The dimensions of a cylinder which has this maximum volume are equal to 1.83 units and 3 units.
<u>Given the following data:</u>
- Height of cylinder, h = 5.5 units.
- Radius of cylinder, r = 4.5 units.
<h3>How to calculate the volume of this cylinder?</h3>
Mathematically, the volume of a cylinder can be calculated by using this formula:
V = πr²h
Next, we would convert the above multi-variable function into a single-variable function by applying the properties of 2 similar triangles:
H/H - h = R/r
H - h = r(H/R)
h = H/R(R - r)
V = πHr²/R(R - r)
In order to maximize the volume of this cylinder, we would determine the critical points of the function by differentiating wrt r:
dV/dr = πH/R(2rR - 2r² - r²)
(2rR - 3r²) = 0
r = 2R/3
r = (2 × 4.5)/3
Maximum radius, r = 3 units.
For the max. height, we have:
h = H/R(R - r)
h = H/R(R - 2R/3)
h = H/3
h = 5.5/3
Maximum height, h = 1.83 units.
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Answer:
1) 28.4 miles per gallon
2) 34 miles per gallon
3) the silver car
Step-by-step explanation:
We have the following information:
Blue car:
Travels 35 1/2 miles on 1 1/4 gallons of gasoline
Silver car:
Travels 27 1/5 miles on 4/5 gallons of gasoline
We want to know the unit rate for miles per hour, and to do it we have to divide the miles they travel by the gallons each car uses:
Blue car:
(35 1/2) / (1 1/4) = 28.4 miles per gallon
Silver car:
(27 1/5) / (4/5) = 34 miles per gallon
B. 15m, 20m, 25m
use pythagorean theorem
a²+b²=c²
225+400=625
the square root of 625 is 25
For this case we have by definition, that each of the four internal angles of a square measure 90 degrees.
If we draw the diagonals of the square then the angles are divided by two, that is:
Thus, angle 3 measures 45 degrees.
By definition, the sum of the internal angles of a triangle is 180 degrees.
So:
Thus, angle 2 measures 45 degrees.
Answer:
45 degrees
<em>Correct expression: </em>
Answer:
x = 4
x = -4
x = 7i or
x = -7i or
Step-by-step explanation:
We do factorization of x^2 - 16
(x^2-16) = (x+4)(x-4)
(x+4)(x-4)(x^2+49) = 0
We require that any term in the multiplication to be zero to fulfil the requirement
so:
if x + 4 = 0 then (x+4)(x-4)(x^2+49) = 0
x = -4
if x - 4 = 0 then (x+4)(x-4)(x^2+49) = 0
x = 4
if (x^2+49) = 0 then (x+4)(x-4)(x^2+49) = 0
x^2 = -49
we have two roots:
If your course has already worked with complex number and the root of -1 then:
7i and -7i are solution as well
because 7i will be:
and the same reasoning for -7i: