Answer:
D. She used the beach's ball's diameter when she should have used the radius
Step-by-step explanation:
To find the volume of the beach ball, using the volume of a sphere is the right formula to use, which is ⁴/3πr³.
The formula she used is correct.
Since the diameter of the ball is assumed to be 12 inches, what is needed to find the volume is the radius.
Radius (r) = ½(diameter) = ½(12) = 6 in.
This is where Emily made a mistake.
She used the diameter of the beach ball instead of its radius (r) which is needed in the equation.
She should have gotten,
V = ⁴/3(3.14)(6)² = 904.32 cubic inches
<u>Answer-</u>
<em>The total amount of water wasted this year is 6716 gallons.</em>
<u>Solution-</u>
A study indicated that the citizens of Morris-town wasted 5840 gallons of water last year.
This year they wasted 15% more than that amount they wasted previous year.
15% of 5840 is,

The total amount of water wasted this year =
The amount of water wasted previous year + 15% more of the amount of that
= 5840 + 876
= 6716 gallons
Therefore, the total amount of water wasted this year is 6716 gallons
<em>Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.</em>
Answer:

Step-by-step explanation:
Given the expression

solving the expression

apply the rule: 


simplify

Therefore, the simplified form is:

<em>Note: Your answer choices remain a little unclear. But, I have solved the concept and solution, so you can easily figure it out.</em>
Sin³ x-sin x=cos ² x
we know that:
sin²x + cos²x=1 ⇒cos²x=1-sin²x
Therefore:
sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0
sin³x=z
z³+z²-z-1=0
we divide by Ruffini method:
1 1 -1 -1
1 1 2 1 z=1
-------------------------------------
1 2 1 0
-1 -1 -1 z=-1
--------------------------------------
1 1 0 z=-1
Therefore; the solutions are z=-1 and z=1
The solutions are:
if z=-1, then
sin x=-1 ⇒x= arcsin -1=π+2kπ (180º+360ºK) K∈Z
if z=1, then
sin x=1 ⇒ x=arcsin 1=π/2 + 2kπ (90º+360ºK) k∈Z
π/2 + 2kπ U π+2Kπ=π/2+kπ k∈Z ≈(90º+180ºK)
Answer: π/2 + Kπ or 90º+180ºK K∈Z
Z=...-3,-2,-1,0,1,2,3,4....