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2 years ago

Marina simplified the expression 4x + 5 (-4x -b) - (x -2) to be -17x -8.

Mathematics

1 answer:

S_A_V [24]2 years ago

7 0

Answer:

C.)

Step-by-step explanation:

4x -20x -5b -x +2=-17x -8

-17x-5b+2=- 17x-8

+17x +17x

-5b +2= -8

-2 -2

-5b = -10

b= 2

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3 years ago

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yKpoI14uk [10]

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3 years ago

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 4xzj + ex

natima [27]

Answer:

The result of the integral is 81π

Step-by-step explanation:

We can use Stoke's Theorem to evaluate the given integral, thus we can write first the theorem:

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

Finding the curl of F.

Given $F(x,y,z) = < yz, 4xz, e^{xy} >$ we have:

$curl \vec F =\left|\begin{array}{ccc} \hat i &\hat j&\hat k\\ \cfrac{\partial}{\partial x}& \cfrac{\partial}{\partial y}&\cfrac{\partial}{\partial z}\\yz&4xz&e^{xy}\end{array}\right|$

Working with the determinant we get

$curl \vec F = \left( \cfrac{\partial}{\partial y}e^{xy}-\cfrac{\partial}{\partial z}4xz\right) \hat i -\left(\cfrac{\partial}{\partial x}e^{xy}-\cfrac{\partial}{\partial z}yz \right) \hat j + \left(\cfrac{\partial}{\partial x} 4xz-\cfrac{\partial}{\partial y}yz \right) \hat k$

Working with the partial derivatives

$curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(4z-z\right) \hat k\\curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k$

Integrating using Stokes' Theorem

Now that we have the curl we can proceed integrating

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot \hat n dS$

where the normal to the circle is just $\hat n= \hat k$ since the normal is perpendicular to it, so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S \left(\left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k\right) \cdot \hat k dS$

Only the z-component will not be 0 after that dot product we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3z dS$

Since the circle is at z = 3 we can just write

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3(3) dS\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 9\int \int_S dS$

Thus the integral represents the area of a circle, the given circle $x^2+y^2 = 9$ has a radius r = 3, so its area is $A = \pi r^2 = 9\pi$ , so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = 9(9\pi)\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 81 \pi$

Thus the result of the integral is 81π

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3 years ago

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egoroff_w [7]

Answer: 8

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2 years ago

What is the value of x ?

4vir4ik [10]

Answer:

What is the value of x?

Whenever we have a problem to solve we assume the unknown quantity(or value to be identified) as x. This is just a convention followed in algebra by using a variable to denote the unknown quantity and then arrive at the solution.

What is the value of X?

What's the value of X?

X + X = X, what is the value of X?

What is the value of x ? How can I find it?

Do you know the value of x?

Value of X can be any numerical value or anything but depends solely on your question .But I find no question ok lets take an example .

If an equation is given ,

X+2=4

=> X=4–2

=>X=2

We X's value as 2 .

Now another ,

X + Y = 5 , 2X + 5Y = 10

Now taking first equation

X = 5-Y ………………………..(1)

Now taking second equation

X= 10–5Y/2…………………(2)

Now,

2(5-Y) = 10–5Y

=> 10–2Y = 10–5Y

=> 2Y = 5Y

Y has no value here because this equation not correctly represented .

Hence ,

We conclude the value of X varies with equation .

Thank You ,

4 0

3 years ago

Read 2 more answers