Emma and Anna went to the market to buy 25 fruits. Emma got a few apples that cost $2 each, and Anna bought some oranges which c
1 answer:
You might be interested in
Answer:
20.78feet
Step-by-step explanation:
The question made us to understand that the man is standing and also there is angle of elevation, then we need to draw a right triangle having a base equal to 36 feet with an angle from the base to the top of the pole which is 30 degrees.
tan= opposite side / adjacent side
Let height of the pole =h
Tan(30)= h/36
But tan 30degree= 1/√3
h= 36 × 1/√3
h= 20.78feet
Therefore, the height of the pole= 20.78feet
CHECK THE ATTACHMENT FOR DETAILED FIGURE
Answer:
Maximum Area of the basketball court = 1250 ft²
Maximum area of the playground = 400 ft²
The basketball is 3.125 times larger than than the playground.
Step-by-step explanation:
The diagram representing the description is attached to this solution.
The big rectangle represents the basketball court.
The small rectangle represents the playground.
Let the length and width of the basketball court be y and x respectively.
The length and width of the small playground will be (y-30) and (x-5) respectively
The Area of the basketball court is
A(x, y) = xy
But, 2x + y = 100
We can maximize the Area by turning the two variable function into a one variable function and substituting for y in the Area equation.
2x + y = 100
y = 100 - 2x
A(x, y) = xy
A(x) = x(100 - 2x) = 100x - 2x²
A(x) = 100x - 2x²
At maximum point, (dA/dx) = 0 and (d²A/dx²) < 0, that is, negative.
(dA/dx) = 100 - 4x = 0
(d²A/dx²) = -4 < 0
Hence, it's a maximum point.
At maximum point,
(dA/dx) = 100 - 4x = 0
100 - 4x = 0
4x = 100
x = 25 ft
y = 100 - 2x = 100 - 2(25) = 100 - 50 = 50 ft
Hence, the length and width of the basketball court that maximizes the Area are 50 ft and 25 ft respectively.
For the small playground,
The length = (y - 30) = (50 - 30) = 20 ft
The width = (x - 5) = (25 - 5) = 20 ft
Maximum Area of the basketball court = xy = (50)(25) = 1250 ft²
Maximum area of the playground = (y-30)(x-5) = (20)(20) = 400 ft²
Ratio of the Areas = (1250/400) = 3.125
The basketball is 3.125 times larger than than the playground
Hope this Helps!!!
