Average velocity could be found by dividing the position difference to the time difference.

Since negative numbers do not have square roots,x²-4y² must be non-negative. Thus:

x²-4y²≥0

(x-2y)(x+2y)≥0

This can be true only if both (x-2y) and (x+2y) are non-negative or both are non-positive.

I. First we take the first case (both are non-negative).

Thus:

x-2y≥0 which means x≥2y

x+2y≥0 which means x≥-2y

Thus the solution set is x≥2y ∩ x≥-2y

II. Now we take the second case (both are non-positive)

Thus:

0≥x-2y which means 2y≥x

0≥x+2y which means -2y≥x

This can only be true when x=y=0, which is included in the solution set of case 1.

Thus the answer is x≥2y ∩ x≥-2y

2² = (d1)² + (d2)² = ((x1)² + (y1)²)+ ((x1)² + (2 - y1)²) = ((x1)² + (x1)²) + ((x1)² + (2 - x1)²) = (2 (x1)²) + ((x1)² + 4 – 4 (x1) + (x1)²) = 4 (x1)² + 4 – 4 (x1) ; 4 (x1)² – 4 (x1) = 0 ; x1 = 1
y1 = 1 ; d2 = 2^1/2 . pg. 193. Correct answer is E.

The answer is D.

(f.g)(3) =f(3).g(3)=3^-1.2.3-1=3^-1.5=5/3

f(x)=x³

f '(x)=3x²>0 for all values of x other than x=0.

For all other functions f '(x)<0 for (-?,0) and f '(x)>0 for x>0.

The statements regarding to sets in the options;

I “The sets A = {4, 8, 11, 15} and B = {8, 15, 4 ,11} are the same.”

II “The empty set Ø is a subset of any set.”

III “The equality A = B is equivalent to two inclusions: A ? B and B ? A.”

IV “The set of elements that are in either A or B or both is called the union of the sets A and B and is denoted by A ? B.”

V “x ? A ? B if and only if x ? A and x ? B.”

VI “If A ? B = Ø then the sets A and B are called disjoint sets.” are correct, so the correct answer is D.

The statement in the option VII “Universal set is unique.” is not correct. Universal set is not unique. It varies depending on the problem.

The answer is D.

The slope of the demand function is

So, we find the slope as (2500-3000)/(6000-5000)=-1/2.

The slope of the demand function is

If x denotes the quantity of supply, and p is the price then we can
write (x1, p1)=(300,100) and (x2,p2)=(500,150). So, the slope is equal to 50/200=1/4.

The answer is B.

. The answer is C.

f(x, y)=5x²+xy-y²

f_x=10x+y (since the derivative of y² is zero)

If f(x)=2x³-3x²+4x-3, then f'(x)=6x²-6x+4. And for x=2 f'(x)=16

Break-even point is the point where the total cost and the total revenue are equal (C(x)=R(x)).

The graph tells us that the equation has 2 positive roots. The equation in A has two roots which are 0 and -5. The equation in C has two roots which are -3 and -2. The equation in D has two roots which are -6 and 1. The equation in E has 2 roots which are -?6 and ?6.

Finally the equation in B has 2 roots which are 2 and 3. Thus only this equation has 2 positive roots.