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Pie
3 years ago
12

Solve the differential equation dy dx equals the quotient of y times the cosine of x and the quantity 1 plus y squared with the

initial condition y(0) = 1.
Mathematics
1 answer:
geniusboy [140]3 years ago
8 0
We rearrange the given differential equation to combine all the y terms on the left side of the equation and the x terms on the right side:
     [(1 + y^2) / y] dy = cos(x) dx
     [(1/y) + y] dy = cos(x) dx

We integrate both sides to get
     ln y + (y^2 / 2) = sin(x) + C

Then, we apply the initial condition y = 1 at x = 0 to get the value of C:
     ln (1) + (1^2 / 2) = sin(0) + C
     C = ln (1) + (1^2 / 2) - sin(0)
     C = 1/2

Therefore, our final answer is
     ln (y) + (y^2 / 2) = sin(x) + 1/2
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A major airline is concerned that the waiting time for customers at its ticket counter may be exceeding its target average of 19
sertanlavr [38]

Answer:

a) Statement is true

b) Statement incorrect. Company goal is to attend customer at 190 second at the most. So test should be one tail test  (right)

c) We have to reject H₀, and differences between sample mean and the hypothesized population mean should not be attributed only to sampling error

Step-by-step explanation:

a)  as the significance level is = 0,02  that means  α = 0,02 (the chance of error type I )  and the β (chance of type error II   is

1  -  0.02  =  0,98

b) The company establishe in 190 seconds time for customer at its ticket counter (if this time is smaller is excellent ) company is concerned about bigger time because that could be an issue for customers. Therefore the test should be a one test-tail to the right

c) test statistic

Hypothesis test should be:

null hypothesis                H₀   =  190

alternative hypothesis    H₀   >  190

t(s)  =  ( μ  -  μ₀ ) / s/√n      ⇒   t(s)  = ( 202 - 190 )/(28/√100 )

t(s)  = 12*10/28

t(s)  = 4.286

That value is far away of any of the values found for 99 degree of fredom and between  α  ( 0,025 and 0,01 ). We have to reject H₀, and differences between sample mean and the hypothesized population mean should not be attributed only to sampling error

If we look table  t-student we will find that for 99 degree of freedom and α = 0.02.

3 0
3 years ago
What is the range of this relation?
riadik2000 [5.3K]
The range of the relation is 35,40,45,60,75
Reason being in relation range is the set of all second elements of ordered pairs (y-coordinates).
5 0
3 years ago
Y= x^2 -5 solve for x
dexar [7]

Y= x^2 -5

We need to solve for x, we need to get x alone

Y= x^2 -5

Lets start by removing -5

Add 5 on both sides

y + 5= x^2 -5 + 5

y + 5= x^2

Now to isolate x , we need to remove the square from x

To remove square , take square root on both sides

+-\sqrt{y+5} = \sqrt{x^2}

square and square root will get cancelled

+-\sqrt{y+5} = x

So x = +\sqrt{y+5} and  x = -\sqrt{y+5}


7 0
3 years ago
Nikolai is taking a taxi to school. He has to
adoni [48]
7 because the first mile will be 3 dollars then if you add the rest of the miles it will be seven because you are adding four more miles
5 0
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Solve this math problem -2 1/3-(-5)= ​
dmitriy555 [2]

Answer:

8/3 or 2.6 repeating

4 0
3 years ago
Read 2 more answers
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