Let {u1,u2,u3} be an orthonormal basis for an inner product space V. If v=au1+bu2+cu3
is so that ∥v∥=42, v is orthogonal to u3, and ⟨v, u2⟩=−42, find the possible values for a, b, and c.

Hillel is juggling flaming torches to raise money for charity. his initial appearance raises $500\$500 $500 , and he raises $15\$15 $15 for each minute of juggling performance. the amount rr r of money hillel raises is a function of tt t , the length of his performance in minutes. write the function's formula.

17. a researcher measures three variables, x, y, and z for each individual in a sample of n = 20. the pearson correlations for this sample are rxy = 0.6, rxz = 0.4, and ryz = 0.7. a. find the partial correlation between x and y, holding z constant. b. find the partial correlation between x and z, holding y constant. (hint: simply switch the labels for the variables y and z to correspond with the labels in the equation.) gravetter, frederick j. statistics for the behavioral sciences (p. 526). cengage learning. kindle edition.

At the beginning of 1974/75,2 years a man invested #2000 in a bank at 12.5% compound interest, if it degree #650 at the end of each two years to pay his son's school fees, after payment of interest to pay his son's school fees, how much did he have left at the beginning of the 1978/79 school year?