Answer:
Step-by-step explanation:
Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.
120 = L + 2W
Where
LW = area.
Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60
On substituting, we have
A = LW = (120 - 2W) W
From the first equation, making L the subject of the formula, we have this
L = 120 - 2W, which then we substituted above.
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
Answer:
B. 1469.52 cubic units
Step-by-step explanation:
6 squared is 36, 36 x 13 is 46s, 468 x 3.14(pie) is 1469.52
<h2>
Answer:</h2>
<em> The side of the triangle is either 38.63ft or 10.35ft</em>
<h2>
Step-by-step explanation:</h2>
This problem can be translated as an image as shown in the Figure below. We know that:
- The side of the square is 10 ft.
- One of the vertices of an equilateral triangle is on the vertex of a square.
- Two other vertices are on the not adjacent sides of the same square.
Let's call:
Since the given triangle is equilateral, each side measures the same length. So:
x: The side of the equilateral triangle (Triangle 1)
y: A side of another triangle called Triangle 2.
That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:

We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:

Therefore, for Triangle 3, we have that by Pythagorean theorem:

Matching equations (1) and (2):

Using quadratic formula:

Finding x from (1):

<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>
<span>A slope of 1/2 means that for every two units you go to the right horizontally, the graphed line
goes up 1 unit vertically.</span>