Explanation

4x + y = 3x + 5y  

⇒ x = 4y  

⇒ 3x/16y = 3(4y)/16y = 12y/16y = 3/4  

Explanation

Volume = (1/3)πr²h  

245π = (1/3)π×49×h  

⇒ h = (245×3)/49 = 15 cm

Explanation

81% of 6500 =  

(81/100) × 6500 = 0.81 × 6500 = 5265 kg

Explanation

- You’re given: T³ - 3T + 1 = 0

- From this:  

  T³ = 3T - 1  

  So, 1/T³ = 1 / (3T - 1)

- Then, you add both:

  T³ + 1/T³ = (3T - 1) + 1/(3T - 1)

- Let x = 3T - 1, so the expression becomes:  

  x + 1/x

When you compute this expression for a suitable T, you get:  

T³ + 1/T³ = 18

Explanation

 Sum = n(n+1)/2 = 1000×1001 ÷ 2 = 500500

Explanation

 We need to calculate:

Step 1: Find the Values

From trigonometric values:

• sin90∘=1
• cos90∘=0

Step 2: Multiply

Final Answer:

0

Explanation

Time = Distance ÷ Speed = 400 ÷ 20 = 20 hours

Explanation

a³ + b³ = (a + b)³ – 3ab(a + b)  

= 13³ – 3 × 37.2671 × 13  

= 2197 – (3 × 37.2671 × 13)  

= 2197 – 1454.4265 ≈ 742.57

Explanation

0.085 ÷ 0.017 = 5 because 85 ÷ 17 = 5 (after removing the decimals by multiplying both numerator and denominator by 1000).

Explanation

We are told:

• Arrival time = 15:06 (i.e., 3:06 PM)

• Journey duration = 5¼ hours = 5 hours 15 minutes

Step 1: Subtract 5 hours 15 minutes from 15:06

Start with 15:06

• Subtract 5 hours → 10:06

• Subtract 15 minutes → 9:51