Let () be the piecewise linear function with domain 0≤≤8 shown in the graph below (which is determined by connecting the dots). Define a function () with domain 0≤≤8 by ()=∫0().

Notice that () is the net area under the function () for 0≤≤. If you click on the graph below, a full-size picture of the graph will open in another window.

Graph of =()

(A) Find the following values of the function ().
(0)=

(1)=

(2)=

(3)=

(4)=

(5)=

(6)=

(7)=

(8)=

(B) Use interval notation to indicate the interval or union of intervals where () is increasing and decreasing.
() is increasing for in the interval

() is decreasing for in the interval

(C) Find where () has its maximum and minimum values.
() has its maximum value when =

() has its minimum value when =

Which is the standard form for this number? (4 x 1 100 ) + (8 x 1 1,000 ) + ( 3 x 1 100,000 ) ? a) 0.004803 b) 0.04803 c) 0.0483 d) 0.483

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.

Diane’s bank is offering 5% interest, compounded monthly. if diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? round to the nearest tenth of a year.