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-Dominant- [34]
3 years ago
5

The family of solutions to the differential equation y ′ = −4xy3 is y = 1 √ C + 4x2 . Find the solution that satisfies the initi

al condition y(−2) = 4.
1. y = 4 p 1 + 16(x2 − 4)
2. y = 1 p 1 + 64(x 2 − 4)
3. y = 4 p 1 + 4(x2 − 4)
4. y = 4 p 1 + 64(x 2 − 4)
5. y = 1 p −4(x2 − 4) + 1
Mathematics
2 answers:
slega [8]3 years ago
8 0

Answer:

The correct option is 4

Step-by-step explanation:

The solution is given as

y(x)=\frac{1}{\sqrt{C+4x^2}}

Now for the initial condition the value of C is calculated as

y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(-2)=\frac{1}{\sqrt{C+4(-2)^2}}\\4=\frac{1}{\sqrt{C+4(4)}}\\4=\frac{1}{\sqrt{C+16}}\\16=\frac{1}{C+16}\\C+16=\frac{1}{16}\\C=\frac{1}{16}-16

So the solution is given as

y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}

Simplifying the equation as

y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1-256+64x^2}{16}}}\\y(x)=\frac{\sqrt{16}}{\sqrt{{1-256+64x^2}}}\\y(x)=\frac{4}{\sqrt{{1+64(x^2-4)}}}

So the correct option is 4

Nitella [24]3 years ago
8 0

Answer:

All the answers are incorrect

Step-by-step explanation:

We substituted the indicated value of y in to the solution y(x) inorder to solve for C as follows:

[\tex]y(-2)=1\frac{1}{\sqrt{C+4(-2)^2}}=4[\tex]

[\tex]1\frac{1}{\sqrt{C+16}}=4[\tex]

Squaring both sides, we have

[\tex]1\frac{1}{C+16}=16[\tex]

Therefore, [\tex]C =\frac{1}{16}-16[\tex]

The solution is now

[\tex]y(-2)=1\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}=4[\tex]

You might be interested in
The probability of a getting a new sales contract with any given client is 0.29. A sales representative works with 18 clients th
Radda [10]

Answer:

The expected number of contracts the sales representative will get this week is 5.22

Step-by-step explanation:

For each client, there are only two possible outcomes. Either there is a sales contract, or there is not. The probability of having a sale contract with each client is independent of other clients. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

E(X) = np

In this problem, we have that:

n = 18, p = 0.29

What is the expected number of contracts the sales representative will get this week?

E(X) = np = 18*0.29 = 5.22

The expected number of contracts the sales representative will get this week is 5.22

7 0
3 years ago
How do i put 1/6 2/5 3/5 and 3/7 from least to greatest
DanielleElmas [232]
3/5 1/6 3/7 2/5
------------------------
7 0
3 years ago
QUICK PLEASE HELP. I'm offering 15pt and brainliest answer.
worty [1.4K]
X would be equal to 6
4 0
3 years ago
Read 2 more answers
Can somebody help me? I’m already failing :(
Yuliya22 [10]

Answer:

125

Step-by-step explanation:

f(1)= the first time (32,000)

n= 9

r= .5 (each term is being mulitplied by .5 to get the next one

We have

32,000*(.5)^(9-1)

32,000*(.5)^8

=125

5 0
3 years ago
40.51x+12.45y=666.64
irga5000 [103]

Answer:

The graph of the equation 40.51x+12.45y=666.64 is attached with the answer where the horizontal axis represents the X axis and the vertical axis represents Y axis.

To plot the graph physically just find two points lying on the line. Mark the points on the graph sheet and then join them. This will give you the line represented by the equation.

To find points on the line assume the value of any one variable, substitute it in the equation, then solve the equation to find the value of other variable. For example : assume y = 1; substitute the value of y in the equation;

⇒ 40.51x + 12.45×1 = 666.64

⇒ 40.51x = 666.64 - 12.45

⇒ 40.51x = 654.19

⇒ x = \frac{654.19}{40.51}

⇒ x ≈ 16.149

Therefore point ( 16.149 , 1 ) lie on the graph of the equation.

***Only two points are required to plot this graph just because it represents a straight line, that we can conclude just by observing the equation. If in an equation the power of x is 1 or 0 and power of y is 1 or 0 then only it will represent a straight line in 2-D plane.***

5 0
3 years ago
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