Explanation

Explanation

x = 3+ √8

x = (3+√8)(3-√8) / (3-√8)

x = (9 -8) / (3-√8)

x = 1/ (3 -√8)

Or we can write 1/x = (3-√8)

Put the value and find out

x² +(1/x²) = x² + (1/x)²

So x² + 1/ x² = (3 +√8)² + (3 -√8)²

= 9+6√8+8 + 9–6√8+8

= 34.

Explanation

Let Price be 75

Now 15% of 75 = (15/100) x 75 = 15 

Cost After discount is = 75 – 15 = 60

Explanation

√(x - 1)^2 + √(3 - x)^2

Since 1 < x < 2, we can simplify the expressions inside the square roots:

(x - 1)^2 = (x - 1)(x - 1) = x^2 - 2x + 1

(3 - x)^2 = (3 - x)(3 - x) = 9 - 6x + x^2

Now, add the two expressions:

x^2 - 2x + 1 + 9 - 6x + x^2

= 2x^2 - 8x + 10

Take the square root of the result:

√(2x^2 - 8x + 10)

Since 1 < x < 2, we can plug in x = 1 and x = 2 to find the maximum and minimum values:

At x = 1: √(2 - 8 + 10) = √4 = 2

At x = 2: √(8 - 16 + 10) = √2

So, the minimum value of the expression is 2, which occurs when x = 1.

Therefore, the correct answer is: 2

Explanation

Hour hand moves 225° (7.5 hours).

Minute hand moves 180° (30 minutes).

Angle between them: 45° (difference) + 30° (hour hand's extra move) = 75°.

OR

= 8h x 30 - 30 x 11/2

= 240 - 165

= 75°

Explanation

The player's average runs in 10 innings is 32, so the total runs scored is: 10 x 32 = 320 runs.

To increase the average by 4, the new average will be: 32 + 4 = 36 runs.

Since the player has played 11 innings now (10 previous + 1 next), the total runs required to achieve the new average is: 11 x 36 = 396 runs.

To find out how many runs the player needs to score in the next innings, subtract the runs already scored from the total runs required: 396 - 320 = 76 runs.

So, the correct answer is: 76

Explanation

60 women spin 48 kg of cotton in 8 hours.

First, find the total hours worked by 60 women: 60 women x 8 hours = 480 hours.

Now, find the total cotton spun per hour: 48 kg ÷ 480 hours = 0.1 kg/hour.

Since 30 women work 12 hours daily, find their total hours: 30 women x 12 hours = 360 hours.

Finally, find the total cotton spun by 30 women: 360 hours x 0.1 kg/hour = 36 kg.

So, the correct answer is: 36 kg

Explanation

The sum of money doubles in 3 years, which means it becomes 2 times itself.

Since it's compounded annually at the same rate, the interest rate is consistent.

To become 4 times itself, it needs to double twice more (2 × 2 = 4).

Since it doubles every 3 years, it will double twice more in 2 × 3 = 6 years.

So, the correct answer is: 6 years

Explanation

The average of 50 numbers is 30, so the sum of all 50 numbers is 50 x 30 = 1500.

If we discard 35 and 40, we subtract these from the total sum: 1500 - 35 - 40 = 1425.

Now, we have 48 numbers left (50 - 2 = 48).

To find the new average, we divide the remaining sum by the number of remaining numbers: 1425 ÷ 48 ≈ 29.68.

So, the correct answer is: 29.68

Explanation

Algebra is a branch of mathematics.

Just as mathematics is a branch of science.

The relationship is of a part to its whole.