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Lina20 [59]
3 years ago
10

99 POINT QUESTION, PLUS BRAINLIEST!!!

Mathematics
1 answer:
Basile [38]3 years ago
3 0
1.Disc method.
In this method the volume is given by:

\boxed{V=\pi\int\limits_a^b\big[f(x)\big]^2}

so:

V=\pi\int\limits_1^3x^4\,dx=\boxed{\pi\int\limits_1^3\big[x^2\big]^2\,dx}

A) Function f(x)=x^2 over the interval [1,3]
B) We use disk method and f(x) is function of variable x, so we <span>rotate the curve about the x-<span>axis.


2. Shell method.

In this case volume is given by:

</span></span>\boxed{V=2\pi\int\limits_a^bx\cdot f(x)\,dx}

So there will be:

V=\pi\int\limits_1^3x^4\,dx=\dfrac{2}{2}\cdot\pi\int\limits_1^3x^4\,dx=2\pi\int\limits_1^3\dfrac{x^4}{2}\,dx=&#10;\boxed{2\pi\int\limits_1^3x\cdot\dfrac{x^3}{2}\,dx}

A) Function f(x)=\dfrac{x^3}{2} over the interval [1,3]
B) We use shell method and f(x) is function of variable x, so we <span>rotate the curve about the y-<span>axis.</span></span>
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[ 2 ( 7 . 25 ) + 2 ( 24 )] - 10
Mekhanik [1.2K]

Answer: 57 over 2

57

2

=28 and 1 over 228

1

2

=28.5

Result57 over 2 equals 28 and 1 over 2 equals 28.5

Step by step

Step 1 of 4: Multiply.

Multiply

( Highlighted:2 Highlighted:× Highlighted:7.25 + 24 ) − 10 = ( Highlighted:1450 over 100

1450

100

+ 24 ) − 10

Step 1 of 4: Multiply, sub-step a: Multiply.

Multiply

725 over 100

725

100

× 2 = ( 725 × 2 ) over 100

725 × 2

100

= 1450 over 100

1450

100

Step 1 of 4: Multiply.Hide

Step 2 of 4: Add.

Add

( Highlighted:1450 over 100

1450

100

Highlighted:+ Highlighted:24 ) − 10 = ( Highlighted:3850 over 100

3850

100

) − 10

Step 2 of 4: Add, sub-step a: Convert integer to fraction.

Convert integer to fraction

24 = 24 over 1

24

1

Step 2 of 4: Add, sub-step b: Find common denominator.

Find common denominator

1450 over 100

1450

100

+ 24 over 1

24

1

= ( 1450 × 1 ) over ( 100 × 1 )

1450 × 1

100 × 1

+ ( 24 × 100 ) over ( 1 × 100 )

24 × 100

1 × 100

= 1450 over 100

1450

100

+ 2400 over 100

2400

100

100 is the least common multiple of denominators 100 and 1. Use it to convert to equivalent fractions with this common denominator.

Step 2 of 4: Add, sub-step c: Add.

Add

1450 over 100

1450

100

+ 2400 over 100

2400

100

= ( 1450 + 2400 ) over 100

1450 + 2400

100

= 3850 over 100

3850

100

Step 2 of 4: Add.Hide

Step 3 of 4: Subtract.

Subtract

3850 over 100

3850

100

− 10 = 2850 over 100

2850

100

Step 3 of 4: Subtract, sub-step a: Convert integer to fraction.

Convert integer to fraction

10 = 10 over 1

10

1

Step 3 of 4: Subtract, sub-step b: Find common denominator.

Find common denominator

3850 over 100

3850

100

− 10 over 1

10

1

= ( 3850 × 1 ) over ( 100 × 1 )

3850 × 1

100 × 1

− ( 10 × 100 ) over ( 1 × 100 )

10 × 100

1 × 100

= 3850 over 100

3850

100

− 1000 over 100

1000

100

100 is the least common multiple of denominators 100 and 1. Use it to convert to equivalent fractions with this common denominator.

Step 3 of 4: Subtract, sub-step c: Subtract.

Subtract

3850 over 100

3850

100

− 1000 over 100

1000

100

= ( 3850 − 1000 ) over 100

3850 − 1000

100

= 2850 over 100

2850

100

Step 3 of 4: Subtract.Hide

Step 4 of 4: Simplify.

Simplify

2850 over 100

2850

100

= 57 over 2

57

2

= 28 and 1 over 228

1

2

Step-by-step explanation:

7 0
3 years ago
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