Derive/prove following relations: a) (A x B) (C × D) = A· [B x (C x D)] = A• [(B. D)C - (B. C)D] (A. C) (B D) – (A D) (B C) |

Q: du - 2 yco tex a 2CSC 2X

A:

Q: Show that 2 (-r × B)² = (r² B² – (r. B)²) And, further that r² B² (r. B)² = B² (x² + y²) - If B = B₂

A:

Q: (x + 2)2 + (y + 1)2 =

A: Use the formula a+b2=a2+b2+2ab (x+2)2=x2+22+2(x)(2) =x2+4+4x Also, (y+1)2=y2+12+2(y)(1) =y2+1+2y So,…

Q: Are any of these expressions are valid? State your reason for each. If an expression is invalid, you…

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Q: Find two positive numbers a and b such that 2a + 3b = 1 and so that a3 + b2 is as small as possible.

A: Find  two positive numbers a and b such that 2a + 3b =1 and so that a3  + b2  is a small as…

Q: 3) Use the functions f(x)= 12 - 2x and g(x) = 4x² – x – 7 to evaluate the following: %3D a) f(4) b)…

A: The given functions are fx=12-2x,gx=4x2-x-7.

Q: 5. Let P(x) be the statement "x spends more than five hours every weekday in class," where the…

A: Introduction: Quantification is the application of numerical indicators to the subject or predicate…

Q: 1. Find a b (a) a =, b = (b) a =, b = (c) a= 27 +3j - 4k, b = i-3j+k

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Q: Evaluate the function f(r) = √(r + 6) + 3 at the given values of the independent variable a. f(-6)…

A: a). Put r = -6 in f(r), we get b). Put r = 10 in f(r), we get

Q: 2. Find the V.A and H.A r(x) = 2+2x+3 x2-5x V.A- H.A-

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Q: Find the real numbers x and y if  2x –i = 6 + ( 1 – y )i

A: Given that  2x –i = 6 + ( 1 – y )i Find the real numbers x and y if

Q: b. 3+V5-x 3I

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Q: 3x Evaluate x² +¹+e³ª)dx.

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Q: Find (u + v) ∙ (2u − v) when u ∙ u = 4, u ∙ v = −5, and v ∙ v = 10.

A: u·u=4,  u·v=-5  &  v·v=10

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.