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[Avinash Physics Math tutor @avisahay]

@Airaasayss 30
If the side length of each smallest square is 1 unit, then
4 x 4 = 16 squares of length 1 unit
3 x 3 = 9 squares of length 2 units
2 x 2 = 4 squares of length 3 units
1 square of length 4 units

Total 30 squares

[Avinash Physics Math tutor @avisahay]

@real_hotaru This is an even number, so it is divisible by 2.

[Avinash Physics Math tutor @avisahay]

@H0H0v Let y = f(x)
f(f(x)) = 259
f(y) = 259
y^2 - 6y + 12 = 259
(y - 3)^2 + 3 = 259
(y - 3)^2 = 256
y - 3 = 16, -16
y = 19, -13
x^2 - 6x + 12 = 19, -13
(x - 3)^2 + 3 = 19, -13
(x - 3)^2 = 16, -13
If x is real, then
(x - 3)^2 = 16
x - 3 = 4, -4
x = 7, -1

[Avinash Physics Math tutor @avisahay]

@sonuydv87 40 + 30 + 20 + 10

[Avinash Physics Math tutor @avisahay]

@Milkshake54_ Both A and D are correct. Either use team as singular or as plural but do not mix up.

[Avinash Physics Math tutor @avisahay]

@PhilosophyOfPhy The above integrand is an even function of u. Therefore, the
integral = 2 integral(0 to pi/2) 2 cos^2 u du
= 2 integral(0 to pi/2) cos(2u) + 1 du
= 2 [sin(2u)/2 + u] (0 to pi/2)
= [sin(2u) + 2u] (0 to pi/2)
= sin(pi) - sin(0) + pi - 0
= pi

[Avinash Physics Math tutor @avisahay]

@PhilosophyOfPhy Put x = 2 sin(u)
sqrt(4 - x^2) = sqrt(4 - 4 sin^2 u) = 2 cos(u)
dx = 2 cos(u) du
When x = -2, then sin(u) = -1 and u = -pi/2
When x = 2, then sun(u) = 1 and u = pi/2

The integral
= (1/2) integral(-pi/2 to pi/2) 4 cos^2 u du
= integral(-pi/2 to pi/2) 2 cos^2 u du

[Avinash Physics Math tutor @avisahay]

@RuksanaAnsar 85
Multiply the two numbers. Then multiply by 2. Then add 1.

[Avinash Physics Math tutor @avisahay]

@Jabir826945 The letter R.

[Avinash Physics Math tutor @avisahay]

@MathyMari @mathladyhazel For any integer n, the value of n(n+1) is even.
This is because if n is even, then (n+1) is odd.
And if n is odd, then (n+1) is even.
In either case, we are multiplying an even integer and an odd integer. The result is even.

[Avinash Physics Math tutor @avisahay]

@mathladyhazel We can simply write
n = n^2 + n - n^2
n = n(n+1) - n^2

[Avinash Physics Math tutor @avisahay]

@sonukg4india It is a vertical parabola and the vertex is (-1, 4)
Therefore, the equation is of form:
y = a(x + 1)^2 + 4
Substitute (1, 0)
0 = a(1 + 1)^2 + 4
0 = 4a + 4
a = -1

Answer:
y = -(x + 1)^2 + 4

[Avinash Physics Math tutor @avisahay]

@Ldphobiawatch 80
Multiply the two numbers and then multiply by 5.

[Avinash Physics Math tutor @avisahay]

@H0H0v Increase
Mouse accelerates up. Net force on mouse is up. Bag exerts up force on mouse. Mouse exerts a down force on bag.
Forces on bag:
1) Force of gravity down
2) Force by mouse down
3) Force by scale up
(3) = (1) + (2)
Because of (2), the (3) increases.
Scale reading increases.

[Avinash Physics Math tutor @avisahay]

@sonukg4india Part C

Case 3L x > -1
(x + 1)/(x + 2) >= 2
x + 1 >= 2(x + 2)
x + 1 >= 2x + 4
2x + 4 <= x + 1
x <= -3
Not possible.

[Avinash Physics Math tutor @avisahay]

@sonukg4india Part B
Case 2: -2 < x < -1
|x + 1| = -(x + 1)
|x + 2| = x + 2
-(x + 1)/(x + 2) >= 2
-(x + 1) >= 2(x + 2)
-x - 1 >= 2x + 4
2x + 4 <= -x - 1
3x <= -5
x <= -5/3
Therefore, -2 < x <= -5/3

[Avinash Physics Math tutor @avisahay]

@Math_files Answer is 5
Question does not ask how many liters. It asks how many barrels.

[Avinash Physics Math tutor @avisahay]

@umeh098 Look at the left column.
6 x 2 = 12
12 x 3 = 36
36 x 4 = 144

See the middle column.
5 x 3 = 15
15 x 4 = 60
60 x 5 = 300
So, the number that we multiply with to get the next number keeps increasing by one.

See the right column.
12 x 3= 36
36 x 4 = 144
144 x 5 = 720 (answer)