Calculus #3: 1. a) Let A = (2,4,6),B = (1,2,3) and C = (5,5,5). Find point...

Calculus #3:

1.

a) Let A = (2,4,6),B = (1,2,3) and C = (5,5,5). Find point D so that ABCD is a parallelogram.

b). Two points X and Y are colinear if they lie on the same line. Are the points A = (3,6,−1), B = (2,0,3) and C = (−1, 3, −4) colinear? Justify your answer.

Expert Solution

milcah answered 2 years ago

Let B={2,4,6} be the event that we roll an even | number. Find P(B) and type...

Let B={2,4,6} be the event that we roll an even | number. Find P(B) and type the fraction

Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations...

Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations for the perpendicular bisectors of segments AB and BC, and coordinates for their common point K. Calculate lengths KA, KB, and KC. Why is K also on the perpendicular bisector of segment CA?

3. Let A = D + 1, B = D − 3, C = D +...

3. Let A = D + 1, B = D − 3, C = D + x, where D = dx. Calculate the differential operators AB, BC, CA and their effect on y(x) = e^3x

A)Let S = {1,2,3,...,18,19,20} be the universal set. Let sets A and B be subsets of...

A)Let S = {1,2,3,...,18,19,20} be the universal set. Let sets A and B be subsets of S, where: Set A={3,4,9,10,11,13,18}A={3,4,9,10,11,13,18} Set B={1,2,4,6,7,10,11,12,15,16,18}B={1,2,4,6,7,10,11,12,15,16,18} LIST the elements in Set A and Set B: { } LIST the elements in Set A or Set B: { } B)A ball is drawn randomly from a jar that contains 4 red balls, 5 white balls, and 9 yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) PP(A...

part a . Let A = {1,2,3,4,5},B ={0,3,6} find 1. A∪B 2. A∩B 3. A\B 4....

part a . Let A = {1,2,3,4,5},B ={0,3,6} find 1. A∪B 2. A∩B 3. A\B 4. B \ A Part b . Show that if A andB are sets, (A\B)⊆A 2. A∪(A∩B)=A Part c. Determine whether each of these functions from Z to Z is one-to one 1. f(x)=x−1 2. f(x)=x2 +1 3. f(x) = ⌈x/2⌉ Part c. Let S = {−1,0,2,4,7}, find f(S) if 1. f(x)=1 2. f(x)=2x+1 3. f(x) = ⌊x/5⌋ 4. f(x)=⌈(x2 +1)/3⌉ Part D. Determine whether...

7. Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5). (a) Find an equation...

7. Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5). (a) Find an equation for the plane that passes through these three points. (b) Find the area of the triangle determined by these three points. 8). Find an equation of the tangent plane to the surface z = x at (−4, 2, −1).

Let A, B and C be events. Express for k = 0, 1, 2, 3, the...

Let A, B and C be events. Express for k = 0, 1, 2, 3, the probabilities that: a) Exactly k of events A, B and C occur. b) At least k of events A, B and C occur.

(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then a∣c. (B) Let p ≥ 2....

(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then a∣c. (B) Let p ≥ 2. Prove that if 2p−1 is prime, then p must also be prime. (Abstract Algebra)

Let S = {1,2,3,...,10}. a. Find the number of subsets of S that contain the number...

Let S = {1,2,3,...,10}. a. Find the number of subsets of S that contain the number 5. b. Find the number of subsets of S that contain neither 5 nor 6. c. Find the number of subsets of S that contain both 5 and 6. d. Find the number of subsets of S that contain no odd numbers. e. Find the number of subsets of S that contain exactly three elements. f. Find the number of subsets of S that...

Let X = {1, 2, 3, 4}, Y = {a, b, c}. (1) Give an example...

Let X = {1, 2, 3, 4}, Y = {a, b, c}. (1) Give an example for f : X → Y so that ∀y ∈ Y, ∃x ∈ X, f(x) = y. 1 2 (2) Give an example for f : X → Y so that ∃y ∈ Y, ∀x ∈ X, f(x) = y. (3) Give an example for f : X → Y and g : Y → X so that f ◦ g = IY

Question