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koban [17]
3 years ago
9

6

Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
4 0

Step-by-step explanation:

a+b+c=180°

64°+b+c=180°

b=c

2b+64°=180°

2b=180-64

2b=116°

b=116/2

b=58°=c

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2
HACTEHA [7]

This question is incomplete, the complete question is;

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis

Answer:

V = π (512/15)

Step-by-step explanation:

Given that;

region of rotation

y² = 2x, x = 2y

Region is rotated about y-axis as shown in the image

for the point of intersection,

y²/2 = 2y

y² - 4y = 0

y(y-4) = 0

∴ y = 0, y = 4

so the region lies in 0 ≤ y ≤ 4

Now cross section area of washer is

A(y) = π(outer radius)² = π(inner radius)²

A(y) = π(2y)² - π(y²/2)²

A(y) = π(4y²) - π(y⁴/4)

A(y) = π(4y² - (y⁴/4))

now volume of the solid of revolution is

V = ⁴∫₀ A(y) dy

V = ⁴∫₀ π(4y² - (y⁴/4))dy

V =  π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }

V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }

V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }

V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }

V = π { 256/3 - 1024/20 }

V = π { (5120 - 3072) / 60 }

V = π (512/15)

8 0
3 years ago
Will give Brainliest to correct answer!
nadezda [96]

Answer:

Step-by-step explanation:

1. 4x=7(x-3)      Reason: Starting equation

2. 4x=7x-21      Reason: Distributive Property

3. -3x=-21        Reason: Subtracting Combining like terms

4. x=7               Reason: Division

4 0
2 years ago
Read 2 more answers
Area: 28.67 sq m and the side is 4.7 m The missing side length is equal to:??? m
Mice21 [21]

Answer:

6.1

Step-by-step explanation:

area =leanth x breath.

if one side=4.7,

then, missing length=area/given side

= 28.67/4.7

=6.1

4 0
2 years ago
determine whether the equation represents a direct varation. if it does, find the constant, find the constant variation. 2y = 5x
SVETLANKA909090 [29]
Is it 5x1?
or 5x+1   cause i'm confused 
6 0
3 years ago
Why does (x-2)^2+9=0 have no real solutions?
alex41 [277]

Answer:

see explanation

Step-by-step explanation:

Given

(x - 2)² + 9 = 0 ( subtract 9 from both sides )

(x - 2)² = - 9  ( take the square root of both sides )

x - 2 = ± \sqrt{-9}

\sqrt{-9} yields no real solutions

There is no real number when multiplied by itself gives - 9

In fact the solutions to \sqrt{-9} are said to be imaginary, that is ± 3i

where i = \sqrt{-1}

If interested investigate further.

7 0
3 years ago
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