Let the side length of the square be x, then A = x^2
but diagonal (z) = sqrt(2x^2)
z^2 = 2x^2
x^2 = 1/2 z^2
Thus, A = 1/2 z^2
dA/dz = 1/2 (2z) = z
The rate of change is z.
When z = 4, the rate is 4.
{(2, 3), (1, 5), (2, 7)} - NOT because 2->3 and 2->7
{(11, 9), (11, 5), (9, 3)} - NOT because 11->9 and 11->5
{(3, 8), (0, 8), (3, -2)}
- NOT because 3->8 and 3->-2
{(-1, 5), (-2, 6), (-3, 7)} - YES
Answer:
Step-by-step explanation:
Sec B
1) 5p⁻³ = 8*5⁻²
p⁻³ = 2³*5⁻²/5
p⁻³ =2³*5⁻³ { 1/a^m = a^-m}
p⁻³ = 5⁻³ /2⁻³ {a^m = 1/a^-m}
p⁻³ = (5/2)⁻³
p= 5/2
2) 4x² = 81
x² = 81/4
x² = 9² /2²
x² =(9/2)²
x = 9/2
3) 9^x/3 =81
9^x/3 = 9^2
Comparing the powers, x/3 = 2
x = 2*3 =6
x = 6
