Question

50 points for 4 question class 11th

Answer 1

1) contrapositive of "something is cold implies that it has low temperature" is if something is not at low temperature then it is not cold.
2)take any two given points (1,1) (2,3) Put these points in the line equation y=mx+c to get two equations m+c=1 and 2m+c=3 Solve them to get m=2 and c=-1 Therefore the line equation is 2x-y-1=0 3)Let the imaginary multiplicative inverse be z.

So, (4-3i)z = 1

or z = 1/(4-3i)

Rationalizing the R.H.S, we get,

z = (4+3i)/(4 - 3i)(4 + 3i)

or z = (4 + 3i)/(42 + 32)

or z = (4 + 3i)/25

or z = (4/25) + (3/25)i

So, the required multiplcative inverse is z = (4/25) + (3/25)i.

4)given points (a,b) (a+b,a-b)
Slope(m) = ((a-b)-b)/(a+b)-a
= (a-2b)/b
Line equation will be
(y-y1) = m(x-x1)
=> y-b = (a-2b)/b (x-a)
=> b(y-b) = (a-2b)(x-a)
=> by-b^2 = ax+a^2 - 2bx+2ab
=> (a-2b)x-by+(a-b)^2

Answer 2

1) contrapositive of "something is cold implies that it has low temperature" is if something is not at low temperature then it is not cold.

2)take any two given points (1,1) (2,3)

Put these points in the line equation

y=mx+c to get two equations m+c=1 and 2m+c=3

Solve them to get m=2 and c=-1

Therefore the line equation is 2x-y-1=0

3)Let the imaginary multiplicative inverse be z.

So, (4-3i)z = 1

or z = 1/(4-3i)

Rationalizing the R.H.S, we get,

z = (4+3i)/(4 - 3i)(4 + 3i)

or z = (4 + 3i)/(42 + 32)

or z = (4 + 3i)/25

or z = (4/25) + (3/25)i

So, the required multiplcative inverse is z = (4/25) + (3/25)i.

4)given points (a,b) (a+b,a-b)

Slope(m) = ((a-b)-b)/(a+b)-a

= (a-2b)/b

Line equation will be

(y-y1) = m(x-x1)

=> y-b = (a-2b)/b (x-a)

=> b(y-b) = (a-2b)(x-a)

=> by-b^2 = ax+a^2 - 2bx+2ab

=> (a-2b)x-by+(a-b)^2