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
Answer:
Area = 210
Step-by-step explanation:
Given:
To find:
Steps:
A = b · h
= 15 · 14
= 210
Answer:
64
Step-by-step explanation:
To find m, it has given you √x = 8. The opposite of a square root is squaring (exponentials). Simply just square 8 and you should get x = 64. You can check by square rooting 64, and you should get 8.
Answer:
Cards with Mark = 30
Cards with Drew = 120
Cards with Katie = 12
Step-by-step explanation:
The complete question is
Drew has 4 times as many baseball cards as Mark. Katie has 3 fewer than than half as many cards as Mark. In all they have 162 baseball cards. How many does each have?
Solution -
Let the number of cards with Mark be "X"
Number of cards with Drew = 4 *X = 4X
Number of Cards with Katies = 0.5 X -3
Sum of all the cards is equal to 162
X+4X + 0.5 X -3 = 162
5.5 X = 165
X = 30
Cards with Mark = 30
Cards with Drew = 4 * 30 = 120
Cards with Katei = 15-3 = 12
