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).

Expert Solution

milcah answered 2 years ago

(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)

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.

1)Find the equation for output F as a sum of minterms: Inputs A, B, C Output...

1)Find the equation for output F as a sum of minterms: Inputs A, B, C Output F 000 1 001 0 010 0 011 0 100 1 101 1 110 0 111 1 2)Find the equation for output F in sum of product form: 3)Find the equation for output F as a product of sums: 4

a)Find the value or values of c that satisfy the equation f(b)-f(a)/b-a = f′(c)in the conclusion...

a)Find the value or values of c that satisfy the equation f(b)-f(a)/b-a = f′(c)in the conclusion of the Mean Value Theorem for the function and interval. Round to the nearest thousandth. f(x) ln(x-3), [4,7] b)Suppose that c(x)=3x^3-40x^2+6844x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items. c)A rectangular field is to be enclosed on four sides with a fence. Fencing costs $6 per foot for two opposite sides,...

Find the value of a : b : c : d, if a : b = 2 : 3, b : c = 4 : 5 and c : d = 6 : 7.

Let A, B, C be arbitrary sets. Prove or find a counterexample to each of the...

Let A, B, C be arbitrary sets. Prove or find a counterexample to each of the following statements: (b) A ⊆ B ⇔ A ⊕ B ⊆ B

question 11 a, b, and c a. Find the equation of the hyperbola satisfying the given...

question 11 a, b, and c a. Find the equation of the hyperbola satisfying the given conditions. Vertices at (-12, 0) and (12, 0); focus at (3squareroot 17, 0) b. Determine whether the given function is one-to-one. If it is one-to-one, find a formula for the inverse f(x)=6x-3/6x+3 c. Solve. How long will it take for $1600 to grow to $14,000 at an interest rate of 3.7% if the interest is compounded continuously? Round the number of years to the...

(b) Find the equation of the line containing the points (2,4) and (7,19).

x y 2 4 3 7 4 8 6 16 7 19 (b) Find the equation of the line containing the points (2,4) and (7,19). (d) By hand, determine the least-squares regression line (Round to three decimal places as needed). (f) Compute the sum of the squared residuals for the line found in part (b) /(Round to three decimal places as needed). (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d)....

Prove 1. Let f : A→ B and g : B → C . If g...

Prove 1. Let f : A→ B and g : B → C . If g 。 f is one-to-one, then f is one-to-one. 2. Equivalence of sets is an equivalence relation (you may use other theorems without stating them for this one).

Let a, b, c the last three digits of your QUID. Find the dimension of the...

Let a, b, c the last three digits of your QUID. Find the dimension of the rectangular box of maximum volume that can be inscribed in the ellipsoid (x/a)^2+(y/b)^2+(z/c)^2=1 a=4, b=8, c=9

Question