A 200 foot long zipline cable is attached to the top of a tree and extends to an anchor on the ground. The cable makes an angle of 61º with the ground. Calculate how far away the foot of the cable is to the base of the tree.

Answers

Answer 1

Answer:

~ 97 ft

Step-by-step explanation:

cos = adj/hyp

cos61 = adj/200

200 * cos61 = adj

adj = 96.961924049267406

~ 97 ft

Answer 2

The foot of the cable is 95 feet away from the base of the tree.

What is Trigonometric Function?

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of the sides of the triangle.

We have,

The angle between the ground and the cable is given as 61º.

In a right triangle, the side opposite the angle (in this case, the height of the tree) is related to the hypotenuse (the length of the cable) and the adjacent side (the distance from the foot of the cable to the base of the tree) by the trigonometric function cosine.

Cosine(angle) = adjacent/hypotenuse

Cos(61º) = adjacent/200 ft

adjacent = Cos(61º)x200 ft

adjacent ≈ 0.475 x 200 ft

adjacent ≈ 95 ft

Therefore, the foot of the cable is 95 feet away from the base of the tree.

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Related Questions

The question is in the screenshot. ( I really need help in this one)

Answers

Answer:

V=A*L

V=72*6

V=432 in cube

A company is testing and comparing two hair spray formulas. The box plots show the number of hours each hair spray lasts before reapplication is necessary. Which statement is best supported by the information in the plots?
1.Hair spray B will always last two hours longer than hair spray A.
2.Hair spray A will likely last longer than hair spray B.
3.Hair spray B will likely last longer than hair spray A.
4.Hair spray B will always last longer than hair spray A.

Answers

Answer:

Foundations of Financial Management with Time Value of Money card (15th Edition) Edit edition Solutions for Chapter 4 Problem 9P: Vitale Hair Spray had sales of 13,000 units in March. A 70 percent increase is expected in April. The company will maintain 30 percent of expected unit sales for April in ending inventory.

Step-by-step explanation:

3 is the correct answer because box plots are averages. Hair spray B averages a longer time

The following table shows the salary of 7 people in an office last year.
Name
Income
Andy
£13500
Bevan
£27500
Cheryl
£13750
Deva
£79000
Elliott
£19250
Frankie
£29000
Grace
£15000
a) Work out the mean income to 2 DP.
b) Deva was given a large bonus for 30 years service..
Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?

Answers

Answer:

23 poudsfgghhhhhhhxcvbnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

Given
f (x) = x3 + 1
and
g(x) = x – 1
find the composition
f(g(x))

Answers

Answer:

(x-1)³+1

is correct option

Felix is a quality control expert at a factory that paints car parts. Their painting process consists of a primer coat, color coat, and clear coat. For a certain part, these layers have a combined target thickness of 150 microns. Felix measured the thickness of 50 randomly selected points on one of these parts to see if it was painted properly. What is Felix's margin of error? "Round to 2 decimal places​

Answers

Answer:

0.9

Step-by-step explanation:

His sample had a mean thickness of 148 microns and a standard deviation of 3.3 microns with a 95% confidence interval for the mean thickness.

Solution:

The z score shows by how many standard deviations the raw score is above or below the mean.

Given that:

The mean (μ) = 148 microns, standard deviation (σ) = 3.3 microns, sample size (n) = 50 and confidence interval (C) = 95%

α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 is the same as the z score of 0.475 (1 - 0.025) which is equal to 1.96

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } \\\\E=1.96*\frac{3.3}{\sqrt{50} } \\\\E=0.9\ microns[/tex]

The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.

Answers

Step-by-step explanation:

Feel free to ask for more help. I love Linear Algebra

b) Find x and y.
x = 10-6

Answers

Answer:

to find y you have to do trigonometry

Please help me I will give you 16 points I don’t know what that do but I will

Answers

Answer:

40

Step-by-step explanation:

The serving sizes, [tex]x[/tex], of 20, 80, and 120 have a required amount of meat in pounds, [tex]y[/tex], of [tex]y=\frac{1}{10}x[/tex] (the number of pounds of meat is equal to 1/10th the serving size)

However, for the row with a serving size of 40, the number of pounds of meat is equal to [tex]\frac{6}{40}=\frac{3}{20}[/tex] the serving size. Therefore, the serving size of 40 has a different ratio of serving size to pounds of meat than the other ratios.

Con procedimiento por favor

Answers

Answer:

C

Step-by-step explanation:

straight line graphs

Answers

Answer:

I don't get it what is the question ❓


When a cup of coffee at 100 degree Celsius cools down ,it loses 12%of its current temperature
per minute. What will the temperature be after 10 minutes.

Answers

Answer:

Temperature after 10 minute = 27.9 degree Celsius

Step-by-step explanation:

Current temperature, P = 100 degree Celsius

% rate in temperature loses = 12% per minute = 0.12

Time,  t = 10 minutes

Temperature after t minutes ,

                                           [tex]= P ( 1 - r )^t\\\\=100( 1 - 0.12)^10\\\\=100(0.278500976)\\\\=27.85[/tex]

                                           = 27.9 degree Celsius

what is the percent increase between 8,863,052 and 9,149,840?

Answers

Answer:

[tex]increase = 9149840 - 8863052 \\ = 286788 \\ \% \: increase = \frac{286788}{8863052} \times 100\% \\ = 3.24\%[/tex]

Answer:

=3.23577% increase

Step-by-step explanation:

1) subtract final value minus starting value

2) divide that amount by the absolute value of the starting value

3) multiply by 100 to get the percent increase

4) if the percentage bis negative, it means there was a decrease and not an increase

y = x2
-2
What is the Domain:

Answers

Answer:

all real numbers

Step-by-step explanation:

The domain is the values that x can take

x can be any real number

what is the slope of the line y = 8x - 10

Answers

Answer:

slope is 8

Step-by-step explanation:

y=Mx+c

m is the slope therefore the slope is equal to 8

The slope of the line y = 8x - 10 is 8.

What is Slope?

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Given line is y = 8x - 10

Equation of a line in slope intercept form is given by,

y = mx + c

Here, m is the slope and c is the y intercept.

The given equation is in the slope intercept form.

y = 8x - 10

The coefficient of x is the slope.

So slope of the given line = 8

Hence the slope of the line y = 8x - 10 is 8..

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1. The function below models the value of Tiana's car, where x represents
the number of years since she purchased the car. What is the rate of
growth or decay?*
f(x) = 24,000. 0.88
O Option 2 -88% Growth
O Option 3 -12% Decay
O Option 1 - 88 % Decay
O Option 4 - 12% Growth

Answers

Answer:

option 4

Step-by-step explanation:

Option 3 -12% Decay

Step-by-step explanation:

.y is inversely proportional to (x + 3) ?.
When x = 2, y = 8.
Find y when x = 7.
A 100
B. 4
C. 2.
D. 16
OA

Answers

Answer:

B

Step-by-step explanation:

y = k/(x + 3)

Let x = 2

Let y = 8

k = ?

8 = k/(2 + 3)      Combine the terms on the right

8 = k/(5)            Multiply both sides by 5

8*5 = k

k = 40

Let x = 7

y = 40/(7 + 3)

y = 40/10

y = 4

simplify 3^3 - 2x(5x-5) + √25

Answers

-10x^2+10x+32 is the simplified answer

Solve for the value of x in the diagram: Show your work and explain the steps you used to solve.

Answers

Answer:

x = 20

Step-by-step explanation:

The triangles are similar

3          (3+5)

----- = ----------

12        (12+x)

Using cross products

3(12+x) = 12*(3+5)

3(12+x) = 12*8

3(12+x) = 96

Divide by 3

3(12+x)/3 = 96/3

12+x = 32

Subtract 12

12+x-12 =32-12

x = 32-12

x =20

A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2).
Use the graph to determine the input value for which f(x) = g(x) is true.

Answers

Answer:

x=2/3

Step-by-step explanation:

Most of that information is unnecessary. Just plug in the values of f(x) and g(x) into the equation where they are equal to each other and solve.

-3x+4=2

-3x=-2

3x=2

x=2/3

What is the answer ?????

Answers

Step-by-step explanation:

very difficult............

Nala and lily are playing a dice game where they score points. After one round, the ratio of nala point to lily's point is 7 to 9. If nala has 14 more points than lily, determine how many points lily has.

Answers

Answer:

Lily has 63 points and Nala has 49.

Step-by-step explanation:

Since Nala and Lily are playing a dice game where they score points, and after one round, the ratio of Nala's points to Lily's points is 7 to 9, if Nala has 14 more points than Lily, to determine how many points Lily has se you must perform the following calculation:

9 - 7 = 2

14/2 = 7

7 x 7 = 49

7 x 9 = 63

63 - 49 = 14

Therefore, Lily has 63 points and Nala has 49.

What is the answer I need helppppp

Answers

Answer:

y= 4 x=0 (0,4)

Step-by-step explanation:

5x+y=4

-5x +y=4

the 5x would cancel out because they equal zero

2y=4

divide both sides by 2

y=4

put the y into one of the equations

5x +4 =4

subtract 4 from both sides

5x=0

divide five from both sides

x=0/5

so x=0

Step-by-step explanation:

5x+y=4 --> y=-5x+4

Plug this into the other equation:

-5x+(-5x+5)=4

Simplify:

-10x=1

x=-.1 (save this answer)

Plug into first simplified equation:

y=-5(-.1)+4

Solve:

y=4.5

(-.1 , 4.5)

Please help me with this

Answers

Answer:

O = 29

P = 61

Step-by-step explanation:

90 = (x+3) + (2x+9)

90 = 3x + 12

90 - 12 = 3x

78 = 3x

x = 26

26 + 3 = O = 29

(26 * 2) + 9 = P = 61

61 + 29  = 90 = Complementary Angles

How many in five days?

Answers

Answer:

d

Step-by-step explanation:

Answer:

I think it is B

Step-by-step explanation:

help i give many points

Answers

Answer:

Step-by-step explanation:

The pic doesnt wrk comment question and ill answer

true or false : A triangle can have interior angles of 50 degrees, 70 degrees, and 68 degrees​

Answers

false, because the 3 interior angles must all add up to a total of 180°

Answer:

it is false as the sum of the degrees of the triangle should be 180 but here it is 188 so it is false

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Polygon ABCD is a parallelogram, and m-ABC = 127º. The length of BC is 10 units, and the length of AB is 5 units.
1271
D
units, and m_BCD is
The perimeter of the parallelogram is

Answers

Answer:

Perimeter = 30 units

m<BCD = 53°

Step-by-step explanation:

Recall: in any parallelogram, consecutive angles are supplementary. Also, the pairs of parallel sides are equal in length.

We would use this knowledge to solve the problem given.

m<ABC = 127° (given)

BC = 10 units

AB = 5 units

✔️Perimeter of the parallelogram = AB + BC + CD + AD

AB = CD = 5 units (pair of parallel sides)

BC = AD = 10 units (pair of parallel sides)

Perimeter = 5 + 10 + 5 + 10

Perimeter = 30 units

✔️m<BCD = 180° - m<ABC (consecutive angles are supplementary)

m<BCD = 180° - 127° (Substitution)

m<BCD = 53°

Nolan plots the y-intercept of a line at (0, 3) on the y-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan’s line?

y = 2x + 1
y = 2x + 3
y = 3x + 2
y = 3x + 5

Answers

I think the answer is the first option.

Answer:

B

Step-by-step explanation:

The equation of Nolan's line is  

The slope-intercept form of a line is given by:

Here

m is the slope of the line

and b is the y-intercept.

Given

y-intercept = b = 3

slope = m = 2

The values of m and b can be put into the equation to find the line's equation

So,

Putting the value

Hence,

The equation of Nolan's line is

I swear there are never tutors

Answers

Answer:

5-2y (the last option)

hope this helps!

please give brainiest<3

Answer:

2y-5

Step-by-step explanation:

Plsss help I will give brainliest

Answers

The correct answer is A. Grade 7
In the table, it shows that for both grades 7 and 8 there are 10 students in band so it’s equal
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