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frozen [14]
2 years ago
15

Let f(x) =

Mathematics
1 answer:
Oxana [17]2 years ago
7 0

Answer:

Step-by-step explanation:

Hi there!

Please see the attached picture.

Hope it helps!

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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. y = 8 sin(x
V125BC [204]

Answer with explanation:

The equation of two curves are

y=8 sin x

y=8 cos x

The point of intersection of two curves are

→8 sin x=8 cos x

sinx = cos x

x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2}

When you will look between points , 0 and x=\frac{\pi}{4}\\\\y=8\sin\frac{\pi}{4}\\\\y=4\sqrt{2},the curve obtained is right angled triangle.

Now, rotate the curve that is right angled triangle along the line , y= -1, to obtain a shape similar or resembling with Right triangular prism.

Draw a circular disc in the right triangular prism , having radius =x,and small part on the triangle having length dx.dx varies from 0 to \frac{\pi}{4}.

Required volume of solid obtained

    =\int\limits^{\frac{\pi}{4}}_0 {8 \sin x} \, dx \\\\=|-8\cos x|\left \{ {{x=\frac{\pi}{4}}} \atop {x=0}} \right.\\\\=8-4\sqrt{2}

    =8-4√2 cubic units    

5 0
3 years ago
What is the least common denominator of 2/9 and 2/3
julsineya [31]

Answer:

2\9=1

2\3=1

Step-by-step explanation:

3 0
3 years ago
The double box plot shows the test scores for Miss Robinson's second and fourth period
Gennadij [26K]
We can’t see the box plot?
4 0
3 years ago
Based on the work shown on the left, what is the simplest form of StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Bas
Gnoma [55]

Answer:

It's A on E2020;  StartRoot StartFraction 250 c cubed Over 9 d Superscript 6 Baseline EndFraction EndRoot

Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are s
Kay [80]

Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

<h3>Find the expression for the area of the shaded regions:</h3>

From the question we can say that the Hexagon has three shapes inside it,

  • Pentagon
  • Square
  • Triangle

Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

  • Area of first shaded region = Area of the hexagon - Area of pentagon

An equilateral triangle is shown inside a square.

  • Area of second shaded region = Area of the square - Area of equilateral triangle  

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,        

⇒ Shaded area  = area of the hexagon – area of the pentagon + area of the  square – area of the equilateral triangle.

 

Learn more about area of a shape here:

brainly.com/question/16501078

#SPJ1

8 0
1 year ago
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