Answer:
x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.
Step-by-step explanation:
Let x be the length of wire that is cut to form a circle within the 5050 wire, so 5050 - x would be the length to form a square.
A circle with perimeter of x would have a radius of x/(2π), and its area would be
A square with perimeter of 5050 - x would have side length of (5050 - x)/4, and its area would be
The total combined area of the square and circles is
To find the maximum and minimum of this, we just take the 1st derivative, and set it to 0
Multiple both sides by 8π and we have
At x = 2221.5:
= 392720 + 500026 = 892746 [/tex]
At x = 0,
At x = 5050,
As 892746 < 1593906 < 2029424, x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.
Answer:
The triangles are similar.
Step-by-step explanation:
They are similar because they have the same angles. They may be the same size, but it would be best to refer to whatever definition you were given.
Answer:
Using the height theorem:
Now we can easily use the pythagorean theorem:
Answer:
104
Step-by-step explanation:
32+22+20+30=104
Since the figures are congruent, their side lengths are the same. Each figure has half of the side lengths provided to you. Take the 32 and 22 from A'B'C'D' and combine it with the 20 and 30 from ABCD and add them all together to get 104.
Answer:
There are 42 red colour socks and 44 green color socks
Step-by-step explanation:
Let there are r red socks and g green socks.
ATQ,
He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks.
4g-3r=50 ....(1)
Half the number of green socks plus one-third of the number of red socks is 36.
Multiply equation (1) by 2 and equation (2) by 3.
8g-6r = 100 ....(3)
9g +6r = 648 ....(4)
Add equation (3) and (4)
8g-6r + 9g +6r = 100+648
17g = 748
g = 44
Put the value of g in equation (1).
4(44)-3r=50
176-3r = 50
176-50 = 3r
r = 42
Hence, there are 42 red colour socks and 44 green color socks.