dy pronounced 'dee y by dee x' was developed by Leibniz in 1684. The notation, dx This is popular than Newton's notation, which is x, pronounced 'x dot' sometimes we called this time derivative. There are also other notations for the derivative f'(x), pronounced f dashed x'. The derivative describes the rate of change of one quantity with respect to another. The laws of physical sciences and engineering can be described in the language of calculus because lots of these laws are based on instances of a rate of change. Answer all the practical questions below using your knowledge on differential calculus. (i) The current I through an inductor is given by t, 0sts2 i = 2

Q: 2. Eight persons are to be assigned to two different rooms. Let A one room must have 3 persons. B…

A: Probability can be found by using combinations.

Q: Let a = (5, 4, 2) and b = (-1, -2, -3), then 3a 5b (10, 2, -9). = - Select one: O True O False

A:

Q: 2. Determine in each case whether ACB. Explain each answer in one sentence. (a) A = {0, 2, 5} and B…

A: Answer  A) A is improper subset of B

Q: 4-(3n+2) = 4(- 3n+5) %3D

A: Given : 4 - 3n + 2 = 4-3n + 5

Q: e g(-2, -7), R(1, -5), S(4, -7), T(1, -9) QRST is a

A: Please see the explanation below

Q: 1 y Let A = [1 1 2 0. and %3D -1 2 B = -1 0 Find 1 3 W AB

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Q: (D-C) n (B-A)C

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Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

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Q: Show that

A: Our Aim is to Prove that:-111abca2b2c2=a-bb-cc-a   -(i)

Q: Show that (A¹)¹ = A for: A 4 3 3 2

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Q: Evaluate s(s³ – 4) ³ -4) 3 ds Vs –10s² + 6 99. |

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Q: 5+2-5+p 13) 3. 3) 28

A: Given: The equation 53p+23=5+p2p, To determine: The value of p,

Q: If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 },C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D =…

A: Since you have asked multiple sub parts in a single request, we will be answering only the first…

Q: Hi,I am doing some practice questions and I was wondering how to go about doing the problem in the…

A: Probability of an event:The formula for probability of an event is as follows:

Q: If P( A U B) = 0.5 , P (B) = 0.2, P (A)=0.4 then || P(B|A) Is?

A: GivenP(A∪B)=0.5P(B)=0.2P(A)=0.4

Q: Find the value of n(An B) if n(A) = 10, n(B) = 13, and n(A U B) = 18. n(An B) = (Type a whole…

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Q: ave a single slot. Suppose that eight of the 20 radios are randomly selected to be stor the number…

A: Note: As per the students requirement solving b and c The probability density function of Hyper…

Q: Which of the following is equivalent to 3 - V2 O A. V2 А. O B.-V2 3- V2 O C. 3+ v2 O D.

A:

Q: Let A be a 3 x 6 matrix and suppose that the SLE Ax = b is inconsistent where b is: (-) 3 b: =…

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Q: In a certain office, 1/3 of the workers are women , 1/2 of the women are married and 1/3 of the…

A:

Q: 1. There are two boxes, each of which contains a certain number of cubes and balls, painted in…

A: Given:   Box 1 Box 2   Red Blue Red Blue Cube 6 24 28 42 Ball 14 56 12 18 Total 20 80 40…

Q: ind AxB for A = {1,2} and B = {r,s, t} %3D

A:

Q: If A= 3 6 B= then, 3A-2B= 0- 1 Select one: O a. 9-6 0 29 O b. -9-6 029 O C. 9 -6 0 31 d. 11 -6 0 29

A: We will solve the following

Q: Consider the graph below of the second derivative, f" (x), of somę function f(x). On what intervals…

A: our objective is to check the concavity of function

Q: 4 5 6 6 1 A = 2 1 1 b 3 If ronk CA) =2, a+ b = ?

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Q: [-1 2 Q5/ Let A = |-2 5 -3] 3 4 ,then the C33 is 0 1 -1 -10 -2

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Q: If n(A) = 61, n(8) = 21, and n(AN B) = 2, find n(A U B). %3D

A: Sets Question

Q: A={1,2}and B={1,5,7}find AxB

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Q: 1. If A = B = 2 - find (a) A +B, (b) A - B, (e) 2A – 3C, (d) 3A + 28 - 4C, () AB, S BA, (9) (AB)C,…

A: Note: Please repost remaining subparts as i can answer 3 subparts as per my policy.

Q: Compute A-413 and (413)A, where A = A-413 = 6 - 4 - 3 - 2 4 3 - 6 1 3

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Q: Choose the best answer O II1 ab: = ar......a O IE1 ai = a*r+. i3D1 = aLi-1 b; 1 All of the above…

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Q: 100 students were interviewed. 28 took Linear Algebra, 31 took Discrete Math, 42 took Calculus, 9…

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Q: If n(A) = 67, n(8) = 15, and n(A N B) = 9, find n(A U B).

A: Topic- sets

Q: WHAT IS O H|5 Se-5x dx 1 e -5x + C -e e-5x + C -¹e-5x + C 5 e-5x + C

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Q: 2 0 2 1 1 - 4 Let A= and B= - 4 3 0 7 5 7 Find 54– 6B.

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Q: If n(A)=40, n(B)=24, and n(A n B)=6, find n(A u B).

A: We use Venn diagram to solve the given question.

Q: Q = {E, A, A², A³, B, BA, BA², BA³} X,

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Q: C. In the picture, prove that a(a+b)=c(c+d). a

A: Given : To prove : aa+b=cc+d

Q: 3. a. b. 4 18 Simplify (11) - vw - 3 ) - ( + W + 13 - - Pvw – 16 c. 2(w) - Tw Svw + 10 d. 18 - SW +…

A: (11v2-6vw-3w2)-(-7v2+vw+13w2)=11v2-6vw-3w2+7v2-vw-13w2…

Q: d. (7, -5) h. (0, 1) c.(-8, 7) g. (7,-1) b. (-6, 6) a. (3, 8) f. (-4,-8) e. (5,-4) Part 1 out of 8…

A:

Q: If n(A) = 46, n(B) = 19, and n(A n B) = 8, find n(A u B) %3D

A: Given Data: The number of elements in set A is: n(A)=46 The number of elements in set B is: n(B)=19…