Discrete Math Let a be an odd integer. Show that (a) 8 | a^2 − 9; (b) 16 | a^4 − 81.

Q: Determine the Laplace transform o sin (8t + 붕). +64 -a +(a) #() +64 +64 O 43 #() 2+64 O 4v3 7+64 +(a...

A:

Q: log x Find the maximum value of - 0 <x <∞

A: Note: Let the function f(x) has a local maximum value at x=a, then f'(a) =0 and f''(a)&lt;0.  Let th...

Q: Q. 8. A gas cooking range is available for Rs. 2500 cash or for Rs. 520 cash down payment followed b...

A:

Q: Solve the congruence x6 ≡ 4mod(23) by using the primitive root a = 5. There are two solutions..

A:

Q: Problem 1. Find a* that maximizes the following functions: i) f(x) = x (2-x) where r ER (i.e., no co...

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since th...

Q: Apply the Chain Rule to find the tangent line to f(x) = 4/2x – 6e²-*at x = 2

A: The given problem is to find the tangent line to the given function at given point x=2 Given f(x)=4√...

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your f(t) = t2 + 2t - 4 L{f(t)}

A:

Q: Show that gcd(a,n)=1 if these exist m and k such that ma+nk = 1.

A:

Q: Consider the following optimization problem: Prime Paints manufactures two types of paints, one for ...

A: We will construct a linear programming problem according to the given conditions. Let x ton and y to...

Q: 7. (a) cosh?1 (b) 2 sinh² 20

A:

Q: Let S ⊆ N, and for any c, d ∈ N, consider a relation R such that cRd if and only if there exists a ∈...

A:

Q: W= sin (xyZ) %3D find: Wx Wx z Wxy

A:

Q: Simplify the expression xyz + x’y + x’y’

A: We have to simplify the expression xyz+x'y+x'y'.

Q: III. INTEGRATION A. Express the null hypothesis H, and the alternative hypothesis H, in notation for...

A: 1. The mean annual income of workers who are college graduates is greater than Php 100,000 a year Th...

Q: Question 3: Let (M, d) be a discrete metric space. Give explicitly a simplified expression for the f...

A:

Q: na approxim Uf the polync p (z) = 25 + 24 – 5 z3 – 4 and enter them in the box below. Your approxima...

A: Since there is the power of 5 and coefficient is positive,  p(z)=z5+z4-5z3-4 There will be two real,...

Q: Question 3: Let ť = |1 a) Is there any linear transformation L such that L(u) = v and L(w) = t? If y...

A: For any finite dimensional vector space, any linearly independent subset can be extended to a basis ...

Q: Show proof of the following. Provide all derivations used. 1. The coefficient of kurtosis of a norma...

A:

Q: 2. (a) 41e-2 (b) te- -3t

A:

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Maxi...

A:

Q: The function f: Z3 → Z denotes a function that maps an ordered tuple onto an integer. Consider such ...

A:

Q: Find the solution of the equation cos y which tends to zero as x → o and has the value cos y when x=...

A:

Q: certain differential equation has the form f(x)dx + g(x)h(y)dy = 0. th none of the functions f(x), g...

A: We have to prove that given statement .

Q: Allison wants to pay off the loan on her jet ski that she has owned for 18 months. Allison's monthly...

A: Given,  Allison's monthly payment is $284.67 Loan duration :- 2 years (24 months)  Annual rate :- 8....

Q: y'=loga (Zy -4y +5) %3D by U =Zx-4y +5 7(2)

A: If we want to change the variable of the differential equation for find solution easily from previou...

Q: In each of the following cases, determine whether a significant degree of rank correlation exists, u...

A:

Q: Consider the pair of differential equations dx dy 1- Y, dt = x² – y?. dt (a) Find all the equilibriu...

A:

Q: Please write if the set that is given is a semigroup or a monoid or a group of none of all wi consid...

A:

Q: If f(x) = x -5x +6, find (i) f (0), (ii) f(a), (iii) f(-2)

A: given f(x)=x^2-5x+6

Q: GOO (500 -c) 0.09 (07.0)(0.85) (0)(20) 1536T C= 300.2929976

A:

Q: Consider the following 3 dimensional equation 3ェる Write down implicit difference equation for above ...

A: Considered the 3-dimensional equation, i.e ?2p?x2+?2p?y2+?2p?z2=?p?t                        ...

Q: Result n! Sn has !... dn! permutations of kype [14igt nt]

A:

Q: Try this: Solve the following DE. 1. (x2 + y2)dx + x(x- 2y)dy = 0

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2, sh...

A:

Q: log (a cos 0+b sin 6) do=w log ,a>0, b>0 2

A:

Q: Graph f(x). Identify the domain and range of f(x). Choose the correct graph of f (x). OA. OB. y= fx)...

A:

Q: The object shown in the figure is axially symmetric and its curved surface is described in cylindric...

A: The given problem is to find the volume of the given surface described in cylindrical coordinates r=...

Q: Provide the steps and reasons to establish the following logical equivalence: [(-p v ¬4)→ (p^qar)]ep...

A: To establish the logical equivalences of the following: A. ¬p∨¬q→p∧q∧r⇔p∧q B. p∧¬q→r∧r∨¬q∨r∧s∨r∧¬s⇔p

Q: The activity in the credit card account of Mara for one billing period shows the following transacti...

A:

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: odulo 26 Arithmetic this part of the project, we will learn what is arithmetic and linear algebra mo...

A:

Q: APPIOXimate e)sinl3?)cba with h=05-using the ComPosite Simp son 3 fue (a) 72 b) 88545. (O one of he ...

A:

Q: 3. Consider the following simple statements. p: The boxing game will be shown on GMA network. q: The...

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for yo...

Q: (c) Solve the difference equation Yt+2 - 4Y¢+1 + 4Y; = 2(2') + t² Given initial values Yo = 2 and Y,...

A: Using Z-transform

Q: Solve the initial value problem y" + 2y' + 3y = H(t – 4) y(0) = y'(0) = 0

A:

Q: A. The sequence of the multiples of 7. Step 1: 1. 2 3 4 nth term (u) value Step 2: %24 Step 3: Condi...

A: A Given statement is "The sequence of the multiples of 7" First complete the table, which is given b...

Q: The Bernoulli equation is a differential equation of the form y'(x) = p(x)y(x) + q(x)[y(x)]",n± 0, 1...

A:

Q: 1. Consider the following 3 x 3 matrices, [4 1 31 2 1 41 A = 0 -2 1 B = -1 3 13 3 2 5. (a) Calculate...

A:

Q: log x Find the maximum value of 0<x <∞ X

A:

Q: a) Find the center of mass of the unit square if p(x, t) = 3 – 2P,P2 P1 r = Position vector m 2 b) W...

A: To find: The value of density of the unit square if its center of mass is at the point 0.5,0.5.