Calculate the order of magnitude ?( ) of the following functions, assuming that T (1) =...
Calculate the order of magnitude ?( ) of the following functions, assuming that T (1) = ? (1).
T(n) = 5T(n/7) + nlogn
T(n) = 3T(n/4) + log3n
T(n) = 4T(n/4) + nlogn
T(n) = 9T(n/10) + log3n
T(n) = 2T(n/3) + n/log2n
T(n) = T(n-1) + 1/n
Homework Answers
Answer:
1. T(n) = 5T(n/7) + nlogn
Using Master's theorm , we have :
a = 5 , b = 7 , c = 1 , k = n
log a base b = log 5 base 7 = 0.827
log a base b < c
Therefore T(n) = theta(n^c) = theta(n^0.827) = theta(n)
2. T(n) = 3T(n/4) + log3n
Using Master's theorm , we have :
a = 3 , b = 4 , c = 0 , k = 3
log a base b = log 3 base 4 = 0.792
log a base b > c
therefore T(n) = theta(f(n)) = theta(log3n)
3. T(n) = 4T(n/4) + nlogn
Here a = 4 , b = 4 , c = 1 , k = 1
log4 base 4 = 1 , here log a base b = c
Therefore , T(n) = theta(n^clog^k+1n) = theta(n^1log^k+1n) = theta(nlog^2n
4. T(n) = 9T(n/10) + log3n
Here a = 9 , b = 10 , c = 0 , k = 3
log 9 base 10 = 1 , c = 0
here loga base b > c , therefore T(n) = theta(f(n) = theta(log3n)
Add Answer to:
Calculate the order of magnitude ?( ) of the following
functions, assuming that T (1) =...
• Only one submission is necessary for each group. = 1. At time t, particle P...
• Only one submission is necessary for each group. = 1. At time t, particle P has position plt) (1 + 2t, 2 + 5t, 3 – 4t), particle Q has position a(t) (-6+t, -14 + 2t, 2 + 3t), and particle R has position F(t) = (18 – 3t, 10 – 2t, –4 + 4t). (a) Do any of the particles ever collide? Which particles, and when and where do they collide? (b) Do any of the paths of...
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1...
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3. recurrenсes T(п) log n n 4T .3 3.1 n 5T 2 n2 log n T(п) 3.2
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3
Т(п) 2T (п — 2) + 5 2.2
Solve the following using Master Theorem. 3....
Find the curvature of the curve defined by F(t) = 227 + 5tj K= Evaluate the...
Find the curvature of the curve defined by F(t) = 227 + 5tj K= Evaluate the curvature at the point P(54.598, 10). Find the Tangent vector, the Normal vector, and the Binormal vector (T, Ñ and B) for the curve F(t) = (4 cos(5t), 4 sin(5t), 2t) at the point t = 0 T(0) - N(0) = BO) - Find the Tangent, Normal and Binormal vectors (T, Ñ and B) for the curve F(t) = (5 cos(4t), 5 sin(4t), 3t)...
1 (1 point) Find the Laplace Transform of the following functions: f(t) = 2e-9t + 7++...
1
(1 point) Find the Laplace Transform of the following functions: f(t) = 2e-9t + 7++ 4t+3 F(s) = f(t) = 2e9t sin(7t) + 4ť + 3et F(s) = -9t f(t) = 2te-94 sin(7t) F(s) = Note that there is a table of Laplace transforms in Appendix C, page 1271 thru 1273 of the book.
Q1) Find the Laplace Transform of the following functions: 1. e +5 2. cos(2t)+7sin(2) 3t)+sin(3) 4....
Q1) Find the Laplace Transform of the following functions: 1. e +5 2. cos(2t)+7sin(2) 3t)+sin(3) 4. 10+ 5t +12-4 5. (+2)e 6. Gcos(21)-
a) Let (N(0.620}be a non-homogenous Poisson process with a variable rate 1(t) = 3t +9t+2 Calculate...
a) Let (N(0.620}be a non-homogenous Poisson process with a variable rate 1(t) = 3t +9t+2 Calculate the expected number of events of the process in (1:4) b) Events occur according to a non-homogeneous Poisson process whose mean value function is given by m(t) = 46° -2t+3 What is the probability that n events occur between times t = 2 and t=5?
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u...
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u = a, (2) (∂/∂t − ∂/∂x) v = b, and (3) (∂/∂t + 3 ∂/∂x) w = c, where a, b, and c are the functions that you calculated in Problem 3... a=f(x+t)= (x+t)^2+(x+t)+1 b=f(x-2t)= (x-2t)^2+(x-2t)+1 c=f(x-3t)= (x-3t)^2+(x-3t)+1
For a given law of motion of a particle M find a location of a particle for a time ty (in sec), trajectory, velocuty, t...
For a given law of motion of a particle M find a location of a particle for a time ty (in sec), trajectory, velocuty, tangential, normal and full acceleration -2t +3 4 cos (xt/3) 2 4 sin2(xt/3) sin(rt/3) -1 4t +4 2sin(t/3) 3e2 +2 3t2 + 7 sin(rt/6) +3 -3cos(nt/3) + 4 -141 1/2 2os(t/6) 4 cos(t/3) 10 83t 5 cos (t/6)-3 -5 sin rt2/3) 1/2 5 sin2(xt/6) 5 cos(rt2/3) -2t-2 412 13 14 4 cos(xt/3) 3sin(rt/3) 16 3t 1/2...
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the...
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the solution using big-O notation. Explain your reasoning. If the “master theorem” does not apply to a recurrence, show your reasoning, but you need not give a solution. (a) T(n) = 3T(n/2) + n lg n; (b) T(n) = 9T(3/3) + (n? / 1g n); (c) T(n) = T([n/41) +T([n/4])+ Vn; (d) T(n) = 4T([n/7])+ n.
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t)...
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet
• Only one submission is necessary for each group. = 1. At time t, particle P has position plt) (1 + 2t, 2 + 5t, 3 – 4t), particle Q has position a(t) (-6+t, -14 + 2t, 2 + 3t), and particle R has position F(t) = (18 – 3t, 10 – 2t, –4 + 4t). (a) Do any of the particles ever collide? Which particles, and when and where do they collide? (b) Do any of the paths of...
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3 Т(п) 2T (п — 2) + 5 2.2 Solve the following using Master Theorem. 3. recurrenсes T(п) log n n 4T .3 3.1 n 5T 2 n2 log n T(п) 3.2
Solve the following using iteration method. Note: T(1) = 1. 2. recurrences GE) T(п) 2T 2.1 3
Т(п) 2T (п — 2) + 5 2.2
Solve the following using Master Theorem. 3....
Find the curvature of the curve defined by F(t) = 227 + 5tj K= Evaluate the curvature at the point P(54.598, 10). Find the Tangent vector, the Normal vector, and the Binormal vector (T, Ñ and B) for the curve F(t) = (4 cos(5t), 4 sin(5t), 2t) at the point t = 0 T(0) - N(0) = BO) - Find the Tangent, Normal and Binormal vectors (T, Ñ and B) for the curve F(t) = (5 cos(4t), 5 sin(4t), 3t)...
1
(1 point) Find the Laplace Transform of the following functions: f(t) = 2e-9t + 7++ 4t+3 F(s) = f(t) = 2e9t sin(7t) + 4ť + 3et F(s) = -9t f(t) = 2te-94 sin(7t) F(s) = Note that there is a table of Laplace transforms in Appendix C, page 1271 thru 1273 of the book.
Q1) Find the Laplace Transform of the following functions: 1. e +5 2. cos(2t)+7sin(2) 3t)+sin(3) 4. 10+ 5t +12-4 5. (+2)e 6. Gcos(21)-
a) Let (N(0.620}be a non-homogenous Poisson process with a variable rate 1(t) = 3t +9t+2 Calculate the expected number of events of the process in (1:4) b) Events occur according to a non-homogeneous Poisson process whose mean value function is given by m(t) = 46° -2t+3 What is the probability that n events occur between times t = 2 and t=5?
For a given law of motion of a particle M find a location of a particle for a time ty (in sec), trajectory, velocuty, tangential, normal and full acceleration -2t +3 4 cos (xt/3) 2 4 sin2(xt/3) sin(rt/3) -1 4t +4 2sin(t/3) 3e2 +2 3t2 + 7 sin(rt/6) +3 -3cos(nt/3) + 4 -141 1/2 2os(t/6) 4 cos(t/3) 10 83t 5 cos (t/6)-3 -5 sin rt2/3) 1/2 5 sin2(xt/6) 5 cos(rt2/3) -2t-2 412 13 14 4 cos(xt/3) 3sin(rt/3) 16 3t 1/2...
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the solution using big-O notation. Explain your reasoning. If the “master theorem” does not apply to a recurrence, show your reasoning, but you need not give a solution. (a) T(n) = 3T(n/2) + n lg n; (b) T(n) = 9T(3/3) + (n? / 1g n); (c) T(n) = T([n/41) +T([n/4])+ Vn; (d) T(n) = 4T([n/7])+ n.
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 11 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 11 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 11 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 11 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 11 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 11 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 11 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 11 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 11 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 11 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 11 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 11 months ago