Answer:
c.
Step-by-step explanation:
it would be 1/2 the rest equal 2/5
Answer:
![A_{f}=4\pi (\sqrt[3]{36} r)^{2}\\\\V_{f}=\frac{4}{3} \pi (36r^{3})](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29)
Step-by-step explanation:
In order to find the final radii of the sphere, we need to calculate the volume, knowing that volumes are additive:
![V_{1}=\frac{4}{3} \pi (r^{3})\\\\V_{2}=\frac{4}{3} \pi (2r)^{3}\\\\V_{3}=\frac{4}{3} \pi (3r)^{3}\\\\V_{f}=\frac{4}{3} \pi (r^{3}+(2r)^{3}+(3r)^{3})\\\\V_{f}=\frac{4}{3} \pi (r^{3}+8r^{3}+27r^{3})\\\\V_{f}=\frac{4}{3} \pi (36r^{3})\\\\V_{f}=\frac{4}{3} \pi R^{3}\\\\R=\sqrt[3]{36} r](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%29%5C%5C%5C%5CV_%7B2%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%282r%29%5E%7B3%7D%5C%5C%5C%5CV_%7B3%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%283r%29%5E%7B3%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B%282r%29%5E%7B3%7D%2B%283r%29%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B8r%5E%7B3%7D%2B27r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R%5E%7B3%7D%5C%5C%5C%5CR%3D%5Csqrt%5B3%5D%7B36%7D%20r)
Now that we know the radii of the new sphere, we can calculate the surface area:
![A_{f}=4\pi R^{2}\\\\A_{f}=4\pi (\sqrt[3]{36} r)^{2}](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20R%5E%7B2%7D%5C%5C%5C%5CA_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D)
The triangle has sides "a", "b" and "c", where side a = side b and the hypotenuse (side "c") equals side "a" or "b" times the square root of 2.
Prism volume = triangle area * height
342.1 = triangle area * 13.2
triangle area = 342.1 / 13.2
<span><span><span>triangle area = 25.9166666667
</span>
</span>
</span>
area of a triangle is (1/2) base * height
In a 45 45 90 triangle, the base = height and since we don't know either the base or the height we'll call both "x".
So triangle area = (1/2) * x^2
<span>25.9166666667 = (1/2) * x^2
x^2 = </span><span>51.8333333334
x ( the base and the height) = </span><span><span><span>7.1995370222
</span>
</span>
</span>
<span>
</span>
the hypotenuse of a 45 45 90 triangle = leg * square root (2) =
hypotenuse = <span>7.1995370222 * sq root (2)
</span><span><span><span>hypotenuse = 10.1816828995
</span>
</span>
</span>
So, one of the legs = <span><span>7.1995370222
</span>
Source:
http://www.1728.org/triprism.htm
</span>
Given:
A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.
To find:
The quantity of the 60% solution in the mixture.
Solution:
Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.
Quantity of mixture is 234. So,
...(i)
The mixture has 43% fertilizer. So,
Multiply both sides by 100.
...(ii)
Using (i) and (ii), we get
Divide both sides by -39.
Putting this value in (i), we get
Therefore, 132 liters of the 60% solution must be used.
