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3 years ago

How do you know if a equation is a proportion

Mathematics

1 answer:

erastovalidia [21]3 years ago

6 0

You can set up a proportion to determine the length of the enlarged photo

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Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

3 years ago

Please help me with this!! Thank you.

jolli1 [7]

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3 0

3 years ago

A boat traveled 128 kilometers in

AlekseyPX

Answer:

The Distance cover by boat in 2 hours and 15 minutes is 72 km

Step-by-step explanation:

Given as :

The Distance cover by boat = 128 kilometer

The time taken is 4 hours

As , Distance = Speed ×Time

So , Speed = $\frac{Diastance}{Time}$

Or, Speed = $\frac{128 km}{4 hours}$

∴ Speed = 32 km per hour

Now, again The boat travel 2 hours and 15 minutes further with speed 32 kmph

So, Time2 = 2 + $\frac{15}{60}$

Or, Time2 = 2 + $\frac{1}{4}$

I.e Time2 = $\frac{9}{4}$ hours

Again , Distance = Speed ×Time

So , Distance = 32kmph × $\frac{9}{4}$ hours

I.e Distance = $(\frac{32\times 9}{4})$ = 72 kilometer

Hence The Distance cover by boat in 2 hours and 15 minutes is 72 km Answer

5 0

3 years ago

Which shows one way to determine the factors of x - 9x2 + 5x – 45 by grouping?

EleoNora [17]

Answer:

The last one.

Step-by-step explanation:

6 0

3 years ago

A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur

Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0

3 years ago