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3 years ago

Ratio 45/x=5/7= Quotient or comparison of two numbers

Mathematics

2 answers:

alexira [117]3 years ago

8 0

Given: 45/x=5/7
step1: x*5=45*7
step2: x=315/5
step3: x=63

kogti [31]3 years ago

5 0

5*9 = 45
so
7*9 = 63

answer:

<span>45/x=5/7
45/63=5/7 or x = 63

</span>

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Answer question one and show work.

likoan [24]

Answer:

x = 28

Step-by-step explanation:

angle 1 and angle 2 are complementary (their sum is 90°)

x + 5 + 2x + 1 = 90 add like terms

3x + 6 = 90 subtract 6 from both sides

3x = 84 divide both sides by 3

x = 28

3 0

2 years ago

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

GenaCL600 [577]

Close off the hemisphere $S$ by attaching to it the disk $D$ of radius 3 centered at the origin in the plane $z=0$ . By the divergence theorem, we have

$\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV$

where $R$ is the interior of the joined surfaces $S\cup D$ .

Compute the divergence of $\vec F$ :

$\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2$

Compute the integral of the divergence over $R$ . Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

$\begin{cases}x(\rho,\theta,\varphi)=\rho\cos\theta\sin\varphi\\y(\rho,\theta,\varphi)=\rho\sin\theta\sin\varphi\\z(\rho,\theta,\varphi)=\rho\cos\varphi\end{cases}\implies\begin{cases}x^2+y^2+z^2=\rho^2\\\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi\end{cases}$

So the volume integral is

$\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5$

From this we need to subtract the contribution of

$\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S$

that is, the integral of $\vec F$ over the disk, oriented downward. Since $z=0$ in $D$ , we have

$\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k$

Parameterize $D$ by

$\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

where $0\le u\le 3$ and $0\le v\le2\pi$ . Take the normal vector to be

$\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=-u\,\vec k$

Then taking the dot product of $\vec F$ with the normal vector gives

$\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v$

So the contribution of integrating $\vec F$ over $D$ is

$\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4$

and the value of the integral we want is

(integral of divergence of <em>F</em>) - (integral over <em>D</em>) = integral over <em>S</em>

==> 486π/5 - (-81π/4) = 2349π/20

5 0

3 years ago

WHAT IS 5 TIMES 5 IN MATH

sergij07 [2.7K]

Answer:

that is 25

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

find two numbers that round to 15.5 when rounded to the nearest tenth. besides 15.04 15.55 15.508 15.445 15.0 15.49

Kitty [74]

Two other numbers are 15.48 and 15.52

4 0

3 years ago

A solid cylinder of iron whose diameter is 18 cm and height 12 cm is melted and turned into a solid sphere. Find the diameter of

finlep [7]

Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

<h2>Volume of Cylinder and Sphere:</h2><h3> Cylinder:</h3>

Diameter = 18 cm

r = 18÷ 2 = 9 cm

h = 12 cm

$\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}$

= π * 9 * 9 * 12 cm³

<h3>Sphere:</h3>

$\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}$

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

$\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12$

$\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}$

6 0

1 year ago