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WARRIOR [948]
3 years ago
11

The length of a rectangular picture frame is 4 inches less than three times the width. The perimeter is 136 inches. Find the len

gth and the width.
Mathematics
1 answer:
natulia [17]3 years ago
6 0

Answer:

The width of the rectangle is 18 inches, and the length is 50 inches

Step-by-step explanation:

We can designate a variable, x, to represent the width of the rectangle.  To represent the length and widths of the rectangle, we can say that the length is 3x-4 and the width is just x.  We can then write an equation for the perimeter and solve:

2(3x-4) + 2x = 136

6x - 8 + 2x = 136

8x - 8 = 136

8x = 144

x = 18

To calculate the length

(3x - 4)

3(18) - 4 = 50 in

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G(-4, -8) and H(-15, -3). What is the slope of GH?
Masteriza [31]

Answer:

G(x1,y1)= (-4,-8)

H(x2,y2)=(-15,-3)

Slope = (y2-y1)/(x2-x1)

=(-3-(-8))/ (-15-(-4))

= (-3+8)/(-15+4)

=5/-11

3 0
3 years ago
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

\vec s_u\times\vec s_v=-u\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

8 0
3 years ago
Thank you guys so much
jeka57 [31]

Answer:

B. City P is above sea level and City R is below sea level

Step-by-step explanation:

A. City R is negative meaning it is below sea level however City Q is 0 meaning it is at sea level, so this statement is false.

C. Once again, City P is positive meaning it is above sea level but City Q is 0 meaning it is at sea level, so this statement is false.

D. Like before, City P is above sea level and City Q is at sea level not below, so this is, once again, false.

6 0
2 years ago
[Inequalities]<br> Please help and thanks.
kondor19780726 [428]

Answer:

First blank is >=

Second blank is <=

Step-by-step explanation:

At least means the sign is greater than or equal to

No more than means the sign is less than or equal to

5 0
3 years ago
On Saturday, Cannor drives 62 1/4 miles each hour. If he travels 4 hours, how many miles does he travel altogether?
Kisachek [45]

Answer:

he travels 249 miles on saturday

Step-by-step explanation:

<u>  62.25        </u>    <u>  x</u>

     1          =       4

you must multiple the distance travled in one hour by the number of hours of driving. In this case 4. This is if he did not change speeds ;)

4 x 62.25 = 249 miles

Hope this helps :)  Please mark brainliest if you see fit :)

3 0
2 years ago
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