Suppose that a “word” is any string of five letters. Repeated letters are allowed. For our purposes, vowels are the letters a, e, i, o, and u. Please include detailed steps for this problem so I can understand.  a) How many words are there? Note – these don’t have to be valid English words. b) How many words begin with a vowel? c) How many words have only vowels?

Q: Let R be an equivalence relation on A = {0, 1, 5, 6, 8, 9} and R = {(6, 1), (1,6), (6,6), (1, 1), (0...

A:

Q: Consider the homogeneous ordinary differential equation x² dy with y(x) as a general solution. Given...

A: Cauchy differential equation

Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we w...

Q: Question 6 Find the indicated limit or state that it does not exist. lim 3 sin x (x y)-(0, 1) 01 O N...

A:

Q: ey Maximine 2.

A: This is the problem of multi variable calculus.

Q: 2.it gad Ca,b) = t, prove that god (a be) = gedca,c).

A:

Q: (6) Verify that Y, XY3,and x2y5 are integrating factor f Ydx +2xdy =o and solve. CANS 6): Xy2=C.

A:

Q: Write any formulas that can be derived using S- and l-rules. If nothing follows, write "nil". ((D v ...

A: 1)  Given the premises D∨~M⊃~AA We need to find a conclusion using S and I rules.

Q: In the following problems, the letters A to Z correspond to the numbers 1 to 26, as show below, and ...

A: a). To encode the message BELIEVE YOU CAN, first divide the letters into the group of two. BE  LI  E...

Q: Solve the initial value problem y" + 5y – 36y = 0, y(0) = a, y'(0) = -54. Find a so that the solutio...

A:

Q: In one of the laboratories, it conducted an experiment on 900 insects to prove the effectiveness of ...

A: x = input("Enter no.of insects died in first hour : ")n = 7;f = 900;while n >= 1    n = n-1;    x...

Q: Question 10 Evaluate the definite integral of the following vector-valued function: 1/2 di*< 2

A:

Q: dn -f(D) · P(D) dt di – (23 – 2)f(D) · P(D) ·D |3| dt The average diameter of the drops is simply ex...

A:

Q: b        i        Find the y-coordinates of the points of intersection of the parabola with equation...

A:

Q: 2. Let X1 and X, be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T1 (x1, x2) = x1,...

A:

Q: If ā = 2ī +j -k, 5= -i +2j- 4K, č = T +J+k then find |(āxb).(5xē). %3D

A: This is the problem of vector calculus.

Q: Jc 16.8. For each of the following functions , describe the domain of ana- lyticity and apply the Ca...

A:

Q: Define the line Lo to be a = xo + at, y = yo + bt, z = z0 + ct. If Lo passes through the origin, the...

A:

Q: Find the absolute extrema of the function f(x) = x?e-z on the interval %3D

A:

Q: Use the First Derivative Test to find relative (local) maximum points or mini points, if any, of the...

A: Let us find the local maximum points or minimum points of the given functions and  determine the ope...

Q: Question: Chapter 6 Show That A Topology T On X Is Finite If And Only If T Has A Finite Base.

A:

Q: 1. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-...

A: This is a problem of multi variable calculus.

Q: 2. v=i +k, u= 5i + 12j Find: u.v, |미, lu씨 b. the cosine of the angle between u and v. the scalar com...

A:

Q: Show wheatear the statements are True or False (provid explanation/justification). a. sup A E A' b. ...

A:

Q: Find the volume of a wizard hat that has a diameter of 10 mi and a height of 12 mi. Volume = (Round ...

A: Volume of the cone with base radius r and height h is obtained as Volume of cone =13xArea of basex h...

Q: Hw-4 problem SET 2.1 reduce to Pirs oreler and solve 2. (It Cosn 6 govod luck 1a ^_^

A:

Q: suppose that u=xe+ysinz and that X,y,Z Hiwt can be measured with maximum possible errorsof 180 resfe...

A:

Q: (2x* – 2y* If f(x,y)={3x +3y² if (x, y) # (0,0) then: if (x,y) =(0,0) f(x,y) is continuous at (0,0) ...

A: To check if f is continuous at (0,0), substitute y=mx and check if lim(x,y)→(0,0)f(x,y)=f(0,0).

Q: w did it arrived the answer? no.5

A: (5) Given,               ∫4x3-xx2-x-30dx=

Q: JO 18.9. Let y denote the boundary of the rectangle whose vertices are -2 – 2i, 2 – 2i, 2+ i and -2+...

A:

Q: Show that the translate of an Fδ set is also Fδ.

A:

Q: Determine the values of the variables to satisfy the equation. 4a-b+c+d = 14 , 2a-2b+3c-7d=-21 , a-5...

A: We determine the values of the variables a,b,c and d to satisfy the equations 4a-b+c+d = 14 , 2a-2b+...

Q: Part A: Find the difference between the cost of a two-line ad and the cost of a three-line ad. Diffe...

A: This is a problem of counting.

Q: 4. Prove that 17 - 3V3~ 83 + 47/3 in Z+ZV3. 5. Prove that -6 is not a prime in Z+ ZV-6. 6. Prove tha...

A:

Q: Determine the positive root of f(x) = 4x 3 + 8x - 8 = 0 using the Newton-Raphson method and an initi...

A: The equation in form f(x)=0 is called a transcendental equation. The solution of the equation is def...

Q: 4. Define the followings:            i) Forward and backward difference operator            ii) ...

A:

Q: 7a) Prove that if x is a rational number such that 2x-3 and 5x-4 are integers then x must be an inte...

A:

Q: 7. Find the slope intercept form of an equation of the line that passes through point (4, 10 and is ...

A:

Q: suppose that u= xe+y Sin z and that X,y, Z can be measured with maximum passible errors.of 180 respe...

A:

Q: Find the general (real-valued) solution of the following differential equations. If an initial condi...

A:

Q: 8 5 In the following, let A denote the coetficient matrix in (1). a) Compute the 1-norm of the matri...

A: M

Q: x' + 2 5 x =

A:

Q: Determine the values of p. q, and r so that the function f(z) = pr + qa2 + rz will have an inflectio...

A: Given function is fx =px3 +qx2 +r x The function has an inflection point at (1, 2). The slope of the...

Q: What does it mean to be a "function"? How can you determine function ality of a relation set or equa...

A:

Q: 3. Consider the surface integral / (Vx F)-n dS, where F = (0, 0, zyz) and S is that portion %3D of t...

A: we will draw the surface z=1-x2-y2 and then follow the procedure 

Q: x"+3x+ x*+2 .4 e lim メ→ x'+z x²+3x +l tim メ→。 xとャ! lim x-1

A:

Q: Part 1 a) Given f (z) = + x2 + i(2x2 - y?), show which points where f has y a derivative. b) Show th...

A:

Q: ue of J. Note that the lows

A: Given ∇.V=1r2∂∂rr2vr+1rsinθ∂θ∂∂θsinθvθ+1rsinθ∂vϕ∂ϕ

Q: Find the value of a at which the plane curve traced out by the vector function E + bt> is not smooth...

A:

Q: A perpetuity has payments at the end of each four-year period. The first payment at the end of four ...

A: Present Value = P1×V4 + P2(V4)2 + P3×(V4)3 + ...Where P1 is the first payment, P2 is the second paym...