A gardener has 640 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it doe
s not need any fencing.
What dimensions would guarantee that the garden has the greatest possible area?
What dimensions would guarantee that the garden has the greatest possible area?
1 answer:
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Answer:
- 160 ft (out from the river)
- 320 ft (parallel to the river)
Step-by-step explanation:
Let x represent the length of fence parallel to the river. Then the dimension of perpendicular to the river will be half the remaining fence: (640-x)/2. The total area will be ...
A = x(640-x)/2
This is the equation of a parabola that opens downward. It has zeros at x=0 and x=640, so its axis of symmetry is x = (0+640)/2 = 320. That is, the peak of the area curve is found when x=320.
The dimensions of the garden with the largest area are 160 ft wide by 320 ft long, where the long side is the river side.
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If Jake ate 1/6 of the cookies at the party and we know he ate 5 cookies. We must find out how many cookies there are in all.
Now x here represents how many total cookies are at the party.
We have to simply find out what 1 was multiplied by to get 5.
We can do this by dividing.
5 ÷ 1 = 5
So the numerators (the top numbers) were multiplied by 5. We can do the same to the denominators (the bottom numbers) to get the total number of cookies.
Lets multiply.
6 x 5 = 30
So the total number of cookies is 30
Good Luck! <3
Given:
Three line segments have measures of 4 units, 6 units, and 8 units.
To find:
Will the segments form a triangle?
Solution:
We know that three line segments can form a triangle if the sum of two smaller sides is greater than the largest side.
Three line segments have measures of 4 units, 6 units, and 8 units. Here, the measure of the largest sides is 8 units.
The sum of two smaller sides is
Since the sum of two smaller sides is greater than the largest side, therefore the segments will form a triangle.