The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Answer:
(1,2)
Step-by-step explanation:
The solution to the system is where the two lines cross.
They cross at x=1 and y=2
(1,2)
First, we need to know the smallest two digit prime number. It can't start with one, since one is not prime, so it must start with two (or be in the twenties.) 20 is divisible by 2, 4, 5, and 10, 21 is divisible by 7 and 3, 22 is divisible by 2 and 11, so the smallest prime number is 23.
Now we need the largest two-digit prime number. It cannot start with nine or eight, since both are composite, so it must start with seven (be in the seventies.) 79 is the largest integer in the seventies and also happens to be prime, so there's our largest two digit prime number.
now we just need to add them for the sum:
23+79=102
hope I helped, and let me know if you have any questions :D
Step-by-step explanation:
product=× three=3 a number is unknown =x plus=+ five=5 is=equals to 20
3×x +5=20
3x+5=20
Subtract 5 from both sides
3x+5-5=20-5
3x=15
3x/3=15/3
x=5
Answer:
$1006.20
Step-by-step explanation:
This is an example of compound interest.
To work this out you would first have to convert the percentage into a decimal, you can do this by dividing 3 by 100, which gives you 0.03. You are dividing by 100 as percentages are out of 100. Then you would add 1 to 0.03, which gives you 1.03. This is because you are finding percentage increases. Then you would multiply 894 by 1.03 to the power of 4, which gives you 1006.20. This is because you are finding 3 percent and adding it on and then finding 3 percent of that, this is why we put it to the power of how much time.
1) Divide 3 by 100.
2) Add 1 to 0.03.
3) Multiply 894 by 1.03 to the power of 4.
