<span>It might be helpful to remember that the definitions of R2 and R3 are not geometric at all. R2 is the set of all ordered pairs of real numbers, whereas R3 is the set of all ordered triples of real numbers. W is a subspace fo R3, and so it still consists of elements which are triples, not pairs.
The fact that R2 and W can be visualized with the same geometric picture, namely the xy plane, is one way to see in a concrete way the isomorphism which the second poster refered to.</span>
QUESTION 1
The given logarithm is
We apply the power rule of logarithms;
We now apply the product rule of logarithm;
QUESTION 2
The given logarithm is
We apply the power rule of logarithm to get;
We apply the product to obtain;
We apply the quotient rule;
Answer:
Katie won't have more than 100 seashells until the 6th day.
Step-by-step explanation:
No. of seashells to be collected = 100
Initial number of seashells in the collection = 34
No, of seashells found each day = 12
So, number of seashells collected in d days = 12·d
Total number of seashells collected after d days = 34 + 12·d
Number of days needed by Katie to save more than 100 seashells :
34 + 12·d > 100
Subtracting 34 from both the sides
⇒ 12·d > 66
⇒ d > 5.5
Hence, Katie won't have more than 100 seashells until the 6th day.