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3 years ago

Solve the equation 2^x=512

Mathematics

1 answer:

erica [24]3 years ago

5 0

Answer:

Step-by-step explanation:

we know 2^10 is 1024, so 2^9 is 512.

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Sedaia [141]

You have to get the same denominator

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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:

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

3 0

4 years ago

Help me?<br> 185/100 + 50% + 4%=?

Taya2010 [7]

Answer:

2.39

Step-by-step explanation:

Convert everything to a decimal.

To do that with a fraction divide the numerator by the denominator.

185 divided by 100 = 1.85

185/100 = 1.85

To convert a percent to a decimal divide the number by 100.

50 divided by 100 = 0.5

50/100 = 0.5

4 divided by 100 = 0.04

4/100 = 0.04

Now add:

1.85 + 0.5 + 0.04 = 2.39

6 0

3 years ago

Catherine has $400 in her checking account. She writes a check for $600. What is the balance of her account?

nevsk [136]

Answer:

Her new balance is $-200

$400 - $600 is $-200

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3 years ago

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What’s 5+5 i need help

Triss [41]

Answer:

Step-by-step explanation:

or was it 11??

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3 years ago

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