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3 years ago

The leg of a triangle is 7 cm and the hypotenuse is 13 cm. What is the length of the other leg of the triangle?

Mathematics

1 answer:

defon3 years ago

6 0

Answer:

2√30

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

7^2 + b^2 = 13^2

b^2 = 120

b = 2√30

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Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

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3 years ago

How do I graph (5, -3), (0, -4)

Lorico [155]

Answer:

5 right and down 3 and (0 means the middle) so middle down 4

Step-by-step explanation:

lit : )

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3 years ago

Clair has250 pennies some pennies are in a box the rest are in her bankthere are more then 100 pennies in each place how many pe

9966 [12]

Answer:

In each place there must be more 100 pennies, but as the total 250 pennies, there are several ways that the money is distributed.

Because there may be 101 pennies in the box and 149 pennies in the bank, but it can also be the opposite; in the box 149 pennies and in the bank 101 pennies.

Therefore, there are many options to answer the question, as long as it is met that there are more than 100 pennies in one place.

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3 years ago

Anybody can help me?

Dovator [93]

The proportional relationship is correctly graphed by graph vs.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the relationship that gives the montant M considering the number of items sold n is:

M = 3n.

Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, points (100, 300), (200, 600) and so on, hence the graph is graph vs.

More can be learned about proportional relationships at brainly.com/question/10424180

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1 year ago

A truck is carrying 10 cars weighing an average of 3,500 pounds each. What is the total weight in tons of the cars on the truck?

irina [24]

The total weight is Roughly 17.5 Tons

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3 years ago