Muralists will often make a scale drawing of an art piece before creating the large finished version. A muralist has sketched an art piece on a sheet of drawing paper that is 3 feet by 4 feet. If the final mural will be 42 feet by 56 feet, what is the scale factor for this dilation.

The scale factor is
.

The owner of the wall has decided to only give permission to paint on the lower half of the wall. Can the muralist simply use the transformation (x, y) arrowright parenleftx ,
1
2
yparenright in addition to the scale factor to alter the sketch for use in the allowed space? Select the correct explanation.

A The mural will be distorted. This mapping will shrink the height of the mural in half, but by keeping the original width, the shapes will change.
B The mural will not be distorted, both sides will be changed evenly.
C The mural will be distorted. This mapping will shrink the width of the mural in half, but by keeping the original height, the shapes will change.
D The mural will be distorted. This mapping will shrink the height and width of the mural in half, but by changing the original width, the shapes will change.

Afunction is given: f(x)=3x+12 a. determine the inverse of this function and name it g(x) b. use composite functions to show that these functions are inverses. c. f(g(– explain: what is the domain?

Acylinder has volume 45π and radius 3. what is it’s height?

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.