The area of circle is 113.04 in^2
Further explanation:
The area of circle is calculated by using pi and radius.
We are given
Diameter = d = 12 inches
pi = π = 3.14
![r = \frac{d}{2} = \frac{12}{2} = 6\ inches](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bd%7D%7B2%7D%20%3D%20%5Cfrac%7B12%7D%7B2%7D%20%3D%206%5C%20inches)
![Area = \pi r^2\\= 3.14 * (6)^2\\= 3.14 * 36\\=113.04\ in^2](https://tex.z-dn.net/?f=Area%20%3D%20%5Cpi%20r%5E2%5C%5C%3D%203.14%20%2A%20%286%29%5E2%5C%5C%3D%203.14%20%2A%2036%5C%5C%3D113.04%5C%20in%5E2)
The area of circle is 113.04 in^2
Keywords: Circle, Area of Circle
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The answer is a, i dont think i want the prize tho lol
Answer:
Step-by-step explanation:
<span>y-2x=-6 and 5x-y=9
step 1: isolate y in the first equation
y = 2x - 6
step 2: substitute the y value on the 2th equation:
5x-(2x-6)=9
step 3: solve the present equation:
5x - 2x + 6 = 9
3x = 9-6
3x = 3
x = 1
step 4: get the y value by replacing the value of x in </span>y = 2x - 6:
<span>
y = 2*1 - 6
y = 2 - 6
y = -4
S={1, -4}
</span>
Answer:
15
Step-by-step explanation:
To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula
![x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x= \frac{-b-\sqrt{b^{2}-4ac } }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%2B%5Csqrt%7Bb%5E%7B2%7D-4ac%20%7D%20%7D%7B2a%7D%3B%20x%3D%20%20%5Cfrac%7B-b-%5Csqrt%7Bb%5E%7B2%7D-4ac%20%7D%20%7D%7B2a%7D)
![x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B-700%2B%5Csqrt%7B700%5E%7B2%7D-4%28a%29%28-10000%29%20%7D%20%7D%7B2%281%29%7D%3B%20x%3D%20%5Cfrac%7B-700-%5Csqrt%7B700%5E%7B2%7D-4%28a%29%28-10000%29%20%7D%20%7D%7B2%281%29%7D)
![x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B-700%2B%5Csqrt%7B530000%7D%20%7D%7B2%7D%3B%20x%3D%20%5Cfrac%7B-700-%5Csqrt%7B530000%7D%20%7D%7B2%7D)
![x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-700%2B100%5Csqrt%7B53%7D%20%7D%7B2%7D%3B%20x%3D%5Cfrac%7B-700-100%5Csqrt%7B53%7D%20%7D%7B2%7D%3B)
![x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005](https://tex.z-dn.net/?f=x%3D-350%20%2B%2050%5Csqrt53%20%3D%2014.005%3B%20x%20%3D%20-350%20-%2050%5Csqrt53%20%3D%20-714.005)
In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.
![(-714.005)^2+700(-714.005)-10000=-0.360](https://tex.z-dn.net/?f=%28-714.005%29%5E2%2B700%28-714.005%29-10000%3D-0.360)
Furthermore, we must round to the nearest whole number, as you cannot make part of an item.
Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:
![(14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725](https://tex.z-dn.net/?f=%2814%29%5E2%2B700%2814%29-10000%3D-4%5C%5C%5C%5C%2815%29%5E2%2B700%2815%29-10000%3D725)