Explanation

The learning method that is associated with observing the behavior of others is called "Learning by Imitation."

Explanation

In topology, isometric metric spaces represent an equivalence relation. 

An equivalence relation needs to be reflexive, symmetric, and transitive.

Explanation

Let’s assume two cases:

• If $f = 3$ (monatomic gas), then:

  γ=3+2​/3=5/3​

• If $f = 5$ (diatomic gas), then:

  γ=5+2​/5=7/5​

Since the question asks for γ when degrees of freedom are 3 and 5, and γ = Cp/Cv, then:

• For f = 3 → γ = 5/3

Explanation

The expression p ∨ ¬p (read as "p or not p") is a tautology.

A tautology is a logical statement that is always true regardless of the truth value of its components.

 p ∨ ¬p is always true because either p is true or ¬p (not p) is true.

Explanation

 T = 2π√(L/g)

= 2π√(1/9.8)

≈ 2.006 s

Explanation

 The crystal structures with a coordination number of 12 are Face-Centered Cubic (FCC) and Hexagonal Close-Packed (HCP).

In these structures, each atom is surrounded by 12 other atoms. 

Explanation

This is a product of two functions, so we apply the product rule:

d​[u⋅v]/dx=u′⋅v+u⋅v′

Here,

• u=x^2, sou′=2x

• $v = sin(x)$, so $v' = cos(x)$

Now apply the rule:

$$f'(x) = 2x cdot sin(x) + x^2 cdot cos(x)$$

Explanation

A one-one function means that each element of the domain maps to a unique component of the codomain.

This is the definition of an injective function.

A bijective function is both injective and surjective.

A surjective function covers every element in the codomain.

A constant function maps all domain elements to the same codomain value — it is not injective.

Explanation

What is the value of the integral:

∫e^x2+lnx dx

Step 1: Simplify the integrand

Recall:

e^a+b=e^a⋅e^b

So,

e^x^2+lnx=e^x^2⋅e^lnx=x⋅e^x^2

Step 2: The integral becomes:

∫x⋅e^x^2 dx

Now use substitution:

Let $u = x^2 Rightarrow du = 2x , dx Rightarrow frac{1}{2} du = x , dx$

So,

$$int x cdot e^{x^2} , dx = frac{1}{2} int e^u , du = frac{1}{2} e^u + C = frac{1}{2} e^{x^2} + C$$

=1​/2∫e^u du

=1​/2e^u+C

=1​/2ex^2 +C

Explanation

To find the energy stored in a capacitor, we use the formula:

E=1/2​CV^2

Where:

• $\mathrm{<br>}$

• $V=100\text{V}$

Calculation:

$$E = frac{1}{2} times 4 times 10^{-6} times (100)^2$$E=1/2​×4×10^−6×10000
E=2×10^−6×10000

$$=0.02\text{J}$$