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2 years ago

Please read and answer the problem and show your work

Mathematics

1 answer:

PilotLPTM [1.2K]2 years ago

7 0

Answer:

x > -4.

Step-by-step explanation:

Solving for x by dividing -3 to both side leaving x by itself.

When dividing or multiplying a negative value that has a variable the inequality switches sides. Instead of x < -4 it is x > -4. For more information or to understand inequality search for inequality video online.

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if an exterior angle of a regular polygon measures 15 degrees how many sides does it have ?a.23. b.24. c.25

dimaraw [331]

Answer:

B.24

Step-by-step explanation:

we know,

exterior angle = 360°/n(where 'n' is number of sides)

then,

15° = 360°/n

n = 360°/15°

n = 24

3 0

3 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

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

6 0

3 years ago

The population of Brazil was 162,300,000 in 1995. It was growing at a rate of about 2% per decade. Predict the population, to th

stiv31 [10]

Answer:

The population is 168,900,000 to the nearest hundred thousand

Step-by-step explanation:

In this question, we are tasked with calculating the population of Brazil given its population in 1995 and her growth rate per decade.

Mathematically, we use an exponential function to calculate this population.

This can be written as P = I(1 + r)^n

where P is the population in 2015 which we are looking for,

I is the initial population which is 162,300,000

r is the rate of increase per decade given as 2% = 2/100 = 0.02,

n is the number of times between the years we are expecting this growth. The difference between the years 2015 and 1995 is 20 years which signifies 2 decades(1 decade is 10 years). Thus our n is 2

We plug these values into the equation above;

P = 162,300,000(1+0.02)^2

P = 162,300,000(1.02)^2

P = 168,856,920 which is 168,900,000 to the nearest hundred thousand

7 0

3 years ago

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth. 117.8 cubic units 141.3 cubic u

Tom [10]

Answer:

The answer is 235.5 :)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Tion?<br>What is/are the given in the problem? What are you going to solve?<br>How can you do

djverab [1.8K]

Answer:

Not enough information given. Please type the whole question out.

3 0

3 years ago