The height and radius that will give us the smallest amount of paper, should have should have the perfect dimension, in that the diameter should be equal to the height. thus let the diameter be x, the height will be x and the radius will be x/2
thus the volume of the cone will be:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
hence the value of x will be:
33=0.262x^3
x^3=125.95
x=(125.95)^(1/3)
x=5.0126=5.01 cm
thus the diameter=height=5.01cm
Answer:
If x is an integer, then for values of x ≤ 0 would -x be positive.
General Formulas and Concepts:
<u>Math</u>
Step-by-step explanation:
We know that integers comprise of the number line from -∞ to ∞. We can have numbers like -3, -2, -1, 0, 1, 2 ,3.
If we say that x is an integer, and that -x must be positive, then that means the integer x must be negative, because a negative times a negative is a positive.
∴ x can only be negative integers, thus giving us x ≤ 0.
Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula 
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have
Hence, f(c+1/2) = f(c) as we wanted.
Answer:
Area = 6
Step-by-step explanation:
1/2 is the same as 0.5 feet.
To find the area you have to times the length by the width.
4 feet x 1.5 feet =6
Answer:
(x + 2)² + (y - 1)² = 25
Step-by-step explanation:
radius: r² = (1 - (-3))² + (-2 - (-5))² = 16 + 9 = 25
r = 5
Circle: (x - h)² + (y - k)² = r²
center: (-2 , 1) h = -2 k = 1
(x + 2)² + (y - 1)² = 25
