What is the range and domain of the parent function f(x) = |x|

Answer:

3/4

Step-by-step explanation:

3/4 is one example of a fraction that is greater than 1/2. If 1/2 become 2/4, therefore 3/4 is a fraction which is greater than 1/2.

Answer:

A.

Step-by-step explanation:

Please find the attachment.

We have been given an image of a square pyramid ABCDE. We are asked to find the lateral area of pyramid.

First of all we need to find the height of pyramid.

The lateral height of the pyramid will be the length of altitude drawn from the lateral face of pyramid to the base of pyramid.

Since the base of pyramid is square, so the length of segment CM will be half the length of BC that is 16.

Since tangent relates the opposite and adjacent sides of a right triangle, so we can find the lateral height as:

, where,

p = Perimeter of the base,

l = Lateral or slant height.

Therefore, the lateral surface area of our given pyramid is square inches and option A is the correct choice.

Answer:

256√3 in^2.

Step-by-step explanation:

tan 60 = lateral height of 1 face / 8

Lateral height = 8 tan 60 = 8√3

Area of 1 face = 8 * 8√3 = 64√3

Lateral Area = 4 * 64√3 = 256√3 in^2

Answer:

a) file annex

b) V(c) = π*x²*y

    A(x) = 2*π*x² + 32/x

    C(x) =  0,1695*x²  +  0,48 /x

     Domain C(x) = {x/ x >0}

d) C(min) = 0,64 $

    x = 1.123 in      radius of base

    y = 4,04 in      height of the can

Step-by-step explanation:

See annex file

Lets:

call x = radius of the base of the cylinder  and

y = the height of the cylinder

Then

Volume of the cylinder      ⇒    V(c) =  π*r²*h             ⇒V(c) = π*x²*y

And  y = V / ( π*x²)     ⇒   V = 16 / ( π*x²)

Area of cylinder  = lids area  +  lateral area

lids area = 2*π*x²  ⇒  lateral area = 2*π*x*y

lateral area =2*π*x [16/(π*x²) ]    ⇒   lateral area =  32/x

Then

A(x) = 2*π*x² + 32/x

Function cost C(x)

C(x) = 0.027 *  2*π*x²  +  0.015 * (32/x)

C(x) =  0,1695*x²  +  0,48 /x

Domain C(x) = {x/ x >0}

Now function cost:

C(x) =  0,1695*x²  +  0,48 /x

Taking derivative:

C´(x) =  2*0,1695*x  - 0.48/x²     C´(x)  =  0,339*x  -  0.48/x²

C´(x)  = 0            0.339*x³ - 0.48 = 0   x³ = 0.48/0.339   x³  = 1.42

x = 1.123 in

y = 16/πx²     ⇒  y = 4,04 in

C(min) = 0,64 $