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4 years ago

A monomial is defined as

Mathematics

1 answer:

34kurt4 years ago

6 0

A monomial is an algebraic expression consisting of a single term.

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Consider the force field and circle defined below.

grin007 [14]

By Green's theorem,

$\displaystyle\int_{x^2+y^2=9}\vec F(x,y)\cdot\mathrm d\vec r=\iint_D\left(\frac{\partial(xy)}{\partial x}-\frac{\partial(x^2)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=\iint_Dy\,\mathrm dx\,\mathrm dy$

where $C$ is the circle $x^2+y^2=9$ and $D$ is the interior of $C$ , or the disk $x^2+y^2\le1$ .

Convert to polar coordinates, taking

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta$

Then the work done by $\vec F$ on the particle is

$\displaystyle\iint_Dy\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^3(r\sin\theta)r\,\mathrm dr\,\mathrm d\theta=\left(\int_0^{2\pi}\sin\theta\,\mathrm d\theta\right)\left(\int_0^3r^2\,\mathrm dr\right)=\boxed0$

4 0

3 years ago

the sum of two numbers is 63. one ninth of the first number plus one sixth of the second number is 21. find the numbers

PSYCHO15rus [73]

Answer: x= -189, y =252

Step-by-step explanation:

Let the first number be x and second number be y

x + y = 63

x = 63-y

now

1/9 of x + 1/6 of y = 21

x/9 + y/6 = 21

substituting x's value from equation i

(63-y)/9 + y/6 = 21

(378-6y+9y)/54 = 21

378+3y = 1134

3y = 1134-378

so, 3y = 756

so, y = 756/3

so, y = 252

now

x = 63-252

so, x = -189

6 0

3 years ago

Translate the following verbal statement into an algebraic expression. Use x for your variable.

mafiozo [28]

Answer:

Step-by-step explanation:

We can decipher this algebraic expression going step by step.

1) "Eight more", meaning +8 (we can add this on later).

2) The "quotient of a number (x) squared and eleven", a quotient by definition means the answer to a quantity divided by another. The quantity in this case being x² divided by 11 (so, x²/11).

3) We can combine both of these, getting x²/11 + 8.

Your expression is x²/11 + 8.

- Similarly, you could reposition this equation like 8 + x²/11 (due to the communicative property of addition). Both answers would be acceptable.

5 0

3 years ago

The table shows the approximate area in square miles of the largest and smallest states in the United States.

alexandr402 [8]

Who’s tryna hop on cod tho

8 0

3 years ago

-6x-7=3x+11 how to solve this problem

Shalnov [3]

You have to get the x to one side so you'll subtract 3x from -6x and 3x from 3x, the 3x will cancel out and -6x - 3x is -9x-7=11, you have to add 7 from both sides the 7+7 cancels out and also add 11+7 which leaves -9x=18, you have to divide -9x/-9 and do 18/-9, which gets you x=-2. Here's the work shown if you didn't what i said...
-6x-7=3x+11
-3x -3x
-9x-7=11
+7 +7
-9x=18
-9 -9
x=-2

6 0

3 years ago