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
wlad13 [49]
3 years ago
6

"A 12​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from t

he building at 33 ​feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 55 feet from the​ wall?"
Mathematics
1 answer:
Svet_ta [14]3 years ago
7 0

Answer:

Step-by-step explanation:

The question has typographical errors. The correct question is:

"A 12​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 ​feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the​ wall?

Solution:

The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.

Let x represent the distance from the top of the ladder to the ground(opposite side)

Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)

The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,

dy/dt = 3 ft/s

The rate at which x is reducing would be

dx/dt

Applying Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side², it becomes

x² + y² = 12²- - - - - - - -1

Differentiating with respect to time, it becomes

2xdx/dt + 2ydy/dt = 0

2xdx/dt = - 2ydy/dt

Dividing through by 2x, it becomes

dx/dt = - y/x ×dy/dt- - - - - - - - - - 2

Substituting y = 5 into equation 1, it becomes

x² + 5 = 144

x² = 144 - 25 = 119

x = √119 = 10.91

Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes

dx/dt = - 5/10.91 × 3

dx/dt = - 1.37 ft/s

You might be interested in
Given that sin 28° ≈ 0.469, enter the cosine of a complementary angle.
Lena [83]

Answer:

29 i think not sure ill reach back to you if i find a positive answer

4 0
3 years ago
What is the solution to the equation shown below?
grin007 [14]
x + 5/2 = 2(x + 3)
D. -7/3
6 0
3 years ago
Tonya and Emily each have an online jewelry store. Let T represent the amount of money Tonya earns daily, and let
zubka84 [21]

Answer:

On average, Tonya makes $312 more than Emily on a typical day.

Step-by-step explanation:

I was just studying that question a few hours ago

3 0
3 years ago
Read 2 more answers
X-3y=1<br> -x+6y=-7<br><br> Solve the system using elimination <br> Type ordered pair
Vedmedyk [2.9K]

Answer:

x=-5, y=-2. (-5, -2).

Step-by-step explanation:

x-3y=1

-x+6y=-7

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

3y=-6

y=-6/3

y=-2

x-3(-2)=1

x+6=1

x=1-6

x=-5

3 0
3 years ago
Seth is trying to find the unit price for a package of blank compact discs on sale at 10 for $5.49. Find his mistake and correct
hoa [83]
It is about .55 cents for each disk
3 0
3 years ago
Other questions:
  • What is the value of x?<br> Enter your answer in the box.
    14·1 answer
  • Arthur knows that if he invests $1000 in a bank account, in one year he'll earn $15 in interest. If Arthur invest $24,500
    5·1 answer
  • Jane caught a 4 pound fish. How much did it weigh in ounces.
    5·1 answer
  • Carter Motor Company claims that its old sedan, the Libra, would average less than 19 miles per gallon in the city. Assuming tha
    13·1 answer
  • What is an equivalent expression to 9(2a+1)
    10·2 answers
  • HELP PLZ
    10·1 answer
  • OMG plz help me. IDK how to do thisI need help asap
    15·1 answer
  • I need a answer for this please
    11·1 answer
  • Find the value of x in each case:
    13·1 answer
  • What is trigonometry???????​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!