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3 years ago

List three ordered pairs that represent solutions to the equation 2x - y = 3.

Mathematics

1 answer:

marishachu [46]3 years ago

3 0

Answer:

(0,-3)

(1.-1)

(2,1)

Step-by-step explanation:

those are the only possible solutions to the equation. Choose any value for

x that is in the domain to plug into the equation.

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3 years ago

Consider the force field and circle defined below.

grin007 [14]

By Green's theorem,

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

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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

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

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3 years ago

Mrs. Cho has 24 students in her class. Some of her students are also in the play. Explain why it is not possible for exactly 24%

lora16 [44]

Let's start by calculating how many students does 24% represent.
24% * 24 = 0.24 * 24 = 5.76
We got a decimal number as solution. The reason why exactly 24% students can't be in the play is because this percentage does not represent whole number of students. She can't take 0.76 students

If she wanted 25% students to be in a play it would mean she has to take:
25% * 24 = 0.25 *24 = 6 students

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4 years ago