a) ⇒ cancel 3 up with 3 down

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∴ The slope of A'B' = -1.2

* The slope of A'B' = -1.2

3 0
3 years ago
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