An edge of Cube A is 8 inches, and an edge of Cube B is 5 inches. To the nearest tenth, how many times greater is the volume of
1 answer:
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Answer:
Step-by-step explanation:
<u>Linear Combination Of Vectors </u>
One vector is a linear combination of
and
if there are two scalars
such as
In our case, all the vectors are given in but there are only two possible components for the linear combination. This indicates that only two conditions can be used to determine both scalars, and the other condition must be satisfied once the scalars are found.
We have
We set the equation
Multiplying both scalars by the vectors
Equating each coordinate, we get
Adding the first and the third equations:
Replacing in the first equation
We must test if those values make the second equation become an identity
The second equation complies with the values of and
, so the solution is
Answer:
The minimum possible initial amount of fish:
Step-by-step explanation:
Let's start by saying that
= is the initial number of fishes
John:
When John arrives:
- he throws away one fish from the bunch
- divides the remaining fish into three.
- takes a third for himself.
the remaining fish are expressed by the above expression. Let's call it John
and simplify it!
When Joe arrives:
- he throws away one fish from the remaining bunch
- divides the remaining fish into three
- takes a third for himself.
the remaining fish are expressed by the above expression. Let's call it Joe
and simiplify it
since we've already expressed John in terms of x, we express the above expression in terms of x as well.
When James arrives:
We're gonna do this one quickly, since its the same process all over again
This is the last remaining pile of fish.
We know that no fish was divided, so the remaining number cannot be a decimal number. <u>We also know that this last pile was a multiple of 3 before a third was taken away by James</u>.
Whatever the last remaining pile was (let's say ), a third is taken away by James. the remaining bunch would be
hence we've expressed the last pile in terms of n as well. Since the above 'James' equation and this 'n' equation represent the same thing, we can equate them:
L.H.S must be a Whole Number value and this can be found through trial and error. (Just check at which value of n does 2n/3 give a non-decimal value) (We've also established from before that n is a multiple a of 3, so only use values that are in the table of 3, e.g 3,6,9,12,..
at n = 21, we'll see that 2n/3 is a whole number = 14. (and since this is the value of n to give a whole number answer of 2n/3 we can safely say this is the least possible amount remaining in the pile)
by solving this equation we'll have the value of x, which as we established at the start is the number of initial amount of fish!
This is minimum possible amount of fish before John threw out the first fish