Question

1. If the replacement set = {-7, -5, -3,-1, 0, 1, 3), find the solution set of :
(iii) x > 2
(i) 0 < x < 4.
inequalities ronhi
(1) x>-2
(iv) -5 < x < 5
(ii) x < -2
(0) -8 < x < 1
11​

Answer 1

Answer:

By the end of the 19th century, Indian women themselves began to work for their upliftment. They began to get higher education in universities. Some of them trained to be doctors, some became teachers. Many women began to write and publish their critical views on the status of women in society.

Step-by-step explanation:

Perimeter of trapezium = 104 m

Length of Non-parallel sides = 18 m and 22 m

Altitude = 16m

Area of Trapezium = ½ × (sum of parallel sides)×altitude ------ (1)

Sum of parallel sides = Perimeter - (sum of non-parallel sides) = 104 m - (18+22)m = 104–40 m = 64 m

From (1), Area of Trapezium = 0.5×64×16 = 512 m²

Ans: Area of trapezium = 512 m²

Answer 2

Step-by-step explanation:

Question : Prove that√5 is irrational.

Answer :

Let us assume that √5 is a rational number.

Sp it t can be expressed in the form p/q where p,q are co-prime integers and q≠0

⇒√5=p/q

On squaring both the sides we get,

⇒5=p²/q²

⇒5q²=p² —————–(i)

p²/5= q²

So 5 divides p

p is a multiple of 5

⇒p=5m

⇒p²=25m² ————-(ii)

From equations (i) and (ii), we get,

5q²=25m²

⇒q²=5m²

⇒q² is a multiple of 5

⇒q is a multiple of 5

Hence, p,q have a common factor 5. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√5 is an irrational number

Hence proved