Answer: 274/3 and 137 ft
Step-by-step explanation:
Total fence used: 548 ft
So, perimeter will be 548 ft, including the fence that divides the land.
Consider the playground the drawing below.
__________x________
| |
| | y
| |
|__________________|
Let's consider that the playground is going to be divided parallel to y (and there's no problem, because if you choose parallel to x, the area will be the same). So, the perimeter (the sum of all sides) will be:
2x + 3y = 548
And the area
A = x.y
Isolating x, we have:
x = (548 - 3y)/2
Substituting the x in the Area equation:
A = (548 - 3y)/2 . y = 548y - 3y²/2 = 274y - 3/2y²
A = 274y - 3/2y²
So, it's a quadratic function. And, to find out the maximum area that the playground can have, we need to find the y-vertex of the parabola: y-vertex = Δ/4a
a = -3/2 b = 274 c = 0
Δ = 274² - 4.(-3/2).0 = 274² = 75076
Amax = -Δ/4a = -75076/4.(-3/2) = 75076/6 = 12512.7 ft²
y = -b/2a = -274/2.(-3/2) = 274/3 ft
x = (548 - 3y)/2 = (548 - 3.274/3)/2 = 274/2 = 137 ft
The probability of any particular sequence of N flips of a fair coin is 2^(-N).
Your probability of the given sequence of 3 coin flips is
2^-3 = 1/8
Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
Answer:
a. 37
Step-by-step explanation:
Do 150 divided by 4 so you know how many tables there can be.
150/4
37.5 You can only have 37.5 tables so the awnser is A.37
