Explanation:
Since {v1,...,vp} is linearly dependent, there exist scalars a1,...,ap, with not all of them being 0 such that a1v1+a2v2+...+apvp = 0. Using the linearity of T we have that
a1*T(v1)+a2*T(v1) + ... + ap*T(vp) = T(a1v19+T(a2v2)+...+T(avp) = T(a1v1+a2v2+...+apvp) = T(0) = 0.
Since at least one ai is different from 0, we obtain a non trivial linear combination that eliminates T(v1) , ..., T(vp). That proves that {T(v1) , ..., T(vp)} is a linearly dependent set of W.
Answer:
f(7) = 158
Step-by-step explanation:
To evaluate f(7) substitute t = 7 into f(t)
f(7) = 3(7)² + 11 = (3 × 49) + 11 = 147 + 11 = 158
Answer:
21 / 143
Step-by-step explanation:
Given that:
Number of Eastern conference reps = 8
Number of western conference rep = 7
Probability of selecting 3 from Eastern reps and 2 from western reps
Probability = required outcome / Total possible outcomes
Total possible outcomes:
selection to be made = 3+ 2 = 5
Total Number of players = 8 +7 = 15
Total possible outcomes
Using combination formula :
nCr = n! / (n-r)!r!
15C5 = 15! / 10!5! = (15 * 14 * 13 * 12 * 11) / (5*4'3*2*1) = 360360 / 120 = 3003
Total possible outcomes = 3003
Required outcome :
8C3 * 7C2
8C3 = 56 ; 7C2 = 21
8C3 * 7C2 = 56 * 21 = 1176
required outcome / Total possible outcomes
= 1176 / 3003
= 21 / 143
I think you will have t use theorem
Ba=Rv^2+vo^2
Ba=4^2+7^2
Ba=16+49
Ba=65
Answer:
1st pic:
step 2.
2nd pic:
Rene should add, not multiply 2 volumes.
The correct answer is 48+216 =264
3rd pic:
a, for blue prism: V = Area of base x Height = 48 x a =720
=> a = 720/48 = 15
b, for orange prism: V = Area of base x Height = (12xb)/2 x 15 =720
=> b =(720x2)/(15x12)= 8