The formula for volume of cone is:
V = π
r^2 h / 3
or
π r^2
h / 3 = 36 cm^3
Simplfying in terms of r:
r^2 = 108 / π h
To find for the smallest amount of paper that can create
this cone, we call for the formula for the surface area of cone:
S = π
r sqrt (h^2 + r^2)
S = π
sqrt(108 / π h) * sqrt(h^2 + 108 / π h)
S = π sqrt(108 / π h) * sqrt[(π h^3 + 108) / π h]
Surface area = sqrt (108) * sqrt[(π h + 108
/ h^2)]
<span>Getting the 1st derivative dS / dh then
equating to 0 to get the maxima value:</span>
dS/dh = sqrt (108) ((π – 216
/ h^3) * [(π h + 108/h^2)^-1/2]
Let dS/dh = 0 so,
π – 216
/ h^3 = 0
h^3 = 216 / π
h = 4.10
cm
Calculating
for r:
r^2 = 108 / π (4.10)
r = 2.90 cm
Answers:
h = 4.10 cm
<span>r = 2.90 cm</span>
Answer:
-12
Step-by-step explanation:
Here the coefficients a, b and c are 4, 8 and -8 respectively.
-b
A formula for the axis of symmetry is x = -------
2a
-8
... which yields x = --------- = -1
2(4)
Evaluating f(x) = 4x^2 + 8x - 8 at x = -1 yields f(-1) = 4(-1)^2 + 8(-1) - 8 = -12.
The y-value of the vertex is -12. Note that the vertex lies right smack on the axis of symmetry.
Answer:
the common ration is -0.4. Three terms: 2.56,-1.024, and 0.4096
Step-by-step explanation:
You just keep on multypling the terms by -0.5 ,and you get.
Area=1/2 times height times base
base=2.5
area=3.75
subsitute
3.75=1/2 times height times 2.5
multiply both sides by 2 to get rid of fraction
7.5=height itmes 2.5
divide both sides by 2.5
3=height
sail is 3 meters tall
