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3 years ago

If 40% of a number is 56 what was the original number

1 answer:

5 0

Percent is pars out of 100
40%=40/100=4/10=0.4
'of' means multiply
0.4 times something=56
divide both sides by 0.4
something=140

th enumber is 140

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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

3 years ago

Find a solution to the linear equation y=6x−18 by filling in the boxes with a valid value of x and y.

emmainna [20.7K]

Answer:

x=3

y=0

i hope this helps:)

Step-by-step explanation:

4 0

3 years ago

Suppose that Ayumi rolls a pair of fair six-sided dice. Let A be the event that the first die lands on 2 and B be the event that

Tanya [424]

Answer:

$\frac{1}{6} ,\frac{1}{6} ,\frac{1}{36}\,,\,independent$

Step-by-step explanation:

Given: Let A be the event that the first die lands on 2 and B be the event that the second die lands on 2.

To find:

P(A), the probability that the first die lands on 2

P(B), the probability that the second die lands on 2

P(A and B): the probability that the first die lands on 2 and the second die lands on 2

Solution:

Probability refers to chances of occurrence of some event.

Probability = number of favourable outcomes/total number of outcomes

Sample space = $\left \{ 1,2,3,4,5,6 \right \}$

Total number of outcomes = 6

For P(A):

Number of favourable outcomes = 1

So,

$P(A)=\frac{1}{6}$

For P(B):

Number of favourable outcomes = 1

So,

$P(B)=\frac{1}{6}$

P(A and B) = $P(A)P(B)=\left ( \frac{1}{6} \right )\left ( \frac{1}{6} \right )=\frac{1}{36}$

Yes, A and B are independent events as happening of each of the event does not depend on the other.

5 0

3 years ago

Find three rational numbers between 1/3 and 5/6

ss7ja [257]

First we need to know the meaning of a rational number. A rational number is any number that terminates and doesn't repeat as a decimal, and can be represented as a fraction.

I would say it's 3/6, 4/6, and 5/6, you can also have 2/6 since they can be expressed as a ratio and are between 1/3 and 5/6. (1/3 is equal to 2/6)

6 0

3 years ago

11 is 4% of what number

GenaCL600 [577]

<span>First, we must convert the given fraction into a decimal number. So use a calculator or long division to convert the given fraction 11/4  to a decimal number. In this case, 2.75

Now just multiply the equivalent decimal  2.75 by 100 to convert it into a percent. So 100x2.75=275. Take note that we're simply moving the decimal point two spots to the right.

So the given fraction 11/4  is equivalent to 275%
so the answer is 275</span>

5 0

3 years ago