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Maths Week 4 Graded Assignments IIT Madras

Maths week 4 graded assignment Complete  Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments 

There are some questions which have functions with discrete valued domains (such as day, month, year etc). For simplicity, we treat them as continuous functions.

For NAT type question, enter only one right answer, even if you get multiple answers for that particular question.

Notations:

 = Set of real numbers  = Set of rational numbers
 = Set of integers
 = Set of natural numbers

The set of natural numbers includes 0.

 
 
1 point
 
  1. Let �:�→� and �:�→� be two functions, defined as �(�)=�3−8�2+7 and �(�)=−2�(�) respectively. Choose the correct option(s) from the following.
 

 

 

 

 

 

 

 

 
 
 
1 point
 

2. Which among the following function first increases and then decreases in all the intervals (−4,−3) and (−1,2) and (5,6)?

 

 

 

 

 

 

 

 

 
 
1 point
3. Which of the following is/are correct ?

            
                                                          Fig – 1

             
             
                                                        Fig – 2


 

 

 

 

 

 

 

 

 

 

 

 
 
 
1 point
 

4. Consider a polynomial function �(�)=−(�2−16)(�−3)2(2−�)2(�+9). Choose the set of correct options.

 

 

 

 

 

 

 

 

 
 
1 point
 

5. The height of a roller coaster at a given time is modeled by the polynomial function ℎ(�)=(−0.01�3+0.35�2−3.5�+10)(�+5)2(�−5)(�+1)(2−�)3, where t represents time in seconds. Find the turning point(s) of the height function.

 
 
1 point
6. Choose the correct options based on the data given in 5th question. 

 

 

 

 

 

 

 

 
 
 
 

7. An ant named , wants to climb an uneven cliff and reach its anthill (i.e., home of ant). On its way home,  makes sure that it collects some food. A group of ants have reached the food locations which are at �−intercepts of the function �(�)=(�2−20)((�−7)3−1). As ants secrete pheromones (a form of signals which other ants can detect and reach the food location),  gets to know the food location. Then the sum of the -coordinates of all the food locations is

 
 
1 point
 
 
 

8. The Ministry of Road Transport and Highways wants to connect three aspirational districts with two roads �1 and �2. Two roads are connected if they intersect. The shape of the two roads �1 and �2 follows polynomial curve �(�)=(�−19)(�−17)2 and �(�)=−(�−19)(�−17) respectively. What will be the �−coordinate of the third aspirational district, if the first two are at �−intercepts of �(�) and �(�).

 
 
1 point
A company is manufacturing custom-made boxes with a volume represented by the polynomial �(�)=4�3+16�2+17�+5. If the length of each box is represented by the polynomial �(�)=�+1, given that width and height of the box are �(�) and ℎ(�) respectively. Also given that for all �>0ℎ(�)>�(�), the Degree of polynomials ℎ(�) and �(�) is 1.
Use this information to answer the following questions 9 and 10
 
1 point
 

9. Polynomial expression which represents width of the box �(�)

 

 

 

 

 

 

 

 

 
 
1 point
10. Polynomial expression which represents area of the base.

 

 

 

 

 

 

 

 
A telecommunications company observes that the number of monthly subscribers (S) for its internet service can be modeled by the polynomial function �(�)=�3−2�2−24�+5000, where t represents the number of months since the service was launched.
Use this information to answer the following questions 11 and 12.
 
 

11. The company aims to reach a milestone of 5000 subscribers. How many months will it take to achieve this goal based on the polynomial function? (Note: �>0)

 
 
1 point
 
12. Number of actual subscribers after one year; given that the polynomial function over estimates the actual subscribers by 60%
 

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