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
Bumek [7]
3 years ago
10

Calculus Application

Mathematics
1 answer:
Fiesta28 [93]3 years ago
7 0
<h3>Answer:</h3>

-8/3 ft/s

<h3>Step-by-step explanation:</h3>

<u>We are given:</u>

distance of the top of the ladder from the ground (h) = 12 ft

height of the ladder = 20 ft

rate of change of the distance of the base of ladder from the wall (dx/dt):

2 ft/s

<u>Finding the distance of the base of the ladder from the wall:</u>

From the Pythagoras's Theorem, we know that:

hypotenuse² = height² + base²

<em>replacing the given values</em>

20² = 12² + x²

400 = 144 + x²

x² = 256                            [subtracting 144 from both sides]

x = 16 ft                            [taking the square root of both sides]

<u>The rate of change of the height of the Ladder from the ground:</u>

We know that:

h = 12 ft

(\frac{dh}{dt}) = ?

x = 16 ft

(\frac{dx}{dt}) = 2 ft/s

According to the Pythagoras's Theorem:

20² = x² + h²

<em>differentiating both sides with respect to time</em>

\frac{d(400)}{dt} = \frac{d(x^{2} + h^{2})}{dt}

0 = \frac{d(x^{2})}{dt} +  \frac{d(h^{2})}{dt}

0 = \frac{d(x^{2})}{dx}(\frac{dx}{dt}) +  \frac{d(h^{2})}{dh}(\frac{dh}{dt})

0 = 2x(\frac{dx}{dt}) +  2h(\frac{dh}{dt})

<em>replacing the variables</em>

0 = 2(16)(2) +  2(12)(\frac{dh}{dt})

0 = 64 +  32(\frac{dh}{dt})

-64 =32(\frac{dh}{dt})                                [subtracting 64 from both sides]

\frac{-64}{32} =(\frac{dh}{dt})                                    [dividing both sides by 32]

\frac{dh}{dt} = \frac{-8}{3} ft/s

Hence, the ladder will slide down at a speed of 8/3 feet per second

You might be interested in
Jack is 4 times as old as lacey. 7 years ago the sum of their age was 61. how old are they now?
BaLLatris [955]
I am guessing Jack is 51 and Lacey is 17.

7 0
3 years ago
Please help me with this!
ella [17]

180° - 36° - 39° - 33° = <u>7</u><u>2</u><u>°</u>

x° = 180° - 72°

x° = <u>1</u><u>0</u><u>8</u><u>°</u>

So, the value of x is 108°

<em>Hope it helps and is useful</em><em> </em><em>:</em><em>)</em>

4 0
3 years ago
Thanks you answer quick
olya-2409 [2.1K]
I got 8/3  with my fraction calulator
7 0
3 years ago
Read 2 more answers
8. H={all numbers of the form 3n+1, for n a natural number} under multiplication?
poizon [28]

Answer and Step-by-step explanation:

H= {all numbers of the form 3n+1, for n natural number} under multiplication:

Sol: all number of the form 3n+1, for n natural number so, put n=2, 3(2) +1 = 7, which is a natural number. A natural number under multiplication does not form a group because its inverse does not exist.

J= {all number of the form 3n+2, for n natural number} under multiplication:

Sol: all the number of the form 3n+2, n is the natural number does not form a group under multiplication because the identity element does not form in this set, and inverse does not exist.

K= {perfect squares of integers} under addition:

Sol: perfect square of integers under addition does not form a group because the inverse does not exist. For example, for any element x, inverse (-x) does not exist because of a square integer.

L= {perfect squares of integers} under multiplication:

Sol: a set of the perfect square of integers under multiplication is not a set, because it does not have the inverse property

M= {all numbers of the form 2, for n natural number} under addition:

Sol: natural number in the form of 2n, n is a natural number under addition is not a group as it does not have identity property. Identity property, under addition, is zero.

N= {all number of the form 2n, n is natural number} under multiplication:

All number of the form 2n, n is the natural number under multiplication is not a group. Because its inverse does not exist. For example, an element x belongs to a natural number; its inverse (1/x) does not exist in this set.

8 0
3 years ago
What is the surface area of the cylinder with height 8 in and radius 5 in? Round your answer to the nearest thousandth
alexgriva [62]

Answer:

<u>408.571 in²</u>

Step-by-step explanation:

Surface Area :

  • 2πr (r + h)
  • 2 x 22/7 x 5 (5 + 8)
  • 10 x 22/7 x 13
  • 130 x 22/7
  • 2860/7
  • <u>408.571 in²</u>
5 0
2 years ago
Read 2 more answers
Other questions:
  • Is zero point 32 repeating times square root of 294 end square root rational or irrational? Justify your answer
    9·1 answer
  • How will adding the value 75 affect the mean and median of the data set 1, 5, 7, 9 , 9, 10? * A.The median increases less than t
    6·1 answer
  • What value of x is in the solution set of 3(x – 4) &gt; 5x + 2?
    8·1 answer
  • Which fraction is equal to 0.8? Express your answer in simplest form. A. 3/5 B. 4/5 C. 1/8 D. 5/8
    5·1 answer
  • During the baseball season, marvins team won 5 games and lost 14 games
    9·1 answer
  • Simplify the given equation.
    7·1 answer
  • Gerard has 30$ to spend on lunch's this month lunch costs him 1.50 each day after Gerard buys lunch for 8 days
    9·2 answers
  • What is the equation of the line that has a slope of 1/2 and passes through the point (6,4)? Write your answer in slope intercep
    10·2 answers
  • U(x)= x^2+1<br> w(x)= √x+6<br><br> Find the following.<br> (u o w) (3)=__<br> (w o u) (3)=__
    12·1 answer
  • A bus leaves Flacq at 07 05 and reaches Curepipe at 08 50, after travelling a distance of 91 kilometres. Find the average speed
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!