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3 years ago

Determine the length of side c??

Mathematics

1 answer:

Kisachek [45]3 years ago

3 0

Answer:

c = 13

Step-by-step explanation:

The Pythagorean theorem:

a^2 + b^2 = c^2

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

c^2 = 169

c = 13

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You are planning on using circles to compare the populations of California 37,691,000, Texas 25,675,000, and New York 19,465,000

Aneli [31]

The areas of the circle will represent the population, so:
Area = πr²

5² : 19,465,000
C² : 37,691,000

California circle radius = 6.96 cm

For Texas:
5² : 19,465,000
T² : 25,675,000

Texas circle radius = 5.74 cm

8 0

2 years ago

Alan made a small four sided table for his office .Two sides of the table are 27 inches long and 36 inches long .If the diagonal

Tcecarenko [31]

Answer:

does NOT have right angles at the corners

Step-by-step explanation:

we are given that the sides of a table are 27" and 36" long.

If we assume the table to be rectangular, then by Pythagorean formula, we can find the diagonal and compare it to the 40" that we are given.

(refer to attached)

diagonal² = 27² + 36²

diagonal² = 2025

diagonal = √2025

diagonal = 45 inches

because the diagonal that we found is not the same as the 40" that was given, we can conclude that the table is not a rectangle (i.e does not have right angles at the corners)

6 0

2 years ago

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

Daniels print shop purchased a new printer for $35,000. Each year it depreciates at rate of 5%. How much will the printer be wor

Savatey [412]

Ab^x
a: initial value
b: value remaining after depreciation per year (in percentage)
x: number of years that have passed

35000(0.95)^8= 23219.7151

Round to the nearest hundredth value:
About $23219.72

Let me know if you have any questions :)

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3 years ago

What type of function is represented in the table of values shown below ?

Murljashka [212]

I’m going to go with Exponential

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2 years ago