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
larisa [96]
3 years ago
6

A 10 foot ladder is leaning against a wall. Call x the distance from the top of the ladder to the ground, and call y the distanc

e from the wall to the foot of the ladder. At the instant that the foot of the ladder is 6 feet away from the wall, the foot of the ladder is moving away from the wall at a rate of 4 ft/sec. At what rate is the top of the ladder falling down the wall at this time (in feet/sec)
Mathematics
1 answer:
liq [111]3 years ago
5 0

-5.3\:\text{ft/s}

Step-by-step explanation:

We start by applying the Pythagorean theorem to the ladder, with its length L as the hypotenuse:

L^2 = 100\:\text{ft}^2 = x^2 + y^2

where x is the vertical distance from the top of the ladder to the ground and y is the horizontal distance from the bottom of the ladder to the wall. Taking the derivative of the above expression with respect to time, we get

0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}

Solving for dx/dt, we get

\dfrac{dx}{dt} = -\left(\dfrac{y}{x}\right)\dfrac{dy}{dt} = -\left(\dfrac{\sqrt{L^2 - x^2}}{x}\right)\dfrac{dy}{dt}

We know that

\dfrac{dy}{dt} = 4\:\text{ft/s}

when x = 6 ft. So the rate at which the top of the ladder is going down is

\dfrac{dx}{dt} = -\left(\dfrac{\sqrt{100\:\text{ft}^2 - (6\:\text{ft})^2}}{6\:\text{ft}}\right)(4\:\text{ft/s})

\:\:\:\:\:\:\:= -5.3\:\text{ft/s}

The negative sign means that the distance x is decreasing as y is increasing.

You might be interested in
Josh is an avid reader. His generous grandparents gave him money for the holidays, and he decided to spend at most $120 on books
Lemur [1.5K]

Answer:

A

Step-by-step explanation:

6 0
3 years ago
Help me out please !!!!
Nikolay [14]

Answer:

B) 6<x<90

Step-by-step explanation:

48+42=90

48-42=6

There will be a number greater than and a number less than x.

90>6

6<x<90

Hope this helps :)

6 0
3 years ago
BRAINIEST TO WHOEVER RIGHT
Natalka [10]
It should be Skewed left
5 0
3 years ago
Help me plssssssssss
Sindrei [870]

Answer:

The answers are as follows:

5. 12+3 = 3+12

7. (6+4)+8 = 6+(4+8)

9. (10*5)*7 = 10*(5*7)

Step-by-step explanation:

<u>5. 12 and 3</u>

Commutative property of addition states that the order of two numbers in addition doesn't matter; the result will be the same. If a and b are two numbers then the property will be:

a+b = b+a

For the given question, the commutative property will be:

12+3 = 3+12

Associative property deals with three numbers or variables. It states that when 3 numbers are being added or multiplied their order doesn't affect the result.

It can be stated as:

(a+b)+c = a+(b+c)

<u>7. 6,4 and 8</u>

The associative property will be:

(6+4)+8 = 6+(4+8)

<u>9. 10,5 and 7</u>

(10*5)*7 = 10*(5*7)

Hence,

The answers are as follows:

5. 12+3 = 3+12

7. (6+4)+8 = 6+(4+8)

9. (10*5)*7 = 10*(5*7)

8 0
2 years ago
What is the missing side length in this right triangle? <br> ANSWER :
irina1246 [14]
15 aaaaaaaaaaaaaaaaaaaaa
4 0
3 years ago
Other questions:
  • The radius of the larger circle is 10 cm. The radius of the smaller circle is 3 cm. What is the approximate area of the shaded r
    5·1 answer
  • Help??!?! I honestly forgot
    7·2 answers
  • What is -6 over 0 equal to?
    5·2 answers
  • 0.6 divided by 0.03 equal
    6·2 answers
  • Find the number of tiles in the 43rd picture
    5·2 answers
  • 3 divided by 7 and 6 or both pl
    9·1 answer
  • HELP ME PLEASE!!!!!!! :(
    12·1 answer
  • What percent represents the part of the model shaded green. A.60% B.62.5%. C.66.7% D.75%
    10·2 answers
  • Find both x and y. Leave answers in simplified radical from. (Step by step)
    12·1 answer
  • What is the simplest radical form of the expression? (8x5y3)2/3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!