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3 years ago

Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation?

2 answers:

8 0

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill$

____ [38]3 years ago

6 0

Answer:

k = -1/2

y= -1/2x

Step-by-step explanation:

y = kx

We know y = -4 and x=8

-4 = k*8

Divide each side by 9

-4/8 = 8k/8

-1/2 =k

y= -1/2x

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A student on a piano stool rotates freely with an angular speed of 2.85 rev/s . The student holds a 1.50 kg mass in each outstre

Vlad1618 [11]

Answer:r'=0.327 m

Step-by-step explanation:

Given

$N=2.85 rev/s$

angular velocity $\omega =2\pi N=17.90 rad/s$

mass of objects $m=1.5 kg$

distance of objects from stool $r_1=0.789 m$

Combined moment of inertia of stool and student $=5.53 kg.m^2$

Now student pull off his hands so as to increase its speed to 3.60 rev/s

$\omega _2=2\pi N_2$

$\omega _2=2\pi 3.6=22.62 rad/s$

Initial moment of inertia of two masses $I_0=2mr_^2$

$I_0=2\times 1.5\times (0.789)^2=1.867$

After Pulling off hands so that r' is the distance of masses from stool

$I_0'=2\times 1.5\times (r')^2$

Conserving angular momentum

$I_1\omega =I_2\omega _2$

$(5.53+1.867)\cdot 17.90=(5.53+I_o')\cdot 22.62$

$I_0'=1.397\times 0.791$

$I_0'=5.851$

$5.53+2\times 1.5\times (r')^2=5.851$

$2\times 1.5\times (r')^2=0.321$

$r'^2=0.107009$

$r'=0.327 m$

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3 years ago

Plzzzzzz ans this quickly plzz

elixir [45]

Step-by-step explanation:

Prime factorization of 48 is :

$48=2\times 2 \times 2 \times 2 \times 3\\\\=2^4\times 3^1$

Option (3) is true.

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19 = 19 × 1

Option (c) is correct.

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924 = 2 x 2 x 3 x 7 x 11

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Hence, this is the required solution.

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3 years ago

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Makovka662 [10]

Answer:

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3 years ago

Read 2 more answers

The sum of two numbers is 40 - 13. what are the integers.

Anni [7]

So. let's say the numbers are "a" and "b"

whatever they're, we know a + b = 56

let's say the larger one is "b", so 3 times the smaller is 3*a or 3a
now, 12 less than that, is 3a - 12

and the larger is that, so b = 3a - 12

so $\bf \begin{cases}
a+b=56\\
\boxed{b}=3a-12\\
----------\\
a+\boxed{3a-12}=56
\end{cases}$

solve for "a", to see what the smaller one is

what's b? well, b = 56 - a

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3 years ago

What are two factors to add to give negative 4 and multiply to give negative 10?

SIZIF [17.4K]

-5*-2=-10 The factors to multiply to give negative 10 is -5 and 2 6 plus negative two gives you negative four. The factors to add to give you -4 is 6 and -2

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3 years ago