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
iris [78.8K]
3 years ago
6

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s,

how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall?

Mathematics
1 answer:
shusha [124]3 years ago
3 0

Answer:

-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

Step-by-step explanation:

Let

x= distance between the wall and ladder

Ф = angle between the ladder and ground

The rate of change is: dx/dt = 0.8 ft/s

We need to find dФ/dt when x = 8 ft/s

From the triangle in the figure we see that:

cos Ф = x/10

=> x = 10 cosФ

Now, the rate of change will be

d(x)/dt = d/dt (10cosФ)

dx/dt = -10 sin Ф dФ/dt

dx/dt = 0.8 (given)

to find dФ/dt

we need to find sin Ф when x = 8

By Pythagoras theorem

(hypotenuse)^2 = (Perpendicular)^2+(base)^2

(10)^2 = (8)^2+ (Perpendicular)^2

100 = 64 +  (Perpendicular)^2

=>  (Perpendicular)^2 = 100-64

(Perpendicular)^2 = 36

Perpendicular = 6

sin Ф = Perpendicular/hypotenuse

sin Ф = 6/10 = 3/5

Putting values in:

dx/dt = -10 sin Ф dФ/dt

0.8 = -10(3/5) dФ/dt

0.8 = -6 dФ/dt

=> dФ/dt = 0.8 / -6

dФ/dt = - 0.133 radians/s

So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

You might be interested in
1. Is triangle P’Q’R larger or smaller than triangle PQR? Explain how you know
Salsk061 [2.6K]

Answer:

The length of the line is PQ as this line is parallel to the x - axis. So, the length of the line is the summation of 10 from second quadrant and 20 from first quadrant. So, the sum is 30. Hence the length of the line is 30 units.

Step-by-step explanation:

The length of a line segment can be measured by measuring the distance between its two endpoints. It is the path between the two points with a definite length that can be measured. Explanation: On a graph, the length of a line segment can be found by using the distance formula between its endpoints.

7 0
3 years ago
today, 6 friends went out for lunch. their total Bill was $41.88, including tax and gratuity. they decide to split the Bill equa
Mariulka [41]
Each person will get back $3.02

4 0
3 years ago
Read 2 more answers
00:00
OLEGan [10]
The answer is maybe C lol
4 0
3 years ago
Whats the answer?<br> please help me
timofeeve [1]
The answer would be b
5 0
3 years ago
Viable what is the definition
Neporo4naja [7]

Answer:

capable of working successfully; feasible.

or

Step-by-step explanation:

(of a plant, animal, or cell) capable of surviving or living successfully, especially under particular environmental conditions.

3 0
3 years ago
Other questions:
  • Rewrite the linear function x + 4y =<br> – 12 in slope-intercept form.
    9·1 answer
  • The resting heart rate for an adult horse should average about μ = 43 beats per minute. Let x be a random variable that represen
    13·1 answer
  • There are a total of 34 lions and Hyenas. Each lion eats 4 antelope. Each Hyena eats 3 antelope. 117 antelope are eaten. How man
    14·1 answer
  • (Picture up top) Lines XU and WY intersect at point A. Based on the diagram, determine if the statement is True or False t.
    10·2 answers
  • Carlos drank 2740ML of water after football practice. How many liters did he drink
    6·2 answers
  • Find the radius of each figure. round to the nearest tenth.
    7·1 answer
  • The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to e
    13·2 answers
  • What trig function would I use to solve for x?
    9·1 answer
  • Find the following limit without using a graphing calculator or making a table.
    15·1 answer
  • What value of n makes the equation true?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!