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:
I think it is 441
Step by step explanation:
To make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. So there would be 91 squares and 441 rectangles.
Answer:
6.25 pounds
Step-by-step explanation:
The number of pounds of water the bucket holds is ...
pounds/bucket = (2.5 pounds)/(0.4 bucket) = 6.25 pounds/bucket
Answer:
24 counslers.
Step-by-step explanation:
We can simply break down the equation.
We can start by finding how many times 7 goes into 84. 84/7 is 12. Now their are 12 groups of 7 and their needs to be two at each. All we have to do is multiply 2 by twelve and you've got yourself an answer.
Have A great day! :)
Answer:
12m²
Step-by-step explanation:
For a rectangle, with length L and width W,
the perimeter is given as
Perimeter,
P = (2 x Length) + (2 x Width)
P = 2L + 2W
It is given that the perimeter is 48, hence
48 = 2L + 2W (divide both sides by 2)
24 = L + W
or
L = 24 - W -----> eq 1
Also realize that the Area of a Rectangle is given by
A = L x W -----> eq 2
Substituting eq 1 into eq 2,
A = (24 - W) x W
A = -W² + 24W
Recall that for a quadratic equation y = ax² + bx + c, the maxima or minima is given by y(max) = -b/2a
In this case, b = 24 and a = -1
-b/2a = -24/[ 2(-1) ] = 12
Hence for A to be maximum A(max) = 12m² (Answer)
