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3 years ago

Evaluate 4 a for a = 5 2/3 . Express your answer in simplest form.

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

5 0

Answer:

I think it is 20 8/12

Step-by-step explanation:

i don'y know what to put here

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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

Find the are of the trapizoind

Andreyy89

9514 1404 393

Answer:

7.5 square units

Step-by-step explanation:

The formula for the area of a trapezoid is ...

A = 1/2(b1 +b2)h

where b1 and b2 are the lengths of the parallel bases, and h is the perpendicular distance between them.

Here, the bases are TR = 1 and PA = 4. The height is 3 units, so the area is ...

A = (1/2)(1 +4)(3) = 15/2 = 7.5 . . . . square units

6 0

2 years ago

the temperature changed from 5 degrees Celsius 6pm to -2 degrees Celsius at midnight. How much did the temperature decrease?

telo118 [61]

7 degrees Celsius because to go from 5 to -2 you would subtract 7 so it’s 7.

5 0

2 years ago

1.Mario purchased 15 tickets to a football game for $13.50. How much would it cost to purchase 21 tickets? $ ____________

Mashcka [7]

Answer:

1. $18.90

2. Every statement is true EXCEPT e

Step-by-step explanation:

For number 1. We first need to find how much one ticket costs. To find this we divide profit by number of tickets sold. So,

13.50/15 = $0.90

So to find the cost of 21 tickets we times the cost per ticket by 21

21 x 0.90 = 18.9

So $18.90

They sold 6 cases in 40 minutes.

6/40 = 0.15

They sell 0.15 cases per minute

For a we wanna see if they can sell 27 cases in 180 minutes so

0.15 x 180 = 27

So a is true

0.15 x 80 = 12

So b is true

0.15 x 120 = 18

C is true

0.15 x 160 = 24

D is true

0.15 x 200 = 30

E is false

5 0

2 years ago

Please:)...............

Assoli18 [71]

Answer:

F. 10 30. please brainliest

4 0

3 years ago

Read 2 more answers