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3 years ago

HELP Pllllllzzzzz thank you have a great day

Mathematics

1 answer:

dsp733 years ago

4 0

Answer:

use google that is what I do. it is a good

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The bottom of the ladder rests on a horizontal flat surface and the top of the ladder rests against a wall. The ladder makes an

mihalych1998 [28]

The diagram of the ladder leaning on a wall is shown below

We will use the trigonometry ratio for cosine to solve for 'x'

We choose the cosine ratio because we have the angle, 61° and the side adjacent to the angle

$cos(x)= \frac{adjacent}{hypothenuse}$
$cos(61)= \frac{61}{x}$
$x= \frac{6}{cos(61)} =12.38$ , rounded to 2 dp

6 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + tan z j + (x2z + y2)k and S is the top half of

Romashka-Z-Leto [24]

By the divergence theorem, the surface integral over $S_2$ is

$\displaystyle\iint_{S_2}\mathbf F\cdot\mathrm dS=\iiint_R\nabla\cdot\mathbf F\,\mathrm dR$

where $R$ denotes the space bounded by $S_2$ . Assuming the vector field is given to be

$\mathbf F(x,y,z)=z^2x\,\mathbf i+(y^3+\tan z)\,\mathbf j+(x^2z+y^2)\,\mathbf k$

then

$\nabla\cdot\mathbf F=\dfrac\partial{\partial x}[z^2x]+\dfrac\partial{\partial y}[y^3+\tan z]+\dfrac\partial{\partial z}[x^2z+y^2]=z^2+3y^2+x^2$

Converting to spherical coordinates, we take

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}$

so that the triple integral becomes

$\displaystyle\int_{\varphi=0}^{\varphi=\pi/2}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=3}(\rho^2\cos^2\varphi+3\rho^2\sin^2\theta\sin^2\varphi+\rho^2\cos^2\theta\sin^2\varphi)\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$
$=\displaystyle\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4(\cos^2\varphi+2\sin^2\theta\sin^2\varphi+\sin^2\varphi)\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$
$=162\pi$

Now the integral over $S$ alone will be the difference of the integral over $S_2$ and the integral over $S_1$ , i.e.

$\displaystyle\iint_{S_2}=\iint_{S_1\cup S}=\iint_{S_1}+\iint_S\implies\iint_S=\iint_{S_2}-\iint_{S_1}$

We can parameterize the points in $S_1$ by

$\mathbf s(r,\theta)=\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=0\end{cases}$

so that the integral over $S_1$ is

$\displaystyle\iint_{S_1}\mathbf F\cdot\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\mathbf F(x(r,\theta),y(r,\theta),z(r,\theta))\cdot\left(\dfrac{\partial\mathbf s}{\partial r}\times\dfrac{\partial\mathbf s}{\partial\theta}\right)\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\int_0^{2\pi}\int_0^3(r^3\sin^3\theta\,\mathbf j+r^2\sin^2\theta\,\mathbf k)\cdot(r\,\mathbf k)\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\int_0^{2\pi}\int_0^3r^3\sin^2\theta\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{81\pi}4$

So, the integral over $S$ alone evaluates to

$\displaystyle\iint_S=\iint_{S_2}-\iint_{S_1}=162\pi-\dfrac{81\pi}4=\dfrac{567\pi}4$

3 0

3 years ago

Finding the rate of a tax or commission

Ksju [112]

Answer:

The commission rate in percentage = 16%

Step-by-step explanation:

Given

Commission Amount = $352

Sales Price = $2200

To determine

Find the commission rate in percentage.

Using the formula

Commission percentage = Commission Amount / Sales Price

substituting Commission Amount = 352 and Sales Price = 2200

= 352 / 2200

= 0.16

Multiply by 100 to get the percentage:

0.16 × 100 = 16%

Therefore, the commission rate in percentage = 16%

4 0

3 years ago

Write in slope-intercept form an equation of the

Ira Lisetskai [31]

Answer:

y = 5x - 6

Step-by-step explanation:

8 0

3 years ago

If cos28 = x/4, find x(3sf)

STALIN [3.7K]

Ummmm... Sorry I'm
stuck on that one...

4 0

4 years ago