There would be 2034 students competing in 2012.
We can write a simple equation to find this answer. Let X, be the number of students starting in 2012. Then, we multiply by 0.9 and 1.1 to get to 2014. To work backwards, just divide by 1.1, then by 0.9.
2014 / 1.1 / 0.9 = 2034
Use Multiplication Distribute Property: (xy)^a = x^ay^a
6^2(x^-2)^2(0.5x)^4
Simplify 6^2 to 36
36(x^-2)^2(0.5x)^4
Use this rule: (x^a)^b = x^ab
36x^-4(0.5x)^4
Use the Negative Power Rule: x^-a = 1/x^a
36 × 1/x^4(0.5x)^4
Use the Multiplication Distributive Property: (xy)^a = x^ay^a
36 × 1/x^4 × 0.5^4x^4
Simplify 0.5^4 to 0.0625
36 × 1/x^4 × 0.0625x^4
Simplify
2.25x^4/x^4
Cancel x^4
<u>2.25</u>
2 X 6 = 12
So, it would be 12 orange picks.
Answer:
The volume of the cylinder is about 1256.6 cubic meters.
Step-by-step explanation:
The volume of a cylinder is given by the formula:
Where <em>r</em> is the radius and <em>h</em> is the height.
Our radius is 10 meters and our height is four meters. Substitute:
Evaluate:
Thus, the volume of the cylinder is about 1256.6 cubic meters.
These calculations are based on the drawing of the file enclosed.
There are three right triangles.
From the big right triangle:
a^2 + b^2 = 25^2
From the small right triangle on the left side:
(25-x)^2 + 10^2 = a^2
From the small right triangle on the right side
x^2 +10^2 = b^2
=> (25-x)^2 + 10^2 + x^2 + 10^2 = a^2 + b^2
=> (25-x)^2 + 10^2 + x^2 + 10^2 = 25^2
=> 25^2 - 50x + x^2 + 10^2 + 10^2 = 25^2
=> x^2 -50x + 100 =0
Use the quadratic formular to find the roots:
x = 2.1 and x = 47.9
Distance from back: 25 - 2.1 = 22.9 ft
Answer: 22.9 ft
