Explanation

Given: y = (2x + 3)⁴  

Using the chain rule:  

dy/dx = 4(2x + 3)³ * d/dx(2x + 3)  

= 4(2x + 3)³ * 2  

= 8(2x + 3)³  

Explanation

To convert 0.00416 into scientific notation:  

Move the decimal 3 places to the right → 4.16 × 10⁻³.

Explanation

Original price = Rs. 90  

Discount = 50% of 90 = Rs. 45  

Final price = 90 - 45 = Rs. 45

Explanation

To find the angle between the hour and minute hands at 1:30:

Step 1: Minute hand position  

- Each minute = 6°  

- At 30 minutes → 30 × 6 = 180° from 12 o'clock.

Step 2: Hour hand position  

- Each hour = 30°  

- At 1 o'clock → 1 × 30 = 30°  

- At 1:30, the hour hand has moved halfway between 1 and 2 → 30 + (30 × 0.5) = 45°

Step 3: Difference between the two hands:  

- 180° − 45° = 135°

Explanation

Pattern:  

2 = 1² + 1  

8 = 2² + 4  

18 = 3² + 9  

32 = 4² + 16  

Next = 5² + 25 = 50  

Explanation

To find the required speed, we first calculate the distance covered by the train:

$$text{Distance} = text{Speed} times text{Time} = 45 , text{km/h} times 5 , text{hours} = 225 , text{km}$$

Now, to cover this 225 km in 3 hours, the required speed is:

$$$$Speed=Distance/Time=225 km/3 hours=75 km/h

Explanation

A fly is to an aeroplane as a Sail is to a ship.

The relationship is "verb is to noun."

Where the verb describes how the object is propelled or moves, with an aeroplane flying and a ship sailing. 

Explanation

Loss = 5000 - 4500 = 500  

Loss % = (500 / 5000) × 100 = 10%

Explanation

Given:  

P * Q = P + Q + P / Q

Put P = 8, Q = 2

Now calculate:  

= 8 + 2 + 8 ÷ 2  

= 10 + 4  

= 14

Explanation

- Originally, 20 students shared the cost:  

  Each paid = x / 20

- When 4 students backed out, only 16 shared the cost:  

  Each paid = x / 16

We're told the new amount is $1.50 more than the original amount:

x / 16 - x / 20 = 1.5

LCM of 16 and 20 = 80, so:

(5x - 4x) / 80 = 1.5  

x / 80 = 1.5  

Multiply both sides by 80:  

x = 1.5 × 80 = 120