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Sloan [31]
3 years ago
9

3. (6 Points). Solve the initial value problem y'-y.cosx=0, y(pi/2)=2e

Mathematics
1 answer:
Stells [14]3 years ago
7 0

Answer:

y=2e^{sin(x)}

Step-by-step explanation:

Given equation can be  re written as

\frac{\mathrm{d} y}{\mathrm{d} x}-ycos(x)=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=ycos(x)\\\\=> \frac{dy}{y}=cox(x)dx\\\\Integrating  \\ \int \frac{dy}{y}=\int cos(x)dx \\\\ln(y)=sin(x)+c............(i)

Now it is given that y(π/2) = 2e

Applying value in (i) we get

ln(2e) = sin(π/2) + c

=> ln(2) + ln(e) = 1+c

=> ln(2) + 1 = 1 + c

=> c = ln(2)

Thus equation (i) becomes

ln(y) = sin(x) + ln(2)

ln(y) - ln(2) = sin(x)

ln(y/2) = sin(x)

y= 2e^{sinx}

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3 years ago
If for every 12 blue streamers there is 9 gold streamers, how many blue streamers will I have if I have 36 gold streamers?
neonofarm [45]

Answer:

You will have 48 blue streamers.

Step-by-step explanation:

This question can be solved by proportions, using rule of three.

We have that:

For 12 blue streamers, there are have 9 gold streamers. How many blue streamers are there when there are 36 gold streamers?

12 blue - 9 gold

x blue - 36 gold

Applying cross multiplication

9x = 36*12

Simplifying by 9

x = 4*12 = 48

You will have 48 blue streamers.

4 0
2 years ago
Which algebraic expression represents the phrase below? five times the sum of a number and eleven, divided by three times the su
Umnica [9.8K]
The phrase has two parts:

Five times the sum of a number and eleven, divided by three times the sum of the number and eight

Let the number be x. Five times the sum of a number and eleven means 5 multiplied to the sum of x and 11. In expression this will be written as:

5(x + 11)

Three times the sum of the number and eight means 3 multiplied to the sum of x and 8. In expression this will be written as:

3(x + 8)

So, the overall expression will be:

\frac{5(x+11)}{3(x+8)}
4 0
3 years ago
A game-show spinner has these odds of stopping on particular dollar values: 40% for $5, 25% for $100, 20% for $500, and 15% for
Yakvenalex [24]

Answer:

13÷ 23

Step-by-step explanation:

The computation of the odds of player winning is shown below;

For $5 it is 40%

And, for $100 it is 25%

so for total it is

= 40% + 25%

= 65%

And, the total percentage is 100%

So, the odds in favor is

65:100

13:20

Now for winning it would be 13÷ 23

5 0
3 years ago
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