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Inga [223]
3 years ago
10

A quadrilateral with exactly two parallel lines is a

Mathematics
1 answer:
Troyanec [42]3 years ago
4 0

Step-by-step explanation:

(parallelogram) is the homogeneous mixture

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Solve for x 3(x+2)+4=5x+7
GaryK [48]
Distribute: 3x+6+4=5x+7
Simplify: 3x+10=5x+7
Subtract 3x from both sides: 10=2x + 7
Subtract 7 from both sides: 3=2x
Divide by 2: x=3/2

x=3/2
3 0
3 years ago
Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen
Jobisdone [24]

Parameterize S by the vector function

\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k

so that the normal vector to S is given by

\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k

with magnitude

\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}

In this case, the normal vector is

\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k

with magnitude \sqrt{1^2+2^2+1^2}=\sqrt6. The integral of f(x,y,z)=e^z over S is then

\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx

where T is the region in the x,y plane over which S is defined. In this case, it's the triangle in the plane z=0 which we can capture with 0\le x\le8 and 0\le y\le\frac{8-x}2, so that we have

\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}

5 0
3 years ago
while shopping, betting spent five times as much as meg. if they spent a total of $108, how much did each person spend?
yulyashka [42]

Answer:

meg spen $18 and betting spent $90

Step-by-step explanation:

5 0
3 years ago
Write the expression: the quotient of the quantity k minus 12 and m.
Vlad1618 [11]

the quotient= answer

quantity = ( )

minus= subtraction

final answer:

(k-12) ÷ m

6 0
3 years ago
I need help with this please
chubhunter [2.5K]

Answer:

1000L

Step-by-step explanation:

3000l=1kl

3000l×3kl

8 0
2 years ago
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