Answer:
The answer is below
Step-by-step explanation:
The volume of the cylinder with radius (r) and height (h) is given as:
Volume = πr²h
17 = πr²h
h = 17 / πr²
Let k represent the cost of the side and 2k the cost of the bottom.
The area of the side = 2πrh, hence the cost of the side = k(2πrh)
The area of the top and bottom = 2πr², hence the cost of the top and bottom = 2k(2πr²)
The total cost (T) = cost of side + cost of the top and bottom
T = k(2πrh) + 2k(2πr²)
T = 2kπ(rh + 2r²)
Put h = 17/πr²
T = 2kπ (r×17/πr² + 2r²)
T = 2kπ(17/πr + 2r²)
The minimal cost is at dT/dr = 0
![\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2} =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdr%7D%20%3D0%3D%5Cfrac%7Bd%7D%7Bdr%7D%20%5B2k%5Cpi%28%5Cfrac%7B17%7D%7B%5Cpi%20r%7D%20%2B2r%5E2%29%5D%5C%5C%5C%5C4r-%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%3D0%5C%5C%5C%5C4r%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%5C%5C%5C%5Cr%5E3%3D%5Cfrac%7B17%7D%7B4%5Cpi%20%7D%3D1.35%5C%5C%5C%5Cr%3D%5Csqrt%5B3%5D%7B1.35%7D%5C%5C%5C%5Cr%3D1.1%5C%20m%5C%5C%5C%5Ch%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%20%3D%5Cfrac%7B17%7D%7B%5Cpi%20%281.1%29%5E2%7D%20%5C%5C%5C%5Ch%3D4.42%5C%20m)
Answer:
9409
Step-by-step explanation:
Let's rewrite 97 as 100 - 3.
Identity used :
<u><em>(a - b)² = a² - 2ab + b²</em></u>
Now, evaluating the expression :
⇒ (100 - 3)²
⇒ (100)² - 2(100)(3) + (3)²
⇒ 10000 - 600 + 9
⇒ 9400 + 9
⇒ 9409
Answer:
<h2>(-2, -4)</h2>
Step-by-step explanation:
Put the coordinates of the points to the equation, and check it:
(-4, -1) → x= -4, y = -1
L = -5(-4) - 3(-1) =20 + 3 = 23
R = 22
L ≠ R
(-1, -4) → x= -1, y = -4
L = -5(-1) - 3(-4) = 5 + 12 = 17
R = 22
L ≠ R
(-2, -4) → x= -2, y = -4
L = -5(-2) - 3(-4) = 10 + 12 = 22
R = 22
L = R CORRECT :)
(-4, -2) → x = -4, y = -2
L = -5(-4) - 3(-2) = 20 + 6 = 26
R = 22
L ≠ R
Answer:
720 individuals
Step-by-step explanation:
According to my research, I can say that based on the information provided within the question you can conclude that the population of land snails has about 720 individuals. We can calculate this by using the Rule of Three formula that is attached below.
x ⇒ 80 marked
45 ⇒ 5 marked


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