Answer:
bucket of water = 50.397 lbs
Step-by-step explanation:
Pi(r^2)(h) = volume
3.14(6^2)(12) = 1356.48 in^3 = volume of bucket
one ft^3 = 12 x 12 x 12 = 1728 in^3
1356.48/1728 = 0.785 ft^3 (volume of bucket)
0.785(64.2) = 50.397 lbs
It's the first one. y = 3x
proportional means they are just some multiple of the other.
Note that if

, then

, and so we can collapse the system of ODEs into a linear ODE:


which is a pretty standard linear ODE with constant coefficients. We have characteristic equation

so that the characteristic solution is

Now let's suppose the particular solution is

. Then

and so

Thus the general solution for

is

and you can find the solution

by simply differentiating

.
Answer:
4. (2^6)^-5.
an number to an exponent to another exponent is multiplied
Answer:
45
Step-by-step explanation:
Let the unit place be ‘x'
Tenth place be y
The number is 10y+x
x+y = 9 (according to the condition) (1)
Digits are interchanged Unit place' y ‘& tenth place ‘ x'
New no is 10x +y
This is 9 more than the original number
10x+ y = 10y+x +9
10x-x+y-10y = 9
9x-9y= 9
x-y = 1 (dividing by 9) (2)
Adding the two equations
2x = 10
x= 5
Substituting the value of x in first equation
y = 4
The number is 45, the original number is 54 this is 9 more of the new number.