Cayenne bought 20 pencils for 1.60 dollars at that rate how much would 35 pencils cost
1 answer:
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After performing the transformation on f(x) = |x|+7; reflected across the x-axis and translated 4 units up. We get the function g(x) = -(|x| + 7) + 4
<h3>What is a function?</h3>It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = |x| + 7
First we reflect the function f(x) across the x-axis
Multiply the function by -1
F(x) = -(|x| + 7)
To translated 4 units up add 4 to the function.
g(x) = -(|x| + 7) + 4
Thus, after performing the transformation on f(x) = |x|+7; reflected across the x-axis and translated 4 units up. We get the function g(x) = -(|x| + 7) + 4
Learn more about the function here:
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Answer:
Radius = 1.12 inches and Height = 4.06 inches
Step-by-step explanation:
A soup can is in the shape of a right circular cylinder.
Let the radius of the can is 'r' and height of the can is 'h'.
It has been given that the can is made up of two materials.
Material used for side of the can costs $0.015 and material used for the lids costs $0.027.
Surface area of the can is represented by
S = 2πr² + 2πrh ( surface area of the lids + surface are of the curved surface)
Now the function that represents the cost to construct the can will be
C = 2πr²(0.027) + 2πrh(0.015)
C = 0.054πr² + 0.03πrh ---------(1)
Volume of the can = Volume of a cylinder = πr²h
16 = πr²h
-------(2)
Now we place the value of h in the equation (1) from equation (2)
Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.
Now for C' = 0
r³ = 1.415
r = 1.12 inch
and h =
h = 4.06 inches
Let's check the whether the cost is minimum or maximum.
We take the second derivative of the function.
which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.
Therefore, to minimize the cost of the can dimensions of the can should be
Radius = 1.12 inches and Height = 4.06 inches
