Explanation

In the quadratic equation ax² + bx + c = 0, a cannot be zero.

If a = 0, the equation becomes linear (bx + c = 0), and it's no longer a quadratic equation.

Explanation

Time = Energy / Power

Given Energy = 1.4 × 10⁶ J and Power = 2 kW = 2000 W:

Time = (1.4 × 10⁶ J) / (2000 W)

Time = 1.4 × 10⁶ / 2000

= 700 s

Explanation

The derivative of y = x² is dy/dx = 2x.

At x = 2, the slope is 2(2) = 4.

The tangent line equation is y - 4 = 4(x - 2), which simplifies to y = 4x - 4, or 4x - y = 4.

Explanation

To find the center of the circle, rewrite the equation in standard form:

45x² - 60x + 45y² + 36y = -19

Divide by 45:

x² - (4/3)x + y² + (4/5)y = -19/45

Complete the square:

(x - 2/3)² + (y + 2/5)² = ...

The center is (2/3, -2/5).

Explanation

In a reversible adiabatic process, there is no heat transfer (Q = 0).

As a result, the entropy change (ΔS) is zero because entropy change is directly related to heat transfer in a reversible process (ΔS = Q / T).

Explanation

The orbital speed (v) of a satellite is given by:

v = √(GM / (R + h))

If the orbital radius (R + h) is halved:

v' = √(GM / ((R + h) / 2))

= √(2GM / (R + h))

= √2 * √(GM / (R + h))

= √2 * v

So, the orbital speed will increase √2 times.

Explanation

Given:

Magnification M = 5

Distance between lenses L = f₀ + fₑ = 24 cm

Magnification formula M = f₀ / fₑ

Let's solve for f₀ and fₑ:

1. f₀ / fₑ = 5 => f₀ = 5fₑ

2. f₀ + fₑ = 24

Substituting f₀ = 5fₑ into the second equation:

5fₑ + fₑ = 24

6fₑ = 24

fₑ = 4 cm

Now, f₀ = 5fₑ = 5 × 4 = 20 cm

Explanation

The total time of flight (T) for a projectile is given by:

T = 2v₀sin(θ) / g

The maximum height (H) is:

H = (v₀sin(θ))² / (2g)

Using T = 2v₀sin(θ) / g, we can express v₀sin(θ) = gT/2. Substituting this into the height equation gives:

H = (gT/2)² / (2g) = g²T² / 8g = gT² / 8

Explanation

True or False is a selection-type question where students choose between given options.

It does not require constructing an answer, just selecting the correct one.

Explanation

Counseling helps not just in solving existing problems (remedial) but also in avoiding future ones (preventive).

A preventive approach focuses on early guidance to reduce potential issues.