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3 years ago

-UIVIT UUNNU INTEREST

Mathematics

1 answer:

Jobisdone [24]3 years ago

5 0

Answer:

Step-by-step explanation:

Principal, P = $4,000

Interest rate, r = 3% = 0.03

Period, t = 20 years

Number of times compounded in a year = 4

Amount , A = P( 1 + r/n)^tn

A = 4000( 1 + 0.03/4)^4*20

A = 4000( 1 + 0.0075) ^80

A =4000( 1.0075) ^80

A = 4000* 1.818

A = $7272.18

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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

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

6 0

4 years ago

Please resolve this is for today

Fynjy0 [20]

Answer:

A Square plus B square equals

Step-by-step explanation:

5 0

3 years ago

What is the 9th multiple of 15

MArishka [77]

135 because
15x1=15 15x7=105
15x2=30 15x8=120
15x3=45 15x9=135
15x4=60 15x10=150
15x5=75 15x11=165
15x6=90 15x12=190

5 0

4 years ago

What is the compound interest of 10400 at 12.7% for 4 year

Naddik [55]

The Compound Interest of 10400 at 12.7% for 4 years is 6378.

The principal amount is given as 10400.

The rate of interest is given as 12.7%.

The time period to be calculated is given as 4 years.

The compound interest for the given above is to be calculated.

<h3>What is compound interest?</h3>

Compound interest is the interest that we earn both on the principal amount and the interest we earn.

The formula used to calculate compound interest is:

$P [ (1 + \frac{R}{100} )^n - 1 ]$

Where P = principal amount, R = rate of interest, and n = number of years.

We have,

P = 10400

R = 12.7%

n = 4 years

Compound interest:

$P [ (1 + \frac{R}{100} )^n - 1 ]\\\\10400 [ (1 + \frac{12.7}{100} )^4 - 1 ]$

Now,

10400 [ ( 1 + 0.12.7 )^2 - 1 ]

10400 [ 1.127^4 - 1 ]

10400 [ 1.61322 - 1 ]

10400 x 0.6132

6377.56

Rounding to the nearest whole number.

We have,

Compound Interest = 6378.

Thus the Compound Interest of 10400 at 12.7% for 4 years is 6378.

Learn more about Compound Interest here:

brainly.com/question/13155407

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2 years ago

The sum of two numbers is 44 and the difference is 2 What are the numbers

Aleks04 [339]

Answer:

21 & 23

Step-by-step explanation:

44 ÷ 2 = 22

The two numbers are going to be close to 22.

21 + 23 = 44

32 - 21 = 2

4 0

3 years ago

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