Answer:
k=5
Step-by-step explanation:
step 1
Find the equation of the line f(x)
we have the points
(-4,0) and (-2,2)
<em>Find the slope m</em>
Find the equation of the line in point slope form
we have
substitute
Remember that
f(x)=y
so
step 2
Find the equation of the line g(x)
we have the points
(-4,0) and (-2,-10)
<em>Find the slope m</em>
Find the equation of the line in point slope form
we have
substitute
Remember that
g(x)=y
so
Remember that
------>
therefore
k=5
According to my calculations the answer is 69
1. 9
2. 8
I hope this helped! #Sobangcha
The volume of the cylinder is:
V = pi * r ^ 2 * h = 64
The surface area is:
A = 2 * pi * r ^ 2 + 2 * pi * r * h
We write the area as a function of r:
A (r) = 2 * pi * r ^ 2 + 2 * pi * r * (64 / (pi * r ^ 2))
Rewriting:
A (r) = 2 * pi * r ^ 2 + 2 * (64 / r)
A (r) = 2 * pi * r ^ 2 + 128 / r
Deriving:
A '(r) = 4 * pi * r - 128 / r ^ 2
We equal zero and clear r:
0 = 4 * pi * r - 128 / r ^ 2
128 / r ^ 2 = 4 * pi * r
r ^ 3 = 128 / (4 * pi)
r = (128 / (4 * pi)) ^ (1/3)
r = 2.17 cm
The height is:
h = 64 / (pi * r ^ 2)
h = 64 / (pi * (2.17) ^ 2)
h = 4.33 cm
Answer:
The dimensions giving the minimum surface area are:
r = 2.17 cm
h = 4.33 cm
