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:
I would say 32 but I'm so sorry if it's wrong
Composite functions is a way of substituting one function into another. The value of the composite function f(g(1)) is 1
<h3>Composite functions</h3>
Composite functions is a way of substituting one function into another.
Given the function expressed as:
y = 3√x + 1
g(1) from the mapping is 0
Substitute g(1) = 0 into the given function to have:
f(g(1)) = 3√0 .+ 1
f(g(1)) =0 + 1
f(g(1)) = 1
Hence the value of the composite function f(g(1)) is 1
Learn more on composite function here: brainly.com/question/10687170
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Answer:
x = 47°
y = 10
z = 5
Step-by-step explanation:
They share the middle line which is one side. It's given that side y is congruent to the side with a value of 5. Angle X and the non labeled angel are also congruent to each other. Using SAS (side angle side) we can conclude the 2 triangles are congruent, which means all angles and sides are congruent and equal.
The angles of a triangle add to 180.
x+90+43=180
x=47
z is congruent/equal to 5 since they are congruent and equal triangles. Therefore z=5
Y is congruent to side 10, which also means it is equal to 10. Therefore y=10
