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Show that ๐‘Š = {(๐‘ฅ, 4๐‘ฅ, 3๐‘ฅ) โˆˆ โ„2 |๐‘ฅ โˆˆ โ„} is a subspace of โ„ 3 . Also find a basis for subspace ๐‘ˆ of โ„ 3 which satisfies ๐‘Š โŠ• ๐‘ˆ = โ„3


Topic: Integration



Find the antiderivative of the following. Show your comple solution.



1.) Integral (6xโต-4xยฒ+2) dx


2.) Integral (12xยฒ+2x) dx


3.) Integral 8^3/2 dx


4.) Integral 1/xยนยฒ dx


5.) Integral ยณโˆšx dx

If I=V/R and V=250 volts and R=50ohms,find the change in I resulting from an increase of 2 volts in v and an increase of 0.5ohm in R. Using total differential method.

write python program that reads in the number of judges at a competition and reads in a mark for each judge. write out the highest mark, lowest mark and final mark.


. Write a program that performs the following tasks: a) declares an array of 5 books, prompt the user for the details of the book and load them in the declared array. b) The application should allow the user to find and display all the book(s) published by the same author. c) The user should be able to find the number of copies available for the same book. E.g Absolute Java, 7th Edition by Walter Savitch. You want to know, how many copies does this book has? In the array.


Alonzo finished his inglish assignment in 1/2 hours.Then he completed his chemistry assignment in 3/5 hours.How much more time did Alonzo spend on his chemistry assignment?


A random variable x is normally with mean 10 and variance 6.25 what is the value of p(x>12.25)


In a Coulometric redox titration, we have 100 mL water with some KCl from salt bridge in one beaker, and 100 mL water with some KCl and 1 mL of 0.02 M CH3COOH in another beaker. 1.5 amps, 10 V, 500 sec until color change.

. Create class representing a book, assume that this book has, title, author edition. Include all constractors, mutator and accessor methods. This class should override both toString() and equals() methods


A gambler plays only one game for at most one hour each evening. The chance of showing a profit at the end of the hour if he plays roulette and blackjack is 30% and 20% respectively. He chooses blackjack on 60% of the evenings and roulette on the remaining evenings. Suppose he shows a profit after playing one a particular evening. What is the probability that that he played blackjack?


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