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
7 = 10.2
12 = 17.7
Let's take
d = 17.7 - 10.2/ 12 - 7
d = 7.5/ 5
d = 1.5
The common difference is 1.5
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Step-by-step explanation:
best of luck dear.........
Answer:
(a;b)={(17; 64); (64; 17)}
Step-by-step explanation:
a+b=81 => b=81-a
a*b=1088
a*(81-a)=1088
-a²+81a=1088
a²-81a+1088=0
a²-64a-17a+1088=0
a(a-64)-17(a-64)=0
(a-17)(a-64)=0
=> a=17 and a=64
for a=17 => b=81-17=64
for a=64 => b=81-64=17
(a;b)={(17; 64); (64; 17)}
Answer:
(-9/7,-26/7)
[more detailed at the bottom of the explanation]
Step-by-step explanation:
I am assuming that this is a system of equations...
So, knowing that y is equal to x + 5, you would plug that in the second equation and find x. Then you would plug x and find y.
—————
Step 1)
Equation 1:
y = (x + 5)
Equation 2:
5x + 2y = 1
Equation 2 can also be written as:
5x + 2(x+5) = 1
I wrote x+5 instead of y because the first equation tells us that y is equal to x + 5.
—————
Step 2)
Solve for x .
5x + 2(x+5) = 1
5x + 2x + 10 = 1
7x + 10 = 1
7x = 1 - 10
7x = -9
x = -9/7
—————
Step 3)
Plug the x value back in the first equation.
y = -9/7 + 5
y = -26/7
—————
Solution:
x = -9/7
y = -26/7
In ordered pair form:
(-9/7,-26/7)
————— ————— —————
Hope this helps !!!!!!!
