and 10.6 is already written as a decimal.
Answer:
Step-by-step explanation:
Represent the length of one side of the base be s and the height by h. Then the volume of the box is V = s^2*h; this is to be maximized.
The constraints are as follows: 2s + h = 114 in. Solving for h, we get 114 - 2s = h.
Substituting 114 - 2s for h in the volume formula, we obtain:
V = s^2*(114 - 2s), or V = 114s^2 - 2s^3, or V = 2*(s^2)(57 - s)
This is to be maximized. To accomplish this, find the first derivative of this formula for V, set the result equal to 0 and solve for s:
dV
----- = 2[(s^2)(-1) + (57 - s)(2s)] = 0 = 2s^2(-1) + 114s - 2s^2
ds
Simplifying this, we get dV/ds = -4s^2 + 114s = 0. Then either s = 28.5 or s = 0.
Then the area of the base is 28.5^2 in^2 and the height is 114 - 2(28.5) = 57 in
and the volume is V = s^2(h) = 46,298.25 in^3
Answer:
810 is 100 times the size of 0.81
Answer:
-12
Step-by-step explanation:
We start with the equation: 
Substitute the variables: 
Solve using order of operations (start with multiplication): 
And then addition/subtration: 
There are many ways to solve number 5 as it is just an reduce/enlargement of equidistant fractions
The first method that came up to my mind is just dividing denominators.
For A) you can do 72 divided by 18 which would give you 4. Then you can divide the given numerator with the answer you got from dividing the denominators. This would be 8 divided by 4 which would give you two. This means that 2/18 is equal to 8/72. You can check by simplifying the fraction. Both 2/18 and 8/72 equal 9 when simplified, therefore correct.
You can use this method for b, either use a calculator because of the decimals or just remove the decimals and replace them later. Make sure when you use this method, you are always dividing the bigger number. So in B you would do 40.3 divided by 12.4
