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2 years ago

London has a collection of 260 coins. How many coins represent 25% of her collection?

Mathematics

1 answer:

Sergeu [11.5K]2 years ago

8 0

Answer:

65 coins

Step-by-step explanation:

Set this problem up with a porportion.

$\frac{?}{260} \frac{25}{100}$

After that, cross multiple and divide.

25 times 260. Then divide by 100. That is then your answer.

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Answer: D

Step-by-step explanation:

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One leg of a right triangle is 4 less than the other leg. The square of the hypotenuse of the right triangle is 80. How long are

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3 years ago

Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt

Paladinen [302]

Answer:

$y(x)=4a\sqrt{3}* sin(x)-3a$

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

$\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}$

But:

$\frac{1}{tan(x)} =cot(x)$

So:

$\frac{dy(x)}{dx} =cot(x)*(3a+y)$

Multiplying both sides by dx and dividing both sides by 3a+y:

$\frac{dy}{3a+y} =cot(x)dx$

Integrating both sides:

$\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx$

Evaluating the integrals:

$log(3a+y)=log(sin(x))+C_1$

Where C1 is an arbitrary constant.

Solving for y:

$y(x)=-3a+e^{C_1} sin(x)$

$e^{C_1} =constant$

So:

$y(x)=C_1*sin(x)-3a$

Finally, let's evaluate the initial condition in order to find C1:

$y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a$

Solving for C1:

$C_1=4a\sqrt{3}$

Therefore:

$y(x)=4a\sqrt{3}* sin(x)-3a$

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3 years ago

What's the answer ? To this question

Airida [17]

You could use the equation y=mx+b

Find the slope of the two coordinates. I would personally suggest using stack and subtract:

(0,2) 2-5 -3 3
(2,5) -------= ------= -----
0-2 -2 2

We have the slope but we need to find the y-intercept.

y=3
--x+b
2

Plug one of the coordinates in the constructed equation above:

2=3
-- (0)+b
2

2=0+b
-0=-0
------------
b=2

We found the slope and y-intercept. Now we have our complete equation. The equation is:

y=3
--x+2
2

Have a blessed day!

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3 years ago

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3 years ago

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