Answer:
1. y = sin(x²+C)
2. see below
Step-by-step explanation:
1.
separation of variables
integration both sides
you should get :
remember constant of integration!!
2. y = sin(x²+C)
3 = sin(0+C)
y(0) = 3 does not have a solution because our sin graph is not shifted vertically or multiplied by a factor whose absolute value is greater than 1, so our range is [-1,1] and 3 is not part of this range
I would use a chart to solve this problem.
This is a good wya to organize your information.
Down the left side, list the people involved.
I put Bob first and the mom second but the order doesn't matter.
Since Bob's mom is 3 times older than Bob, we can represent
Bob's age now as x and Bob's mom's age now as 3x.
Bob's age in 12 years will be x + 12 and Bob's mom's
age in 12 years will simply be 3x + 12.
Since the second sentence starts with in 12 years,
we will be using the information from our second column.
In 12 years, Bob's mom's age, 3x + 12, will be,
equals, twice of her son's age, 2(x + 12).
Solving from here, we find that x = 12.
This means that Bob's age now is 12 and his mom is 36.
The chart is attached below.
