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3 years ago

How do you work out 5 2/3 - 2 3/4 ???

Mathematics

1 answer:

loris [4]3 years ago

6 0

Hi,
i worked out the problem and I attached the picture

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Say hey certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at and average annual rate of

Mrrafil [7]

D because it is a decline and they are loosing 75% of their jobs

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2 years ago

What is the value of the expression shown below?

Marysya12 [62]

The answer is the one 18

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2 years ago

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judy has a piece of wood that is 4 5/8 feet long. she cuts off 3 feet 6 inches of the wood for a project. how much wood, in feet

Svet_ta [14]

there are 12 inches in 1 foot, so 6 inches is really just half a foot, thus 3'6" is really just 3.5' or 3½ feet.

now, let's convert those mixed fractions to improper fractions and then subtract, bearing in mind our LCD will be 8.

$\bf \stackrel{mixed}{4\frac{5}{8}}\implies \cfrac{4\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{45}{8}-\cfrac{7}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)45~~-~~(4)7}{8}}\implies \cfrac{45-28}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}$

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2 years ago

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Use spherical coordinates to find the volume of the region that lies outside the cone z = p x 2 + y 2 but inside the sphere x 2

Harman [31]

I assume the cone has equation $z=\sqrt{x^2+y^2}$ (i.e. the upper half of the infinite cone given by $z^2=x^2+y^2$ ). Take

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

The volume of the described region (call it $R$ ) is

$\displaystyle\iiint_R\mathrm dx\,\mathrm dy\,\mathrm dz=\int_0^{2\pi}\int_0^{\sqrt2}\int_{\pi/4}^\pi\rho^2\sin\varphi\,\mathrm d\varphi\,\mathrm d\rho\,\mathrm d\theta$

The limits on $\theta$ and $\rho$ should be obvious. The lower limit on $\varphi$ is obtained by first determining the intersection of the cone and sphere lies in the cylinder $x^2+y^2=1$ . The distance between the central axis of the cone and this intersection is 1. The sphere has radius $\sqrt2$ . Then $\varphi$ satisfies

$\sin\varphi=\dfrac1{\sqrt2}\implies\varphi=\dfrac\pi4$

(I've added a picture to better demonstrate this)

Computing the integral is trivial. We have

$\displaystyle2\pi\left(\int_0^{\sqrt2}\rho^2\,\mathrm d\rho\right)\left(\int_{\pi/4}^\pi\sin\varphi\,\mathrm d\varphi\right)=\boxed{\frac43(1+\sqrt2)\pi}$

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2 years ago

Find the distance between the point.(5,5) amd the line -3x-4y+10=0

gayaneshka [121]

Answer:

Step-by-step explanation:

the formula of the distance between

the point (p, q) and the line ax + by +c = 0 =>

d = |p.a + q.b +c| / √(a²+b²)

d = |5(-3)+5(-4)+10| / √[(-3)²+(-4)²]

= |(-15-20+10)|/√25

= |-25|/ 5

= 25/5

= 5

6 0

2 years ago