Can somebody please help me solve these questions?
Question 1:
Many times we think of winter as a hindrance to our modes of transportation, but it is not the case for many First Nations communities in Northern Ontario. Many settlements are only accessible by boat or aircraft, except in the winter when the lake freezes over and more options, such as ice roads, become available. When ice thickness reaches at least 10cm, it is safe for walking or snow shoeing. When the thickness is at least 13 cm, it is safe for a snowmobile or ATV.
The thickness of the ice on a lake for one week is modeled by the function:
T(d) = -0.1d3 + 1.2d2 - 4.4d +14.8
Where T is the thickness in cm and d is the number of days after December 31st .
- a) Graph this function using graphing technology. Ensure your axes are properly set up, and state the domain and range that are appropriate for the situation.
- b) When do you think the warmest day occurred during the week? Justify your answer.
- c) Determine the average rate of change on a short interval near the point you chose in b).
Question 2:
Determine if the following polynomial functions have even or odd symmetry, or neither. Justify your reasoning.
a) f(x)= 3x3 - 144
b) f(x) = 8x4 + x2
c) f(x) = x2 - x6
d)f(x) =x5 + x3 - x
Question 3:
Factor each of these polynomial functions completely. Show all of your work
a)f(x) =x3 - 13x + 12
b)f(x) =-5x3 + 17x2 - 16x - 4
c)f(x) =5x4 - 22x3 +33x2 - 20x + 4
Question 4:
A packaging company has been asked to make cylindrical cans that can hold a volume of 16π cm3. The company owns a machine that only makes cans that have a height which is the square of 3 less than the radius. To achieve the desired volume, what should the dimensions of the finished can be?