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3 years ago

5

You have an aquarium in the shape of a rectangular prism. The base is 4 feet by 2 feet. The height is 3 feet. How many square fe

et of glass were used to build the aquarium? (The top of the aquarium is open.)

1 answer:

gayaneshka [121]3 years ago

3 0

A=2(l+w)h+l×w
A=2(4+2)×3+4×2
A=36+8
A=44 square feet, so there are 44 square feet of glasses were used to build aquarium. Hope it help!

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What is the equation, in point-slope form, for a line that goes through (2, −6)(2, −6) and has a slope of −34−34 ?

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I think the answer might be C, but I'm not 100% sure.

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3 years ago

-3 + (-8)<br> how can i do this

murzikaleks [220]

Answer: -11

Step-by-step explanation:

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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

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3 0

2 years ago

Can you please help me?

garri49 [273]

Answer:

6.2

Step-by-step explanation:

$\frac{10.3}{sin(90)} = \frac{x}{sin(37)}$ *Cross multiply*

10.3(sin(37)) = x(sin(90)) *Divide by sin(90) to isolate x*

$x = \frac{10.3(sin(37))}{sin(90)}$ *Solve*

x = 6.19 ≈ 6.2

4 0

3 years ago

Over 4 months, Ms. Berg wrote 4 equal checks totaling $250 to pay for her salon services. How many did she withdraw from her acc

KiRa [710]

Answer:

$62.50 because

Step-by-step explanation:

250÷4=62r2

62.50•4=250

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3 years ago

Read 2 more answers