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3 years ago

Which one is the right one

Mathematics

1 answer:

olganol [36]3 years ago

5 0

Answer:

Step-by-step explanation:

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Use integration by parts to find the integrals in Exercise.<br> ∫(4x-12)e-8x dx.

stepladder [879]

Answer:

$e(2x^{2} -12x)-4x^{2}+C$

Step-by-step explanation:

We have been given an indefinite integral as $\int \left(4x-12\right)e-8x\:dx$ . We are asked to find the given integral.

Let us solve our given problem.

$\int \left(4x-12\right)e\:dx-\int 8x\:dx$

Take out constant:

$e\int \left(4x-12\right)\:dx-8\int x\:dx$

$e(\int 4x\:dx -\int 12\right\:dx)-8\int x\:dx$

$e(\frac{4x^{1+1}}{2} -12x)-8*\frac{x^{1+1}}{1+1}+C$

$e(\frac{4x^{2}}{2} -12x)-8*\frac{x^{2}}{2}+C$

$e(2x^{2} -12x)-4x^{2}+C$

Therefore, our required integral would be $e(2x^{2} -12x)-4x^{2}+C$ .

5 0

3 years ago

Any one help please

zvonat [6]

Answer:

1: male + female $\leq$ 30

2: 140 + 25x $\geq$ 550

Step-by-step explanation:

8 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

4 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Yakvenalex [24]

The correct answers are :

(5x)² ≥ 46

x² + 5x ≤ 46

5x² > 46

<h3>What is Inequalities?</h3>

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Here, Suppose number is x

1) The square of the product of 5 and a number is not less than 46.

Step 1

Product of 5

Step 2

Square of product of 5

(5x)²

Step 3

A number is not less than 46

(5x)² ≥ 46

2) The sum of square of a number and five times that number is not more than 46

Step 1

Square of a number

x²

Step 2

Five times that number

Step 3

The sum = x² + 5x

Step 4

Is not more than 46

x² + 5x ≤ 46

3) The product of 5 and the square of a number is greater than 46

Step 1

The square of a number

x²

Step 2

The product of 5

5x²

Step 3

Is greater than 46

5x² > 46

Thus, The correct answers are :

(5x)² ≥ 46

x² + 5x ≤ 46

5x² > 46

Learn more about Inequality from:

brainly.com/question/20383699

#SPJ1

3 0

2 years ago

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.

Crank

Answer: 1.25

Step-by-step explanation:

Given: A college-entrance exam is designed so that scores are normally distributed with a mean $(\mu)$ = 500 and a standard deviation $(\sigma)$ = 100.

A z-score measures how many standard deviations a given measurement deviates from the mean.

Let Y be a random variable that denotes the scores in the exam.

Formula for z-score = $\dfrac{Y-\mu}{\sigma}$

Z-score = $\dfrac{625-500}{100}$

⇒ Z-score = $\dfrac{125}{100}$

⇒Z-score =1.25

Therefore , the required z-score = 1.25

6 0

3 years ago