A local grocery store charges for oranges based on weight as shown in the graph below. Find the price (dollars per kilogram) of
oranges at the grocery store.
2 answers:
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Answer:
1. Yes.
2. No.
3. Yes.
Step-by-step explanation:
Consider the following subsets of Pn given by
1.Let W1 be the set of all polynomials of the form , where a is in ℝ.
2.Let W2 be the set of all polynomials of the form , where a is in ℝ.
3. Let W3 be the set of all polynomials of the form , where a is in ℝ.
Recall that given a vector space V, a subset W of V is a subspace if the following criteria hold:
- The 0 vector of V is in W.
- Given v,w in W then v+w is in W.
- Given v in W and a a real number, then av is in W.
So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.
- First property:
Note that for W2, for any value of a, the polynomial we get is not the zero polynomial. Hence the first criteria is not met. Then, W2 is not a subspace of Pn.
For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.
- Second property:
W1. Consider two elements in W1, say, consider a,b different non-zero real numbers and consider the polynomials
.
We must check that p_1+p_2(t) is in W1.
Note that
Since a+b is another real number, we have that p1(t)+p2(t) is in W1.
W3. Consider two elements in W3. Say . Then
So, again, p1(t)+p2(t) is in W3.
- Third property.
W1. Consider an element in W1 and a real scalar b. Then
.
Since (ba) is another real scalar, we have that bp(t) is in W1.
W3. Consider an element in W3 and a real scalar b. Then
.
Since (ba) is another real scalar, we have that bp(t) is in W3.
After all,
W1 and W3 are subspaces of Pn for n= 2
and W2 is not a subspace of Pn.
Answer:
Campsites be chosen in 680 ways.
Step-by-step explanation:
Given:
Number of campsites= 17
Number of campsites that are to be occupied=3
To Find:
Number of ways can the campsites be chosen=?
Solution:
Combination:
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
nCr = n(n - 1)(n - 2) ... (n - r + 1)/r! = n! / r!(n - r)!
No of ways in which campsites can be chosen= 17C3
=>
=>
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=>680