Prove 10^47+67 is not a prime(use Fermat's). Thank you :)

Q: I'h[f(xo) + f(xi) hip. + fino T p1- 호 Fer

A: We derive the trapezoidal rule for approximating                               ∫abf(x)dx

Q: 8. Let F be a field and let f(x) be an irreducible polynomial in F[x] Then if the characteristic of…

A: Let f(x) be an irreducible polynomial in Fx. The characteristic of F is zero. To show: f(x) has no…

Q: Determine why dx converges or diverges.

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Q: Let F be a field, then every polynomial of positive degree in F[x] has a splitting field.

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Q: ters represent 2 × .7?

A: Given as,

Q: Consider the following. B = {(0, -1, -2), (4, 1, 2), (12, 3, 7)}, B' = {(−3, −2, −6), (2, 1, 3), (2,…

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Q: (a) Find the intervals where f(x) is increasing and decreasing. Hence, find the local maxima and…

A: Note: As per our policy, we are allowed to answer only first two part of question kindly post…

Q: Example 10.26. Using Picard's method, find approximate values of y and z corre- sponding to x = 0.1,…

A: Problem is solved using picard's method.

Q: Suppose that f and g are both continuous functions. Also f, g € [a, b] and that f= fg. Prove that 3c…

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Q: 2. Let N (x) be the statement "x has visited North Dakota," where the domain consists of the…

A: We have Nx is "x has visited North Dakota" Now, the universal quantifier ∀x Nx means that the…

Q: Determine the convolution of the following signals using z-transform: 1,(0)-(-)-(4-1). 20)-[1-()*1.0…

A: As per the question we are given two discrete signals x1(n) , x2(n) And we have to find their…

Q: 1) 2-log₂ y = 2log₂ (x+y) log₂ (x+y)+ log₂ (x² − xy + y²)=1

A: We have to solve given problems:

Q: Consider √(x- ·S= x-m+ 3x5 3x4+6x³-3x² - 6x A B C + + x-1 x+1 x+m A) 5 B) 6 C) 17/6 14/3 -dx. Using…

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Q: This figure IS drawn to scale. If the radius of the circle is given by the expression (2x-4), what…

A: The very first task is to find the radius of the circle.

Q: 2y"-3y"- 3y + 2y = (e*+ex)²

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Q: 26 p44 dxdy xy A

A: FIND THE integral value USING SIMPSON RULE

Q: the volume of the solid in the first octant bounded by using z = 1+x² + y² and z = 4 using…

A: The volume is the amount of space occupied by the closed surface. It is measured in terms of the…

Q: H) A class contains 10 students, 6 boys and 4 girls. We need to pick 3 students to represent the…

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Q: Example 10.15. Apply Runge-Kutta fourth order method to find an approximate value of y when x = 0.2…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Solution : Area calculation between the curves, y=x(x-4)(x-6) and y=0 Intercepts of cubic equation…

Q: is R* is contractible?

A: This is a problem of Topology.

Q: 3. Find the volume of the solid formed by revolving the region formed by the curve y = secx about…

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Q: 2°) Write the volume integral of the solid bounded by 2 = √√√ x² + y²² and Z=√√2-x²-y²², in a)…

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Q: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: Pandas are an endangered species. Currently (2021) their world-wide population is 3,500. Their…

A: As per company guidelines i am solving first three sub-parts. The exponential decrease is defined by…

Q: Q1) Given the equations: 10x1 +2x2x3 = 27 -3xl-5x2+2x3 =-61.5 x1 + x2 +6x3 = -21.5 (a) Solve by…

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Q: Use separation of variables to find a product solution to the following ди ди = дх ду И=c - (;) Pu=q…

A: Partial differential equation is a differential equation in which there is one independent variable…

Q: If F is a finite field of characteristic p, then aap is an automorphism of F.

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Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

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Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)^2 = 2y,…

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Q: Use Fermat's Little Theorem to compute 51990 mod 7.

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Q: Given two functions, what can be said of the continuity of their sum? Their product? Their quotient?…

A: Let f and g are continuous function on I ( subset of real number)  ,then i) f + g is also continous…

Q: Consider the following game and the direct correlation device. Show that the device is a correlated…

A: Solution:As we can see that A1  is the best response to P1's arrangement, though P2 is best response…

Q: Example 8.10. Evaluate Sº (ii) Simpson's 1/3 rule, (iii) Simpson's 3/8 rule, dx Jo. 1 + x² by using…

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Q: Solve for x. All final answers must be in Znwhere n is the modulus.   x+ 2 mod 9 ≡ 0

A: We have given that ,  x + 2 mod 9 ≡ 0 We need to find the value of x under modulus 9. We know that…

Q: Q1/ If you have the following data: Sin 45° = 0.7071, Sin 50° = 0.7660, Sin 55° = 0.8192, Sin 60° =…

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Q: Use your learning on exponential functions to answer the following: 1. You take out Php 20,000 loan…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let X and Y be two topological spaces. X is connected and Y is disconnected are they homotopy…

A: Homotopy equivalence  Two topological spaces X and Y are said to be Homotopy equivalent if there…

Q: Rearrange lim x* so that we can apply L'hopital's rule. *→0+

A: Follow the steps.

Q: d plans to increase output eks 1; 5; 10; 15. Estimate t

A: Here company A increase its production by 200 each week and company B increase its production by…

Q: B: 2: Find the first 4 terms of the Taylor series for : f(x)=sin лx near a=0.5

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Q: Given that A and B is a group. Find out if : A→B is a homomorphism. If it is a homomorphism, also…

A: We have given a map ,  ϕ : A → B , where A = ℝ , +   ,  B = ℝ* , · such that  , ϕx = 2x We know that…

Q: The universal relation A x A on A is an equivalence relation anti-symmetric a partial ordering…

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Q: Prove that span (v1,v2,...,vn) is a valid subspace of R

A: Let V = R is a vector space. Let S = v1 , v2 , ..... , vn We need to show that   span(S)  is…

Q: ds dt dQt dt dP dt = μ-μP-BPS, :-(µ + y) S + BPS + αSQ₁ = = −µQ₁ - αSQ₂ + y(1-0) S.

A: As per the question we are given a population model in terms of dynamic system. And we have to find…

Q: The following data define the sea-level concentration of dissolved oxygen for fresh water as a…

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Q: A vector is said to be conservative when it's: curl equal to zero Laplacian equal to zero divergence…

A: We know that ,  A conservative vector field , is a vector field  F  whose line integral  ∫C F·ds…

Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive…

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