Explanation

• The correct answer is: y = vx, dy = vdx + xdv
• This substitution is used to solve homogeneous differential equations, as it allows for the separation of variables.
• By substituting y = vx and dy = vdx + xdv, the original equation can be transformed into a separable equation, which can then be solved by integrating both sides separately.

Explanation

The value of x 10^C1 x 6^C3 is 11760.

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

• A function f from A to B is called an onto function (or surjective function) if its range is equal to the codomain B.
• In other words, every element in B is the image of at least one element in A.
• This means that the function covers all the elements in the codomain B, and no element in B is left out.
• So, the correct answer is B.

Explanation

The word BOTSWANA has 8 letters, but it has two repeated letters (two S's and two A's).

To find the total number of words that can be formed, we need to divide the total number of permutations (8!) by the number of repetitions (2! for each pair of repeated letters).

So, the correct calculation is:

8! / (2! × 2!)

= 40320 / (2 × 2) = 40320 / 4 = 10080

Explanation

• This is because the statements "a > b" and "b > a" are contradictory, and both cannot be true at the same time.
• Therefore, the situation described is impossible.

Explanation

Given the sides of the triangle

$a=13,b=14,c=15$

Semi-perimeter $s=\frac{1}{2}(a+b+c)=\frac{1}{2}(13+14+15)=21$

Area, A = $\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{21(21-13)(21-14)(21-15)}$

$A=84$ $c{m}^2$

Explanation

The total angle around a circle is always 360 degrees.

This represents a full rotation or complete turn.

Explanation

The scintillation nuclear radiation detector detects the alpha rays per second. When the energy of the alpha rays (Eα) in MeV increases, the number of counts (Nc) on the detector also increases linearly as shown in the table below. 

Draw the graph of Nc as a function of Eα (MeV) and find the energy of the unknown alpha ray if the number of counts is 31600.

Explanation

• The trigonometric identity sin²x + cos²x = 1 can be rearranged to isolate sin²x: sin²x = 1 - cos²x
• So, sin²2θ = 1 - cos²2θ