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4 years ago

Pre calculus question how to solve by using sigma notation or summation notation?

Mathematics

1 answer:

lapo4ka [179]4 years ago

7 0

I am assuming you are trying to find the sum.

First, plug in n for 1, then n for 80 to get the following numbers:
5/6 and 163/6
As you go up the sequence, as n is increased by 1, then the next number is increased by 1/3

Use the arithmetic sequence formula to solve for the sum.
n * (a1 + a2)/2 where a1 is 1st number and a2 is last number.
80 * (5/6 + 163/6)/2
Simplify the expression to get 1120.

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iris [78.8K]

4 Bus stops... I hope this helped

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3 years ago

Read 2 more answers

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

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

6 0

4 years ago

II. Using Radians to Measure Arcs and Angles

padilas [110]

Pi radians is 180 degrees.
A
1) 180/3=60
2) 270
3) 45
4) 3240
B
1) 100/180=5/9
3) 30/180=3/18
5) 1/180
C
1) (pi) cm
2) 2pi

4 0

3 years ago

Solve x2 + 7x + x2 + 7x + 9 = 3

algol13

Answer:

x2 + 7x + x2 + 7x + 9 = 3

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3 years ago

Dave rented a limousine for his wife's birthday. The hourly rate is $80. They used the limousine for 4 hours, plus Dave gave the

Pavel [41]

$80 hourly used limousine
80 * .20 = $16 tip

$80 + $16 = $96 <span>he spent hourly charges plus tip

$96 * 4 = $384 total for 4 hours plus tip</span>

7 0

3 years ago