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3 years ago

3y(7 + 2x) + 9ty - 10

Mathematics

1 answer:

kakasveta [241]3 years ago

8 0

What exactly do you need to find? Does it need simplified?

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What is the value of 3

alukav5142 [94]

Answer:

3 tothe one it is the answer

5 0

3 years ago

Read 2 more answers

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

Find the length of side x in simplest radical form with a rational denominator.

madreJ [45]

Answer:

x=2√5

Step-by-step explanation:

<u>1st method:</u>

sin(30)=opposite/hypotenuse=√5/x

sin(30)x=√5

x=√5/sin(30)

x=2√5

<u>2nd method:</u>

cos(60)=adjacent/hypotenuse=√5/x

cos(60)x=√5

x=√5/cos(60)

x=2√5

<u>3rd method:</u>

This is a 30-60-90 triangle, so we can multiply the short side, √5, by 2, to get x=2√5

8 0

3 years ago

Give your answer as a mixed number<br> 4 3/7 - 2 5/7<br> get brainliest urgent plz help

serg [7]

Answer:

$1\frac{5}{7}$

Step-by-step explanation:

$4\frac{3}{7} -2\frac{5}{7}$

Step 1. Simplify left side 4*7+3 , Right Side 2*7+5

$=\frac{31}{7} -\frac{19}{7} = \frac{12}{7}$

Step 2. Re-write 12/7 as mixed number

$\frac{12}{7} = 1\frac{5}{7}$

3 0

4 years ago

A store manager is redesigning a display shelf. The width of an individual deodorant is 2.576 inches. How wide must the shelf be

Inga [223]

A store manager is redesigning a display shelf. The width of an individual deodorant is 2.576 inches

Width of each deodorant = 2.576 inches

We need to store 25 individual deodorants side by side

Width of 1 deodorant = 2.576 inches

Width of 25 deodorant = 2.576 * 25 inches= 64.4 inches

The shelf must be 64.4 inches wide to store 25 individual deodorants side by side

8 0

3 years ago

3y(7 + 2x) + 9ty - 10​

3y(7 + 2x) + 9ty - 10