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3 years ago

I NEED HELP ASAP PLEASE ANSWER !!!!!!!!!!!

Mathematics

1 answer:

Genrish500 [490]3 years ago

3 0

Answer:

2.5(2-(-6))

Step-by-step explanation:

first of all,

the difference between 2 and -6 is

2-(-6)

then product of 2.5 with this difference is

2.5× (2-(-6)=

2.5(2-(-6))

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There are 54 students in a class. The Venn diagram below shows how many students play a sport, take a foreign language, do both,

andrew11 [14]

Doesn't play sport

Plays sport |

| |

V V

Takes language | 21 | 17 |

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Doesn't take language | 12 | 4 |

4 0

3 years ago

Use polar coordinates to find the volume of the given solid. Inside both the cylinder x2 y2 = 1 and the ellipsoid 4x2 4y2 z2 = 6

Anton [14]

The Volume of the given solid using polar coordinate is: $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

V= $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

<h3>What is Volume of Solid in polar coordinates?</h3>

To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.

Consider the cylinder, $x^{2}+y^{2} =1$ and the ellipsoid, $4x^{2}+ 4y^{2} + z^{2} =64$

In polar coordinates, we know that

$x^{2}+y^{2} =r^{2}$

So, the ellipsoid gives

$4{(x^{2}+ y^{2)} + z^{2} =64$

4( $r^{2}$ ) + $z^{2}$ = 64

$z^{2}$ = 64- 4( $r^{2}$ )

z=± $\sqrt{64-4r^{2} }$

So, the volume of the solid is given by:

V= $\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta$

= $2\int\limits^{2\pi}_ 0 \int\limits^1_0 \, r\sqrt{64-4r^{2} } r dr d\theta$

To solve the integral take, $64-4r^{2}$ = t

dt= -8rdr

rdr = $\frac{-1}{8} dt$

So, the integral $\int\ r\sqrt{64-4r^{2} } rdr$ become

= $\int\ \sqrt{t } \frac{-1}{8} dt$

= $\frac{-1}{12} t^{3/2}$

= $\frac{-1}{12} (64-4r^{2}) ^{3/2}$

so on applying the limit, the volume becomes

V= $2\int\limits^{2\pi}_ {0} \int\limits^1_0{} \, \frac{-1}{12} (64-4r^{2}) ^{3/2} d\theta$

= $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta$

V = $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

Since, further the integral isn't having any term of $\theta$ .

we will end here.

The Volume of the given solid using polar coordinate is: $\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta$

Learn more about Volume in polar coordinate here:

brainly.com/question/25172004

#SPJ4

3 0

2 years ago

What is the Perfect square of 44

nataly862011 [7]

2<span>√ ̅11is going to be your answer.

</span>

5 0

3 years ago

The volume of a 36 in 3 . Find the height of the cylinder (in inches) if radius is 3 in.

IceJOKER [234]

Answer:

h=1.27 in.

Step-by-step explanation:

V=πr^2h

Plugin the values and solve

36=π(3)^2h

36/9π=h

h=1.27323954

3 0

3 years ago

PLZ HELP ME ,A room in the shape of a rectangular prism measures 15 feet by x feet by 12 feet. Write a simplified expression for

ipn [44]

Answer:

180x ft cubed

Step-by-step explanation:

1) The formula for the volume of a rectangular prism is length x width x height

... shortened it is "lwh"

2) Plug your numbers (and "x") into the equation doesn't tell you which is which, but since we are multiplying it doesn't matter.

It should now look like this "(15)(12)x"

3) Simplify.

180x ft cubed

5 0

3 years ago