Other Math Answers

1. The number x is multiplied by itself and the result y is less than the number x.

For example, x*x = x² = y and y < x. 

i.   State a set name in which numbers behave in such an assertion above.

ii.     State any number in the stated set in (a) above and verify the assertion. 

(a)               A chemical preparation has a theoretical yield of 16.50g, the actual yield was 12.375g.  Express the actual yield as a percentage of the theoretical yield.

(b)               The experimental value of the water of hydration of copper sulfate was calculated as 36.1%.  What mass of a sample of 18g of hydrated copper sulphate is water?  Write your answer correct to three significant figures.

(c)       A reaction produces a compound at a rate of 12 gmin^-1.  A catalyst raises this rate to 16.5 g min^-1. What is the percentage increase?

a.      Express the roots of (−14+3i)^−2/5 complex number in polar form. 

a.      Let A and B and C be sets, prove that A∩(BC) = (A∩B) ( A∩C). 

b. a.      The number x is multiplied by itself and the result y is less than the number x.

For example, x*x = x² = y and y < x. 

i.   State a set name in which numbers behave in such an assertion above.

ii.     State any number in the stated set in (a) above and verify the assertion. 

The present ages of Andy and Mike are in the ratio 5 : 3. If Andy had been 7 years older and Mike 7 years younger, the age of Andy would have been 3 times the age of Mike. Find their present ages.

If 10^x/2 + 10^-x/2 =4, prove that x = log(7 + 4√3)

4. The population of a certain village at one time was a perfect square. Later, with an increase of 100, the population was one more than a perfect square. Now, with an additional increase of 100, the population is again a perfect square. What was the original population? (Give all possible answers.)

The number of men needed to cement a barangay road vanes directly with the length of the road at a constant

width and inversely with the number of days required to do the job. If a 30m road can be cemented by 10 men in

12 days how wide is the road? How many days will it take 50 men to cement a road that is 1 km long?

A certain college has 52 students participating in games.30 play netball, 25 play football , 10 play handball and football ,13 play netball and handball,9 play netball and football while 2 play all the three games. How many students play handball and no other game?

Determine if the statement is TRUE or FALSE. Justify your answer. All numbers under discussion are

integers.

10. Given a positive integer N ≥ 10, form the number N' by removing the ones digit from N

and subtracting this digit from the remaining truncated integer. (For example, if N = 1309,

N' = 130 0 9 = 121.) If N' is divisible by 11, then N is divisible by 11.