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DedPeter [7]
3 years ago
13

Find the area enclosed by the graphs of y=√(4-4x), y=√(4-x) and x-axis by integrating with respect to x and integrating with res

pect to y g
Mathematics
1 answer:
Sloan [31]3 years ago
6 0

Answer:

(A) 2/3 [√(4-4x)]^3

(B) 2/3 [√(4-x)]^3

Step-by-step explanation:

Integrating the functions,

(A) Any function in square root is equal to or same as the function raised to the power of 1/2

To integrate, add 1 to the power of the function. That's 1/2 + 1 = 3/2

Divide the function by this new power 3/2. This implies multiplying the function by the inverse of 3/2. The inverse of 3/2 is 2/3.

Also, when a function is raised to the power of a fraction instead of a whole number, you take the 'denominator' root of the function, and then raise the function to the power of the numerator.

Here, the denominator is 2, so you take the square root of the function, and raise the function to the power of 3

So the integral of Y = √[4-4x] is

2/3 [√(4-4x)]^3

(B) In like manner, the integral of

Y = √[4-x] is

2/3 [(√4-x)]^3

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Solve for x.<br><br><br><br> 80<br> 22<br> 40<br> 12
kari74 [83]
Use the Pythagorean theorem to solve this problem. So, 81+x^2=1681. ( Pythagorean theorem: a^2+b^2=c^2). x^2=1600. x=40.
4 0
3 years ago
It takes 8 hours for 4 men to paint a room.
eimsori [14]

Answer:

16 men would be needed to paint the room in 2 hours

Step-by-step explanation:

We can use proportion to solve the problem given, but first we need to determine whether it is a direct or indirect proportion.

If the number of men are increase, the time taken to do the work will decrease, If the number of men are decrease, the time taken to do the work will increase. Therefore, this is an indirect proportion.

We are going to arrange the data inversely.

Let x be the number of men needed to paint the room in two hours

8 hours =  2 hours

    x        = 4 men

Cross-multiply

2×x = 8×4

2x = 32

Divide both-side of the equation by 2

2x/2 = 32/2

x = 16 men

16 men would be needed to paint the room in 2 hours

7 0
3 years ago
What is the exact decimal equivalent of 7 half’s 12
Ivenika [448]

The decimal equivalent of 7 half’s is the number in decimal form

The exact decimal equivalent of 7 half’s is 3.5

<h3>What is a decimal number?</h3>

A decimal number is a number represented by an integer and a fractional part

<h3>How to determine the decimal equivalant?</h3>

The number is given as:

7 halves

Express as product

7 * 1/2

Evaluate the product

3.5

Hence, the exact decimal equivalent of 7 half’s is 3.5

Read more about decimals at:

brainly.com/question/1827193

3 0
2 years ago
The gas co2 is diffusin at steady state through a tube 20 cm long having a diameter of 1 cm and containing n2 at 350 k . the tot
Marrrta [24]

The value is J = 1.71*10^-6 kmol/m^2.s

According to the given conditions we get,

The length the tube l= 0.20m

The diameter of the tube d= 0.01m

The total pressure inside the tube P= 101.32kPa

The partial pressure of CO2 at the first end is

P1= 456mm Hg = 60794.832 Pa

The partial pressure of CO2 at the other end is

P2= 76mm Hg = 10132.472 Pa

The temperature is T = 298 K

The diffusion coefficient D= 1.67* 10^-5 m^2/s

Generally the molar flux of CO2 is mathematically represented as

J= D{p1-p2} / R.T

Here R is the gas constant with value R= 8.314 j/kmol

So we get J= 1.71 * 10^-3 mol/m^2.sec

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#SPJ4

       

       

4 0
2 years ago
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