Calculate the slope, or rate of change, of this line. 1) 3 2) 4 3) 2 4) 0.5

What is the range of g(x)?

Mila [183]

Answer:

2

Step-by-step explanation:

I just need for the points

5 0

2 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

1 year ago

Joyce took out a small loan for $1,200. The interest on the loan was 10.5%, but she paid it off in just 18 months. How much did

jasenka [17]

Answer:

She paid back $192 in interest

Step-by-step explanation:

A = P(1+r)^n

P = $1,200

r = 10.5% = 0.105

n = 18 months = 18/12 = 1.5 years

A = 1,200(1+0.105)^1.5 = 1,200(1.105)^1.5 = 1,200×1.16 = 1,392

Amount = $1,392

Principal = $1,200

Interest = amount - principal = $1,392 - $1,200 = $192

7 0

3 years ago

Can someone help me with this question????

frutty [35]

Answer:

Hi! I think I got the answer, it is a tricky one! The answer I got was C) 1029.

Step-by-step explanation:

1. It is good to first know that 40%more means 1.4 (some number). So, if n is 40% more than the sum of the other three numbers: n= 1.4* (l +m+p) .

2. Also note that: n+l+m+p= 1764; so, n = 1764-l-m-p.

3. Since we have two expressions for n, we can equate them to each other. Giving, 1.4* (l +m+p) =1764-l-m-p . Simplifying we get 2.4 (l +m+p)=1764.

4. l +m+p =1764/2=735.

5. 1764-735=1029

Hope that helps! Feel free to message back if there are any questions!

7 0

2 years ago

If 3 employees took 3/4 of a pie Home how much pie did wacho employee receive

Aleksandr [31]

Answer:

2 1/4 pies or 2.25

Step-by-step explanation:

3/4 = .75 = 75%

a whole pie is 100% or 1

3 took 3/4

so

3 x .75 = 2.25

lets break this answer down

if 1 is a whole pie then that would mean 2 would equal 2 whole pies

now with the left over .25 it would be 25% so 2 1/4

3 0

2 years ago