Explanation

• Gravitational potential is always negative, because it is defined as the work done per unit mass to bring an object from infinity to a given point in a gravitational field.
• Since the force of gravity is attractive, work must be done to move an object against the force of gravity, and this work is negative.

Explanation

• Every integer can be expressed as a ratio of integers, i.e., a fraction with a denominator of 1.
• For example, the integer 5 can be written as 5/1, which is a rational number.

Explanation

The combination formula is:

nCr = n! / (r!(n-r)!)

Given that nC12 = nC6, we can equate the two expressions:

n! / (12!(n-12)!) = n! / (6!(n-6)!)

Simplifying the equation, we get:

12!(n-12)! = 6!(n-6)!

Since 12! = 12 × 11 × 10 × 9 × 8 × 7 × 6!, we can cancel out the 6! terms:

12 × 11 × 10 × 9 × 8 × 7 = (n-6)(n-7)(n-8)(n-9)(n-10)(n-11)

This equation is true when n = 18.

Therefore, the correct answer is 18.

Explanation

The equations x = 3cos(t) and y = 3sin(t) are parametric equations of a circle with center at the origin (0, 0) and radius 3.

Explanation

• The correct answer is: y = f(x)
• This is the conventional notation used to represent the relationship between a function f, its input x, and its output y.
• It reads "y is equal to f of x", or "y is the image of x under f".

Explanation

• The given equation (x + 2)^2 = x^2 + 4x + 4 is an identity because it is true for all values of x.
• An identity is an equation that is always true, and this equation is simply the result of expanding the left-hand side using the binomial theorem.

Explanation

Explanation

sin^2 θ/2 = 1 - cos ^2 θ

Explanation

 Short-sight defect could be corrected by using concave lens while long-sight defect could be corrected by using convex lens.

Explanation

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