Explanation

To solve the separable differential equation:

(1 + x)dy - ydx = 0

Rearrange the equation:

(1 + x)dy = ydx

Separate the variables:

dy/y = dx/(1 + x)

Integrate both sides:

∫(dy/y) = ∫(dx/(1 + x))

ln(y) = ln(1 + x) + C

y = e^(ln(1 + x) + C)

= e^C * e^(ln(1 + x))

= c(1 + x)

Explanation

Explanation

C.P. of 1 toy = 375/12 = Rs. 31.25

S.P of 1 toy = Rs. 33

Profit = 1.75/31.25 * 100 = 28/5 = 5.6%

Explanation

Given y = 5x and dx/dt = 2, find dy/dt:

dy/dt = d(5x)/dt

= 5(dx/dt)

= 5(2)

= 10

Explanation

To find the inverse of 3 in modulo 7, we need to find a number x such that:

3x ≡ 1 (mod 7)

We can try multiplying 3 by each number from 1 to 6:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9 ≡ 2 (mod 7)

3 × 4 = 12 ≡ 5 (mod 7)

3 × 5 = 15 ≡ 1 (mod 7)

So, the inverse of 3 in modulo 7 is 5.

Explanation

For matrices A × B ≠ B × A in general, so matrix multiplication is not commutative.

However, matrix addition is commutative and associative, and matrix multiplication is associative, but not commutative.

Explanation

To find the average rate of change:

Average rate of change = (f(3) - f(2)) / (3 - 2)

f(3) = 3^3 + 1 = 28

f(2) = 2^3 + 1 = 9

Average rate of change = (28 - 9) / 1 = 19

Explanation

Onslaught means a fierce or violent attack, which fits well with "by the enemy".

Onslaught means حملہ

Explanation

Skew lines are non-coplanar, do not intersect, and are not parallel.

They exist in 3D geometry, not lying in the same plane.

Explanation