What is 8and21/40s as a decimal?

A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate

LenaWriter [7]

Answer:

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Step-by-step explanation:

A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.

Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.

According to the Pythagorean Theorem:

$\displaystyle x^2+y^2=1521$

Let's take the derivative of both sides with respect to time t. Hence:

$\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right]$

Implicitly differentiate:

$\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$

Simplify:

$\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0$

The area of the triangle formed will be given by:

$\displaystyle A = \frac{1}{2} xy$

Again, let's take the derivative of both sides with respect to time t:

$\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right]$

From the Product Rule:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)$

At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.

$\displaystyle y = \sqrt{1521-(15)^2}=36$

The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:

$\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}$

Evaluate for dy/dt:

$\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}$

Finally, using dA/dt, substitute in appropriate values:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)$

Evaluate. Hence:

$\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}$

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

8 0

3 years ago

The total cost of a shirt and a tie was $75.62. if the price of the shirt was $4.02 less than the tie, what was the price of the

kifflom [539]

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Define x:
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Let the tie be x
Tie = x
Shirt = x - 4.02

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Construct equation :
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The sum of the shirt and tie is $75.62
x + x -4.02 = 75.62
2x - 4.02 = 75.62
2x = 79.64
x = $39.82

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Find the cost of tie and shirt :
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Tie = x = $39.82
Shirt = x - $4.02 = $39.82 - $4.02 = $35.80

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Answer: The price of the short is $35.80
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5 0

3 years ago

Someone give me an easy algebra problem thx

fenix001 [56]

Answer:

Step-by-step explanation:6x+12-2 if x=1/2

4 0

3 years ago

Pants at clothes 4 us are 20% off. with this dicount, the pants cost $25.60. what was the original price of the pants?

Nina [5.8K]

Answer:

The answer is $30.72

Step-by-step explanation:

25.60 + 20% = 30.72

You have to divide 25.60 / 20% and that would be 5.12 so to the original answer 25.60 you add 5.12.

Final Answer

30.72

6 0

3 years ago

Evaluate m-8 when m= 12

finlep [7]

Answer:

4

Step-by-step explanation:

For m = 12

m - 8 = 12 - 8 = 4

4 0

3 years ago

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