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.
Read more on cylinder here: brainly.com/question/315709
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Answer:
2091 tiles
Step-by-step explanation:
(51/4×41/4)÷(1/4×1/4)
2091 tiles
T=0=>initial
s (0)=4.5=9/2
=>s(t)=-16t^2+64+9/2
use s(-b/2a) to find height
it will take -b/2a seconds to reach that height
n I tell a,b coefficients of some
Follow for Solutions.
To solve this problem, we use the t statistic. The formula
for z score is:
z = (x – u) / s
where x is the sample value = 15.5 seconds or below, u is
the sample mean = 14.62 seconds, s is standard dev = 2.13 seconds
z = (15.5 – 14.62) / 2.13
z = 0.41
Using standard distribution tables at z = 0.41, the value
of P is:
P = 0.6591 = 65.91%
<span>Hence there is a 65.91% chance the runner will have less
than 15.5 seconds of time</span>
<span>
</span>
<span>answer:</span>
<span>c. 0.6591</span>