Question: Let [x] denote the greatest integer which is less than or equal to x. For example, [] = 3. S is the integer equal to

  1. Let [x] denote the greatest integer which is less than or equal to x. For example, [] = 3. S is the integer equal to the sum of the 100 terms shown:

S = [] + [ + 1/100] + [ + 2/100] + [ + 3/100] +... + [ + 99/100]

What is the value of S?

  1. Next question: Suppose that x and y satisfy the equations

3 sin x + 4 cos y = 5

4 sin y + 3 cos x = 2

What is the value of sin(x+y)?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Section A Question 2 Question 1 (a) Find the follo (i) lim cos (a) Give the definition of the Gamma function (a), for a > 0. x-+0+ log Show that [(a + 1) = ar (a). (ii ) lim x - - 2x3 (b) (i) Use the...

Q:

(b) Use Taylor's theorem to find the first-order Taylor series for tan a about x = 1 /4 and the asso- ciated remainder term. Hence determine whether the integral TT / 4 dxx o 1 - tan x is convergent...

Q:

Please help me with these questions, detailed answers and explanations please. Computer science math. 1. (12 marks] Number theory. Prove each of the following statements. For each one, you may use...

Q:

2.1 Evaluate: lim (1+3x2)5 cotx cot x+2cosecr 0-x 2.2 Test the following series for convergence: a. 3 + 1 - n); b. n=1 1 3 5 7 + + + + 1.2.3 2.3.4 3.4.5 4.5.6 2.3 Find the sum of the infinite series:...

Q:

For each positive integer n, let 1 ---((n + 1)(n+ 2)....(n+n))/. For x = R, let [x] be the greatest integer less than or equal to x. If lim y = L, then the value of [L] is n-x

Q:

assembly language question please help me the code, thanks! 3. [9 marks] The Root of the Problem In this question, you number. You will write sqrt within the file sqrt.s (part of the care package) 1...

Q:

Recall that the floor of a number x = R, denoted [x], is defined as the greatest integer that is less than or equal to x. And the ceiling of x, denoted [x] is the smallest integer that is greater...

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

The new line character is utilized solely as the last person in each message. On association with the server, a client can possibly (I) question the situation with a client by sending the client's...

Q:

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

Q:

28) All of the following can be expected with polycythemia EXCEPT A) high hematocrit B) low blood viscosity C) increased blood volume D) high blood pressure 29) Which is NOT true of leukocytes? A)...

Q:

Evaluate the following using Complex numbers and rationalize the denominator. 3+16 /5+-25

Q:

George is the owner of SRC Inc., an S corporation that he formed this year with an investment of $50,000. Net business income (ordinary income) for SRC for the first tax year is $20,000. SRC Inc....

Q:

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.