Question 13 (8 points)
If logb(p)=91 and logb(q)=54, then determine
logb(pq).
Your Answer:
Question 13 options:
Answer |
Question 14 (8 points)
If logb(R)=628 and logb(X)=4, then determine
logb(R/X).
Your Answer:
Question 14 options:
Answer |
Question 13 (8 points) If logb(p)=91 and logb(q)=54, then determine logb(pq). Your Answer: Question 13 options:...
Consider the points P(0,0,9) and Q(-3,3,0). a. Find PQ and state your answer in two forms: (a,b,c) and ai + bj + ck. b. Find the magnitude of PQ. c. Find two unit vectors parallel to PQ.
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
The points p(k,2) and Q(2, 1/3) lie on the partial graph of the function f(x) = logb (x) as shown below. Find the value of K.
Question 8 1.25 points Save Answer Two charges 91 at the origin and q2 =.491 at x-151 m. What is the coordinate of point P (in meters), between the two charges on the x-axis where the electric potential is zero?
2) (4 p.) Market demand is PQ) = 40 - Q. A multi-plant monopolist operates two plants, with average cost functions AC (91) = 8 and AC2(92) = 1 +0.2592- a) Find the profit-maximizing price, total quantity and of output produced at each plant. b) Is this multi-plant monopolist allocatively efficient? Explain carefully. Do not calculate socially efficient output.
For the points P(3.4) and Q(3,5), find (a) the distance between P and Q and (b) the coordinates of the midpoint of the segment PO. (a) The distance between P and Q is, d(P,Q) = (Simplify your answer. Type an exact answer, using radicals as needed.) (b) The midpoint of the segment PQ is (Simplify your answer. Type an ordered pair. Type an exact answer for each coordinate, using radicals as needed.)
Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in
Q[x] if and only if the ideal (P, Q) of Z[x] generated by P and Q
contains a non-zero integer (i.e. Z ∩ (P, Q) ̸= {0}). Here (P, Q)
is the smallest ideal of Z[x] containing P and Q, (P, Q) := {αP +
βQ|α, β ∈ Z[x]}.
(iii) For which primes p and which integers n ≥ 1 is the
polynomial xn − p...
6. Let n be any positive integer which n = pq for distinct odd primes p. q for each i, jE{p, q} Let a be an integer with gcd(n, a) 1 which a 1 (modj) Determine r such that a(n) (mod n) and prove your answer.
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
in the direction of the vector OR. Put your answer in the Given the points P 2.3.1). Q (-1.1.2) and R (1.1.0) a) (3 pts) find an equation for the line that passes through the point form r(t) = (x(t), y(t), z(t)). b) (4 pts) find a non-zero vector normal to both Po and QR c) (3 pts) find an equation for the plane containing the points P Q and R. Put your answer in the form ax+by+cz =d.