Every week, Mr. Kirkson uses 3 1/6 gallon of water to water every 1/3 square foot of his garden. How many gallons of water does
2 answers:
Answer:
Mr. Kirkson uses 9.60 gallons of water per square foot to water his garden each week.
Step-by-step explanation:
This problem can be solved by a simple rule of three.
We have that 1/3 = 0.33 square foot of his garden uses uses 3 1/6 = 19/6 = 3.167 gallons of water. How many are used per square foot? So:
1 foot - x gallons
0.33 foot - 3.167 gallons
Mr. Kirkson uses 9.60 gallons of water per square foot to water his garden each week.
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ANSWER
450lb
EXPLANATION
If the weight, m of an object on the moon varies directly as the weight of an object e, on the earth, then we can write the mathematical statement,.
We introduce the constant of proportionality to obtain,
When, m=95, e=570,
This implies that,
The equation now becomes,
We want to find e, when m=2700,
450lb
EXPLANATION
If the weight, m of an object on the moon varies directly as the weight of an object e, on the earth, then we can write the mathematical statement,.
We introduce the constant of proportionality to obtain,
When, m=95, e=570,
This implies that,
The equation now becomes,
We want to find e, when m=2700,
Answer:
See the proof below.
Step-by-step explanation:
What we need to proof is this: "Assuming X a vector space over a scalar field C. Let X= {x1,x2,....,xn} a set of vectors in X, where . If the set X is linearly dependent if and only if at least one of the vectors in X can be written as a linear combination of the other vectors"
Proof
Since we have a if and only if w need to proof the statement on the two possible ways.
If X is linearly dependent, then a vector is a linear combination
We suppose the set is linearly dependent, so then by definition we have scalars
in C such that:
And not all the scalars are equal to 0.
Since at least one constant is non zero we can assume for example that , and we have this:
We can divide by c1 since we assume that and we have this:
And as we can see the vector can be written a a linear combination of the remaining vectors
. We select v1 but we can select any vector and we get the same result.
If a vector is a linear combination, then X is linearly dependent
We assume on this case that X is a linear combination of the remaining vectors, as on the last part we can assume that we select and we have this:
For scalars defined in C. So then we have this:
So then we can conclude that the set X is linearly dependent.
And that complet the proof for this case.