Answer:
0.7 kg = $1
Step-by-step explanation:
7 kg - $10
? kg - $1
7 / 10 = 0.7
0.7 kg = $1
Let me know if I did something wrong :)
Answer:
V candle ≈ 196.9 cm³
Step-by-step explanation:
Volume of cone = ( π·r²·h)/3
V candle = V big cone -V small cone
V candle = [ π·4²·(8+5) - π·2²·5]/3
V candle = ( π·16·13 - π·4·5)/3
V candle = (π·16·13 - π·4·5)/3
V candle = π·(208 - 20)/3
V candle = π·188/3
V candle = 196.8731396
V candle ≈ 196.9 cm³
Answer:
The required width of the field that would maximize the area is = 1250 feet
Step-by-step explanation:
Given that:
The total fencing length = 5000 ft
Let consider w to be the width and L to be the length.
Then; the perimeter of the rectangular field by assuming a parallel direction is:
P = 3L + 2w
⇒ 3L + 2w = 5000
3L = 5000 - 2w
![L = \dfrac{5000}{3} - \dfrac{2w}{3}](https://tex.z-dn.net/?f=L%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B2w%7D%7B3%7D)
Recall that:
The area of the rectangle = L×w
![A(w) = ( \dfrac{5000}{3}-\dfrac{2}{3} ) w](https://tex.z-dn.net/?f=A%28w%29%20%3D%20%28%20%5Cdfrac%7B5000%7D%7B3%7D-%5Cdfrac%7B2%7D%7B3%7D%20%29%20w)
![A(w) = \dfrac{5000}{3}w-\dfrac{2}{3} w^2](https://tex.z-dn.net/?f=A%28w%29%20%3D%20%20%5Cdfrac%7B5000%7D%7B3%7Dw-%5Cdfrac%7B2%7D%7B3%7D%20%20w%5E2)
Taking the differentiation of both sides with respect to t; we have:
![A' (w) = \dfrac{5000}{3} - \dfrac{2}{3} ( 2 w)](https://tex.z-dn.net/?f=A%27%20%28w%29%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B2%7D%7B3%7D%20%28%202%20w%29)
![A' (w) = \dfrac{5000}{3} - \dfrac{4w}{3}](https://tex.z-dn.net/?f=A%27%20%28w%29%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B4w%7D%7B3%7D)
Then; we set A'(w) to be equal to zero;
So; ![\dfrac{5000}{3} - \dfrac{4w}{3}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B4w%7D%7B3%7D%3D0)
5000 = 4w
w = 5000/4
w = 1250
Thus; the required width of the field that would maximize the area is = 1250 feet
Also, the length
can now be :
![L = \dfrac{5000}{3} - \dfrac{2(1250)}{3}](https://tex.z-dn.net/?f=L%20%3D%20%5Cdfrac%7B5000%7D%7B3%7D%20-%20%5Cdfrac%7B2%281250%29%7D%7B3%7D)
L = (5000 -2500)/3
L = 2500/3 feet
Suppose, the farmer divides the plot parallel to the width; Then 2500/3 feet = 833.33 feet and the length L = 1250 feet.
I t s I s w r I n g s I k e I lied