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masha68 [24]
3 years ago
13

Plz help. ik it's long but I mean... 50 points. thx !!!​

Mathematics
1 answer:
aniked [119]3 years ago
7 0

Answer:

Step-by-step explanation:

☹️

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A 1.5-mm layer of paint is applied to one side of the following surface. Find the approximate volume of paint needed. Assume tha
Mariulka [41]

Answer:

V = 63π / 200  m^3

Step-by-step explanation:

Given:

- The function y = f(x) is revolved around the x-axis over the interval [1,6] to form a spherical surface:

                                 y = √(42*x - x^2)

- The surface is coated with paint with uniform layer thickness t = 1.5 mm

Find:

The volume of paint needed

Solution:

- Let f be a non-negative function with a continuous first derivative on the interval [1,6]. The Area of surface generated when y = f(x) is revolved around x-axis over the interval [1,6] is:

                           S = 2*\pi \int\limits^a_b { [f(x)*\sqrt{1 + f'(x)^2} }] \, dx

- The derivative of the function f'(x) is as follows:

                            f'(x) = \frac{21-x}{\sqrt{42x-x^2} }

- The square of derivative of f(x) is:

                            f'(x)^2 = \frac{(21-x)^2}{42x-x^2 }

- Now use the surface area formula:

                           S = 2*\pi \int\limits^6_1 { [\sqrt{42x-x^2} *\sqrt{1 + \frac{(21-x)^2}{42x-x^2 } }] \, dx\\\\S = 2*\pi \int\limits^6_1 { [\sqrt{42x-x^2+(21-x)^2} }] \, dx\\\\S = 2*\pi \int\limits^6_1 { [\sqrt{42x-x^2+441-42x+x^2} }] \, dx\\\\S = 2*\pi \int\limits^6_1 { [\sqrt{441} }] \, dx\\S = 2*\pi \int\limits^6_1 { 21} \, dx\\\\S = 42*\pi \int\limits^6_1 { dx} \,\\\\S = 42*\pi [ 6 - 1 ]\\\\S = 42*5*\pi \\\\S = 210\pi

- The Volume of the pain coating is:

                           V = S*t

                           V = 210*π*3/2000

                          V = 63π / 200 m^3

8 0
4 years ago
Read 2 more answers
What is the gradient of the blue line?
Savatey [412]

Answer:

gradient = 3

Step-by-step explanation:

3/1 = 3

hope this helps

4 0
4 years ago
The altitude of a plane is 1200 meters. From a point on the ground, the angle of elevation of an airplane is 25º. What is the di
gtnhenbr [62]

Answer:

2839.4 meters

Step-by-step explanation:

Given that:

Altitude = 1200 m

Using trigonometry :

The distance from point P to the airplane :

Using trigonometric relation :

Sin θ = opposite / hypotenus

Sin θ = altitude / x

Sin θ = 1200 m / x

Sin 25 = 1200 / x

0.4226182 = 1200 / x

x = 1200 / 0.4226182

x = 2839.4423

Distance from P to airplane = 2839.4 meters

8 0
3 years ago
The area of a rectangle is 0.8 square units. The length is 3.2 units and the width is x units.
Mademuasel [1]
The answer is x=0.25
5 0
3 years ago
PLEASE CAN ANYONE HELP!!!
DiKsa [7]

Answer:

x = 3

y = 4  

hey, I am not 100% sure of the certainty of my answers, I am using what I remember about that topic but I do not know if it is right or wrong, I hope I have helped you, I did what I could.

Step-by-step explanation:

-3x + 2y = 23

5x + 2y = -17

X solution:

(you cancel the y)

-3x = 23

5x = -17

(you combine all the values above with those below)

2x = 6

(solve the ecuation normaly)

x = 6/2 = 3

Y solution:

(you replace the x)

-3(3) + 2y = 23

5(3) + 2y = -17

-9 + 2y = 23

15 + 2y = -17

(you combine all the values above with those below)

6 + 4y = 6

(solve the ecuation normaly)

4y = 0

y = 4  

(I do not really know if the answer here is 0 or 4 since when passing the 4 to divide it would be 0/4 and I do not understand very well how that is solved)

6 0
3 years ago
Read 2 more answers
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