A gardener purchases a ceramic planter, in the shape of a hemisphere, for a small batch of leftover annuals. The volume of a hemisphere is modeled by the function V = 2/3πr 3
<span>A. Write a model for the radius as a function of the volume. </span>
<span>B. The label on the planter says that it holds approximately 134 cubic inches of potting soil. What is the radius of the planter, rounded to the nearest inch? Use 3.14 for π </span>
<span>r = ∛[(3/2)V) / π] </span>
<span>134 = (2/3) (3/14) r^3 </span>
<span>r = ∛[(3/2) (134) / 3.14] ≈ 4.00 inches </span>
For this case we must rewrite the following expression:
By definition of properties of powers and radicals we have to:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
Then, the expression can be rewritten as:
![x ^ {\frac {9} {7}} = \sqrt [7] {x ^ 9}](https://tex.z-dn.net/?f=x%20%5E%20%7B%5Cfrac%20%7B9%7D%20%7B7%7D%7D%20%3D%20%5Csqrt%20%5B7%5D%20%7Bx%20%5E%209%7D)
If we want to simplify:
![\sqrt [7] {x ^ 9} = \sqrt [7] {x ^ 7 * x ^ 2} = x \sqrt [7] {x ^ 2}](https://tex.z-dn.net/?f=%5Csqrt%20%5B7%5D%20%7Bx%20%5E%209%7D%20%3D%20%5Csqrt%20%5B7%5D%20%7Bx%20%5E%207%20%2A%20x%20%5E%202%7D%20%3D%20x%20%5Csqrt%20%5B7%5D%20%7Bx%20%5E%202%7D)
ANswer:
![x ^ {\frac {9} {7}} = \sqrt [7] {x ^ 9} = x \sqrt [7] {x ^ 2}](https://tex.z-dn.net/?f=x%20%5E%20%7B%5Cfrac%20%7B9%7D%20%7B7%7D%7D%20%3D%20%5Csqrt%20%5B7%5D%20%7Bx%20%5E%209%7D%20%3D%20x%20%5Csqrt%20%5B7%5D%20%7Bx%20%5E%202%7D)
Find a common denominator. The lowest one would come from you multiplying 2/5 by 4 on each side and 1/4 by 5 on each side. You are left with 8/20 and 5/20, added together would be 13/20.
Answer:
4 hours
Step-by-step explanation:
2×6=3x
12÷3= 4
x=4 so 4 hours.
Answer:The endpoint of line CD are given.find the coordinates of the Midpoint M.
1: C(3,-5) and D(7,9)
2: C(-8,-6) and D(-4,10)
Step-by-step explanation: explanation:...
