Problema Solution
You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?
Answer provided by our tutors
Make a drawing and denote:
x = half of the length of the enclosure
2x = the length of the enclosure
y = the width of the enclosure
P = 800 ft the perimeter
The perimeter of the two enclosures can be expressed P = 4x + 2y thus
4x + 3y = 800
Solving for y:
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y = 800/3 - 4x/3
The area of the two enclosure is A = 2xy.
Substituting y = 800/3 - 4x/3 in A = 2xy we get
A = 2x(800/3 - 4x/3)
A =1600x/3 - 8x^2/3
We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum:
x max = -b/2a, a = (-8/3), b = 1600/3
x max = (-1600/3)/(2*(-8/3))
x max = 100 ft
y = 800/3 - 4*100/3
y = 133.33 ft
2x = 2*100
2x = 200 ft
Answer: 54.4 mph
Step-by-step explanation:
First find the distance to the train station. If it took Carlos 4 hours to come back driving at 68 mph, the distance is:
= Speed * time
= 68 * 4
= 272 miles
This means that Carlos drove for 5 hours to cover 272 miles the first time. His average speed was therefore:
= Distance / time
= 272/5
= 54.4 mph
Answer:
60 and 40 or 120 and 20
Step-by-step explanation:
60 x 2=120
40 x 3=120
60 x 40=2400
120 x 1=120
20 x 6=120
120 x 20=2400
You can try a few others, but no others have an lcm of 120
56 / 4 = 14 and 44 / 4 = 11, so 14:11
Answer:
3x² - 9x + 5
Step-by-step explanation:
Given
(5x² - 3x + 4) - (2x² + 6x - 1)
Distribute the first parenthesis by 1 and the second by - 1
= 5x² - 3x + 4 - 2x² - 6x + 1 ← collect like terms
= (5x² - 2x²) + (- 3x - 6x) + (4 + 1)
= 3x² - 9x + 5
