On the coordinate grid, the graph of y = -x - 1 is shown

Mathematics

1 answer:

ziro4ka [17]3 years ago

8 0

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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

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

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3 years ago

6x squared+ 4 (x square- 1) Simplify the expression

r-ruslan [8.4K]

i think its
6x4-1 that should be the awnser

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3 years ago

Why might you expect most absolute value equations to have two solutions? Why not three or four?

Travka [436]

Answer:

If the absolute value expression is not equal to zero, the expression inside an absolute value can be either positive or negative. So, there can be at most two solutions. Looking at this graphically, an absolute value graph can intersect a horizontal line at most two times.

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3 years ago

How to solve -13=5(1 4m)-2m?

Paladinen [302]

First, you would multiply: -13 = 70m - 2m. Then, you subtract the like terms, which would be 70m - 2m: -13 = 68m. You are looking for what m is, so you would divide 68 on both sides: m = - 13 / 68. In math, people would usually like fractions more than decimals, but if you are looking for the decimal number, it would be m ≈ - 0.19.

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In the diagram below, line segment bc is an altitude of triangle abd. What is the length of line age meant cd? If necessary, rou

Naddika [18.5K]

Check the picture below.

running a perpendicular line like so from the right-angle, makes three similar triangles, the large, containing the smaller ones, and a medium and a small one. Now, using proportions, you can just use there, the medium and smalle to get "x".

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3 years ago