Prove that any ball (open or closed or half open) in R³ is path connected.

Q: 3. The path of a soccer ball kicked into the air is modelled by s(t) = 0.2+ 19.6t – 4.9t, where s(t)…

A:

Q: Prove that the homogeneous integral equation

A:

Q: Let a, b e R with a < b. Assume that a + <b - for all n E N. Show that 1 = (a, b). a + ,b n n=1

A:

Q: log (a cos 0+6° sin 8) de log - a+b , a>0, b>0.

A:

Q: Example 2.13. Obtain graphically an approximate value of the root of x = sin x + T/2.

A: Please find step by step solution below

Q: b) Evaluate the following limits: 2(-3+h)2 18 i. lim h→0 - h (t-V(3t+4) ii. lim t→4 4-t -2X 6e4x –…

A:

Q: 2. Consider the following nonlinear equation e = 7x. (a) The above equation can be reformulated in…

A:

Q: Define Fredholm , Volterra and Singular integral equations Show that the function 8 (x) = is a…

A: Integral Equation: An integral equation is an equation in which the unknown function appears under…

Q: Find the N-point Discrete Fourier Transform X[k] for the following sequence: 0<n<N-1 x[n] = 0,…

A: The given sequence is xn=13n,0≤n≤N-10,Otherwise. We know the the discrete time Fourier transform of…

Q: a. Show algebraically that fix) - 2 x - 9 is an even function.

A: Even or odd function

Q: If f(x)=-(x² -4), find (a) The x-intercept and the y-intercept (b) The interval where the function…

A: (a) Given, fx=-x2-43.                      ⋯⋯1 Substitute fx=0 in the equation (1) and simplify to…

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

A:

Q: UESTION 4 Graphs that are drawn differently but still represent the same graph are called graphs. a.…

A:

Q: What is the distance between the line with Cartesian equation x-8 = y-9 = z-8 and the line with…

A:

Q: Consider the following two matrices 1 4 0 1 7 - A = 1 В 1 0 0 0 1 1 O a. A is in reduced row echelon…

A:

Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

A:

Q: (1 -5<t<0 is The Fourier Series expansion of f(t) =11+t 0<t<5 (-1)" nnt nnt sin 22- f(t) [[(– 1)" –…

A:

Q: What is the value of the following expression in Polish notation: +* 34-12 3/42 (note: all number.…

A: Given: +*+34-12-3/42

Q: Give an example of each of the following: (a) a set which is a nbd. of each of its points, (b) a…

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

Q: H.W: Which of the sequences {a„} converge and which diverge: 1. a, = 2+(0.1)" 2. an =|1+

A:

Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

A:

Q: If f(x) = 3x2 - 4x, 0 sxs 3, evaluate the Riemann sum with n = 6, taking the sample points to be…

A: Given f(x) =3x2 - 4x , a=0, b=3 and n=6 Now calculate f(x)

Q: 9 Use Remainder Theorem to find each function value. a) f(x) = 6xª – 5x³ + 8x – 11 - b) Find f(4)…

A:

Q: 1. Prove that any ball (open or closed half open) in R³ is path connected. or

A: Definition: A topological space X is said to be a path connected space if given x, y∈X there exists…

Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: Do not use a calculator in this question. integers. 4-3/6 V3+ v2 giving your answer in the form…

A: Using the FOIL method, it can be written that a+bc+d=ac+ad+bc+bd. The conjugate of x+y is x-y.

Q: Approximate the root of the following function using bisection method, approximate error < 0.00001…

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

Q: onsider the equation f(x) = 2x³+x²- 2x- 1 a) Express the equation in factored form. (T4) %3D

A: Given equation fx=2x3+x2−2x−1

Q: 8. Determine the truth value of the each of these statements if the domain consists of all integers:…

A:

Q: 9. : (y²dx + x²dy) = 0 (x – y)²

A:

Q: 3 students are choosing between loose leaf, hardback and electronic texts. Studies have show that…

A:

Q: Directions: Determine whether each of the following propositions is a tautology, a contradiction, or…

A:

Q: If f(x) = 0 is a cubic equation who'se roots are B.Y %3D a, ß, y and a is the harmonic mean of the…

A:

Q: a. all bavarian b. all chocolate filled с. c. all honey dipped

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: In a cubic spline approximation assume that we know that S,(r) = 5 4r– 2² +3x³ S+1(x) = a + br + cr²…

A:

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in.…

A: First we find the volume in terms of length of sides of square cardboard, then after equating it to…

Q: Calculate x + y, [Image 19 ) 9. 12 O 15 O Cannot be determined O 13 O 11 O 17 O 16 o o o o oa

A:

Q: Prove that the only homomorphisms from Z to Z (Z being the ring of integers) are the identity and…

A:

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: .2 An algorithm has time complexity f(n)3n*+200x²+10000. Of is O(1) Ofis O(n?) Of is O(n*) f is…

A: 

Q: If f(x) = 0 is a cubic equation whose roots are a, B, y and a is the harmonic mean of the roois %3D…

A:

Q: Approximate ln 0.5 using three terms of the Taylor series expansion of ln(1−x) about 0.

A:

Q: z1= 11-15i z2= 13+2i z3= 5+31i 24= 9-25i 25= 10-10i 26= 3+4i 4(z1 – z2) , (Z5 – z6) _ (z2 + z3)³ +…

A: To reduce to a+bi

Q: 3. The GCF of any two distinct prime numbers is 1. (Distinct they are not the same number) means

A:

Q: Who is Leonhard Euler and what was one of the significant contributions he made to the field of…

A: Leonhard Euler is a Swiss mathematician. He has discovered Euler's formula and invented calculus of…

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

A:

Q: Consider the following two matrices: -1 4 2 1 A = 2 -1 B 3 1 3 -1 -2 Which of the following four…

A:

Q: primitive root modulo

A: Given: Value of n=223 in  mod n. To find: Primitive root modulo 223.

Q: Question 4 The well-known Fibonacci Sequence Fo, F1, F2, ... is generated by the relation F = F1 +…

A:

Q: Q/show the Converg ence or the divelgence of the follo owing Series: Sinn 2.

A: