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Stells [14]
2 years ago
5

Problem 2: Solve the initial value problem

" alt="y' = xy" align="absmiddle" class="latex-formula">
y(0) = 1
​
Mathematics
1 answer:
atroni [7]2 years ago
5 0

Separate the variables:

y' = dy/dx = xy   ⇒   1/y dy = x dx

Integrate both sides:

∫ 1/y dy = ∫ x dx

ln|y| = 1/2 x² + C

Given that y(0) = 1, we have

ln|1| = 1/2 • 0² + C   ⇒   C = 0

so that the particular solution is

ln|y| = 1/2 x²

Solving for y gives

y = exp(1/2 x²)

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Write 0.7 as a fraction. Show your work
Reptile [31]
0.7 is seven tenths.

Seven tenths as a fraction is 7/10.

Hope this helps!
5 0
3 years ago
Read 2 more answers
Hey can anyone give me the answers to the questions that are blank
Brilliant_brown [7]

The value of the rate of change of the function is 14a + 7h

<h3>Rate of change of function</h3>

The rate of change of function is also known as the slope expressed according to the equation shown below;

f'(x) = f(a+h)-f(a)/h

Given the function below expressed as:

f(x) =1 + 7x^2

<u>Determine the function f(a)</u>

To determine the function, simply replace x with 'a" to have:

f(a) =1 + 7a^2

Determine the function f(a+h)

f(a+h) = 1 + 7(a+h)^2

f(a + h) = 1 + 7(a^2+2ah+h^2)

f(a + h) = 1 + 7a^2 + 14ah + 7h^2

To determine the rate of change

f'(x) = f(a+h)-f(a)/h

f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) =  + 14ah + 7h^2/h

f'(x) = 14a + 7h

Hence the value of the rate of change of the function is 14a + 7h

Learn more on rate of change here: brainly.com/question/8728504

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7 0
2 years ago
To increase sales, an online clothing store began giving a 50% off coupon to random customers. Customers didn't know whether the
ludmilkaskok [199]

To increase sales, an online clothing store began giving a 50% off coupon to random customers Six customers each made purchases from the website the binomial random variable and  mean and standard deviation of X  is mathematically given as

X ~ Bin(n = 6, p = 0.2)

x= 0.9798

<h3>What is a binomial random variable?</h3>

Generally, the equation for is mathematically given as

P(coupon) = 1/5

P(coupon)= 0.2

the binomial distribution

X ~ Bin(n = 6, p = 0.2)

Therefore, The mean and standard deviation of X

пВ = np \\np= 6* 0.2 = 1.2\\

x=\sqrt{ np(1 - p)} \\ x=\sqrt{ 6 * 0.2 + (1 -0.2)} \\

x= 0.9798

In conclusion, mean and standard deviation of X

x= 0.9798

Read more about binomial

brainly.com/question/3560614

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6 0
2 years ago
I really need this answer, the options are
KonstantinChe [14]

Answer:

first one is a 20 prcent decrease from x to y

and for the second one is it a 37.5 percent increase

Step-by-step explanation:

hope this helped

5 0
3 years ago
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Need help ASAP please and thank you
Helen [10]

Answer:

B

Step-by-step explanation:

4 is the outlier

7 0
4 years ago
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