Explanation

The relative speed of the two trains is the sum of their individual speeds, since they're moving in opposite directions: 62 km/h + 40 km/h = 102 km/h

Convert the relative speed from km/h to m/s: 102 km/h x (1000 m / 3600 s) = 28.33 m/s (approximately)

The time it takes for the trains to cross each other is given as 18 seconds.

The total distance covered by the trains during this time is the sum of their lengths. Let's call the length of the other train "x". Then, the total distance = 260 m + x

Since the relative speed is 28.33 m/s, the total distance can also be calculated as: Total distance = Relative speed x Time = 28.33 m/s x 18 s = 510 m

Equate the two expressions for total distance: 260 m + x = 510 m

Solve for x: x = 510 m - 260 m = 250 m

Explanation

Explanation

Explanation: 3.14 x 10^6 = 3.14 x 1000000 = 3140000.

Explanation

Given that 40% of a number is equal to two-third of another number, we need to find the ratio of the first number to the second number.

Let's assume that the first number is x and the second number is y. 40% of x is equal to 2/3 of y.

We can write this as: 0.4x = 2/3 y To find the ratio of x to y, we can divide both sides by y: 0.4x/y = 2/3

Simplifying further, we get: x/y = (2/3)/(0.4) x/y = 5/3

Therefore, the ratio of the first number to the second number is 5:3.

Explanation

$\lambda =\frac{v}{f}$

Let's plug in our given values and see what we get!

$\lambda =\frac{340\frac{m}{s}}{440s^{-1}}$

$\lambda =0.773m$

Explanation

To find |f(1)|, we need to evaluate the function f(x) = -3(x^2) - 2(x) + 1 at x = 1.

f(1) = -3(1^2) - 2(1) + 1

= -3(1) - 2(1) + 1

= -3 - 2 + 1

= -4

Now, we need to find the absolute value of f(1):

|f(1)| = |-4| = 4

Explanation

We know:

- Angle of elevation (θ) = 60°

- Distance of the foot of the ladder from the wall (x) = 12.4 m

- We need to find the length of the ladder (hypotenuse)

Using the cosine function:
cos(θ) = adjacent side / hypotenuse
cos(60°) = 12.4 / hypotenuse
To find the hypotenuse (length of the ladder), we can rearrange the equation:
hypotenuse = 12.4 / cos(60°)
Using a calculator:
hypotenuse = 12.4 / 0.5
hypotenuse = 24.8
So, the length of the ladder is 24.8 meters.

Explanation

Since 12 pumps can empty the tank in 20 minutes, the rate at which they empty the tank is 1 tank / 20 minutes.

With 2 pumps out of order, we have 12 - 2 = 10 pumps left. Since the rate is directly proportional to the number of pumps, the rate of the remaining 10 pumps is:

10/12 × (1 tank / 20 minutes) = 1 tank / 24 minutes

So, the remaining 10 pumps will take 24 minutes to empty the tank.

Explanation

Profit = Selling price - Cost price

So here,

Sp=Rs295

&

Cp=Rs250

Profit = 295-250 =  Rs 45

Explanation

Profit = Selling Price - Cost Price

= 540 - 470

= 70

Profit Percentage = (Profit ÷ Cost Price) × 100

= (70 ÷ 470) × 100

= 15 (14.89%)