Answer:
The general solution of the equation is y = 
+ 5
Step-by-step explanation:
Since the differential equation is given as y'(t) = 3y -5
The differential equation is re-written as
dy/dt = 3y - 5
separating the variables, we have
dy/(3y - 5) = dt
dy/(3y - 5) = dt
integrating both sides, we have
∫dy/(3y - 5) = ∫dt
∫3dy/[3(3y - 5)] = ∫dt
(1/3)∫3dy/(3y - 5) = ∫dt
(1/3)㏑(3y - 5) = t + C
㏑(3y - 5) = 3t + 3C
taking exponents of both sides, we have
exp[㏑(3y - 5)] = exp(3t + 3C)
3y - 5 = 
3y - 5 = 
3y = + 5
dividing through by 3, we have
y = + 5
So, the general solution of the equation is y = + 5
Answer:
C) [-4,0)
Step-by-step explanation:
Look at the endpoints. You have (-3,0) which isn't included in the function and you have (1,-4) which is included in the function.
We use interval notation when we are describing the subset of numbers in a function by using parentheses to show an endpoint is not included and brackets to show an endpoint is included.
In this case, since we are being asked to find the range of the function, that only pertains to y-coordinates.
Given that (1,-4) is included in the function, this means that y=-4 is included in the function. Therefore the answer's interval notation will start with a bracket to show it's included.
Given that (-3,0) isn't included in the function, this means that y=0 isn't included in the function. Therefore the answer's interval notation will end with a parenthesis to show it's not included.
Combining the two elements, we have an interval notation of [-4,0) which means C is the correct answer
Yep! It is an integer!
Any negative, positive number or 0 is an integer.
Hope it helps!
1 1/4 because the 1 would be the 1 in 1 1/4 and .25 is 1/4 so.........
1 1/4
