Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
The number in the three different forms is as follows.
2/5 (fraction), 0.2 (decimal), and 20% (percent).
You could use percentages for the results of a poll. For example, if you held a poll for which flavour of ice cream is your favorite. Let's say you surveyed 100 kids and 50 kids voted chocolate, 30 vanilla, and 20 strawberry. Then you could say 20% voted for strawberry.
You could use the decimal form for money. For example, let's say you want to buy something that costs $10.20 and you only have 10 dollars. You could say that you would need 20 more cents, or $0.20.
As for the fraction, you could use this for measurements. For example, let's say you have a piece of fabric. You want to cut it up into 5 equal pieces, but only use two of those pieces. You could say that you would only use 2/5 of the fabric.
I hope I helped you out! If anything is wrong, please let me know about it! :)
Answer:
Step-by-step explanation:
1. is 0.125x – 3.375
2. 0.6x – 5
3. 0.89x-5
Just use a slope calculator and desmos to see if your answer is right. Also a rounding calculator if the answer for one is too long, example: the third one said 0.88888888888889 for the first number so i rounded that to 0.89 to make sure it doesnt look like a computer did it
I think that It will be symmetric about x axis
Answer:
The probability is 0.31
Step-by-step explanation:
To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.
In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is , where . We have that
Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in
So the probability of having 3 laser printers and 3 inkjets is given by