8. Use divisibility tests to decide whether the given number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 11 and/or 12. YOU MUST SHOW ALL WORK TO RECEIVE CREDIT. Please put a O if the factor divides the given number and an X if it does not. 2 3 4 5 6 8 9 10 11 12 555,555,550 50,076 Show ALL work here:

Q: 15. Find the derivatives of the following functions: (a) = 20 sin 15x; (b) - tan' x: (c)-" c cos x…

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Q: Write the KKT conditions and find the optimal solution (x,y) for the following problem. Minimise 2x…

A: Given that,                Mini     2x-y2+2ysubjected to     y=-3x,                           x≤1,…

Q: Example 10.17. Apply Runge-Kutta method to find approximate value of y for x= 0.2, in steps of 0.1,…

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Q: 3 (x2 За + 2) dx 2

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Q: 2. Using left side of the divergence theorem, find the total charge enclosed in the rectangular…

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Q: Find all the roots of f (z) = 2z% + 81/3 – j81 |3D

A: Introduction: A complex number includes the imaginary number i=-1. Due to the presence of this…

Q: f(x) dx 6十x

A: The given function is fx=116+x2=16+x2-1. The chain rule of derivative is…

Q: Suppose f : N → N is an injective function on the natural numbers which, considered as a relation,…

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Q: Using the answers obtained in getting the LU decomposition, solve the following system of equations.…

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Q: If f is bounded and integrable on [a, b] sch that 1f(x) | 0).

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Q: Considering the following Linear equation set: 2x1 + 6x2 + 15x3 = -12 4x1 + 7x2 + 13x3 = -10 3x1…

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Q: The region bounded by the given curves is x = (y – 2)?, x = 1; about y = 1 %3D

A: Given: Curve x=(y-2)2, x=1. To find : Volume of resulting solid by any method about

Q: Find the value of x, if log, (x)= 5 Оа. 25 1 O b. 32 O c. 10 O d. None For the given Demand and…

A: Solution

Q: Prove that for any integer x, if x mod 3 does not divide 0, then (x2 −3x + 1) mod 3 = 2.

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Q: Find the volume of the solid enclosed by the paraboloid z = 5 + x2 + (y - 2)2 and the planes z = 1,…

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Q: There are 15 students in a class choosing between electronic copy, loose leaf and hardback text. Now…

A: Introduction: Combinatorics is a branch of mathematics that deals with counting as a means and an…

Q: Let S be the quadric with equation 36x2 – 4y2 – 922 – 36x 0. - - (a) Classify the graph of S. (b)…

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Q: ди I Example 11.9. Solve in 0 <x < 5, t 2 0 given that u(x, 0) = 20, u(0, t) = 0, u(5, t) = 100.…

A: Here, we need to use Crank-Nicholson Method.

Q: 13 I. Evaluate each. 6. C, C, C,

A: The general formula for combination is nCr = (n!)/((r!)×(n-r)!) Then 8C2 = (8!)/((2!)×(6!)) and  6C2…

Q: Example 11.3. Given the values of u(x, y) on the boundary of. the square in the Fig. 11.7, evaluate…

A: Here we need to use  a) Jacobi's Method b) Gauss-Seidal Method

Q: 4. (a) Define f : R×R→R×R by f(x,y) = (2x – y, x – 2y). Prove that f is one-to-one. Describe f-1.…

A: We will use the basic knowledge of functions and set theory to answer both the parts of this…

Q: Vicky and Louie go to Xtreme Xpresso for lunch. Vicky order 2 fries and 3 pasta and the total bill…

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Q: Answer the following questions for the graph G below: (1) Find a vertex cover for G. (2) Is V={a, c}…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 7. Find ſxsec¯'xdx using integration by parts made simple or otherwise.

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Q: 3 Let f(x) = 4.x² 5 and g(x)= 3.x + 7, find. -

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Q: Find the minimum value of q(x) = x" x subject to the condition ||x|| = 1. %3D Select one: O A. 2 -…

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Q: Find the general solution: yy" = 2(y')². Select one: O a. Y cos (x)x + e2" sin (x)x ln sin x O b. y…

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Q: Let C2 be the curve defined by R(t) = (t² +t + 3, 4t – 5, 2+ t – t2), t e [0, 1]. %3D | (x + y+ 2)…

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Q: Consider the solid region S that lies under the surface z= 2x? Vy and above the rectangle R= [0, 2)…

A: we will find cross section area in terms of corresponding variable and then apply limit into it . To…

Q: Use the appropriate technique of integration to compute the following antiderivatives.

A: Solution

Q: Example 10.20. Using Milne's method find y(4.4) given 5xy' + y2- 2 = 0 given y(4) = 1, y(4.1)% 3…

A: Given that 5xy'+y2-2=0 and xi 4 4.1 4.2 4.3 yi 1 1.0049 1.0097 1.0143 Find y4.4 using…

Q: 16 Use the properties of logarithm to simplify the following expressions. a) In e0.001 b) eln r? c)…

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Q: transform of the signal

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Q: Let V = R'and let H be the subset of V of all points on the plane 5r + 2y + 7z = 10. Is Ha subspace…

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Q: 7. Consider two enzymes A and B, which are not related. However, the two enzymes coincidentally…

A: Consider two enzymes A and B, which are not related. However, the two enzymes coincidentally share…

Q: Rowena would like to invite 7 friends to go on a trip but has room for only 4 of them. In how many…

A: Here we can use combinations to find the required number of ways. We can choose r things out of n in…

Q: What is true about alternate interior angles? They have equal angles. O Their angles sum up to 360…

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Q: 9. : (y²dx + x²dy) = 0 (x – y)²

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Q: Prove that whenever x ∈Zand d ∈Z+, if d does not divide (x2 −3x), then x mod d does not divide 3

A: The given statement is False.  Consider, x = 5 and d = 4. Then we see, x2 - 3x = 52 - 3x5…

Q: onsider the theorem: “for any integer x, if x mod 6 = 5, then (x2-2x+4) mod 4 = 3.” (a) Give an…

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Q: 5 + 5x – 4) dx

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Q: 15. A letter is chosen from the English alphabet. What is the probability the letter is a consonant…

A: There are 26 English alphabet.Out of which 5 are vowels i.e. a,e,i,o,u. and all other 21 are…

Q: For the differential equation y" + 4y + 4y = x² Part 1: Solve the homogeneous equation The…

A: The given differential equation is y''+4y'+4y=x2 To find: the solution of differential equation.

Q: I Example 10.30. Using Runge-Kutta method, solve y" = xy2-y2 for x decimal places. Initial…

A: Here we use the fourth order Runge kutta method for second order differential equations. We use y'=z…

Q: z.)

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Q: Let u and v be non-zero vectors in 3-space. Prove that u and v are perpendicular if and only if |u…

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Q: Test for an extremal of the functional F[y(x)] = |,´(y'² - y?)dx, y(0) = 0, y = 1 2 0,

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Q: a) Three Sets Å, B and c. EXER:2ト_xS Ex ER: X S 23 EXER: -2 Ź x <3} Fallaws. 4. are A = R £QUIRED…

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Q: A box contains 8 blue balls, 6 white balls, and 4 black balls. In how many ways can we select 4…

A: Here we can use combination to find the number of ways of drawing r balls out of n given choices.…