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2 years ago

12

Eva's new bunny weighted 1 7/8 pounds when she first got him 4 weeks ago. Now he weighs 2 1/4 pounds. How much weight has Eva's

dog actually gained

1 answer:

Serggg [28]2 years ago

4 0

Answer: Eva's dog actually gained 3/8 pounds ( 0.375pounds)

Step-by-step explanation:

Step 1

Given that

old weight = 1 7/8 pounds

New weight = 2 1/4 pounds

weight gained = New weight - Old weight

Step 2

weight gained = New weight - Old weight

2 1/4 pounds - 1 7/8 pounds

2.25 pounds - 1.875 pounds

0.375pounds = 3/8 pounds

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Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 an

Leya [2.2K]

Parameterize the lateral face $T_1$ of the cylinder by

$\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v$

where $0\le u\le2\pi$ and $0\le v\le3$ , and parameterize the disks $T_2,T_3$ as

$\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)$
$\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)$

where $0\le r\le2$ and $0\le\theta\le2\pi$ .

The integral along the surface of the cylinder (with outward/positive orientation) is then

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr$
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$=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr$
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7 0

3 years ago

Justine charges $25 to wash a dog. She washed 5 dogs on Saturday and then some more on Sunday. She made $325 for the weekend. Ho

Marrrta [24]

Answer

• A. Equation: 25(5 + x) = 325

,

• B. Answer: 8 dogs

Explanation

Given

• Charge to wash a dog: $25.

• She washed 5 dogs on Saturday and then some more on Sunday.

• She made $325 for the weekend.

Procedure

She charges $25 per wash, she made $325 for the weekend, and we know that on Saturday she washed 5 dogs, but we don't know how many she washed on Sunday. Thus, we have to build an equation in which the number of dogs washed on Sunday is represented by x (as we do not know the real number).

Considering that the total money made has to be equal to the multiplication of the charge times the dogs washed, the equation is:

$25(5+x)=325$

Then, we have to solve for x to know how many dogs did she wash on Sunday.

0. Multiplying the parenthesis

$125+25x=325$

<em>2. Subtracting 125 from both sides of the equation</em>

$125-125+25x=325-125$ $25x=200$

<em>3. Dividing both sides of the equation against 25</em>

$\frac{25x}{25}=\frac{200}{25}$ $x=8$

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11 months ago

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the

Alexandra [31]

Hello :
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(x²+14x)+(y²+2y)+14=0
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2 years ago

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Musya8 [376]

Answer:

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2 years ago

Find the slope please

zavuch27 [327]

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of this graph; we are provided with two points:

$\star~\mathrm{(6,0)}$

$\star~\mathrm{(0,-5)}$

$\triangle~\fbox{\bf{KEY:}}$

What we need in order to find the slope are two points and the slope formula.

Here's the formula:

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Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Substitute the values:

$\star~\mathrm{\cfrac{-5-0}{0-6}}}$

Simplify!

$\star~\mathrm{\cfrac{-5}{-6}}}$

Simplify more!

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Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

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1 year ago