DSC1520 ASSIGNMENT 4 SEMESTER 1 2025 A tool hiring company has estimated that the rate of increase in the maintenance cost of power drills is given by the equation where is the time that the company is in operation for weeks. Calculate the total main

2/28/25, 1:14 PM Assessment 4




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QUIZ




Question 1

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Integrate the function


3
f (x) = ∫ (2 + 2x + x ) dx.




4
a. 2x + x
2
+
x
+ C
4

4

b. 2x + x
2
+
x

4



c. 2 + 3x
2
+ C

2
d. 2 + 3x


e. None of the given options is correct.

Clear my choice




Question 2

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Integrate the function

12
t − √t
f (t) =
t




1

a. t 2
−
1
√t + C
12 2

1
b. t 2
−
2
+ C
12 √t


1
c. 1
11t 0 + + C
3
2√ t



d. 1
t
12
−
1
√t
12 2



e. None of the given options is correct.

Clear my choice




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Question 3

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A tool hiring company has estimated that the rate of increase in the
maintenance cost of power drills is given by the equation

1,5
C (t) = 2 + t



where t is the time that the company is in operation for weeks. Calculate the
total maintenance cost during the first ten weeks.




a. 146.5


b. 146.5 + C


c. 33.6


d. 33.6 + C


e. None of the given options is correct.

Clear my choice




Question 4

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Determine the integral

−−−−−−−− −
∫ √10x + 15dx .




−−−−−−−− −
a. 1 3
√(10x + 15) + c
15

−−−−−−−−−
b. 1
√(10x + 15) + c
15


1 −−−−−−−−−
c. 3 2
√(10x + 15) + c
15



d. 5

√ 10x+15



e. None of the given options is correct.

Clear my choice




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Question 5

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A firm’s marginal cost function is

2
Q + 2Q + 4.



Find the total cost function if fixed costs are 80.




3

a. Q 2
+ Q + 4Q + 80
3


3
b. Q 2
+ Q + 4Q + C
3



c. 2Q + 2


d. 2Q + 82


e. None of the given options is correct.

Clear my choice




Question 6

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The demand and supply functions for bikes are

−0.1q
pd = 900e



and

0.9q
ps = 3e ,



respectively. Where p is the price, and q the quantity. What is the total surplus at
equilibrium market?


a. 3 350


b. 2 341


c. 1 001


d. 664



Clear my choice




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Question 7

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At a small tool-hire company, the estimated rate of increase in the maintenance
cost of power drills is given by

2t
C (t) = 2e + 2t + 19,



where C is in rand and t is time in weeks. Give the total maintenance cost
during the first 10 weeks.


20
a. 289 + e

20
b. 289 + e + c

20
c. 290 + e


d. e
2t
+ t
2
+ 19t + 10


Clear my choice




Question 8

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Find the area between the curve

2 5x
F (x) = 3x + 5e + 2x + 13



and the x axis over 0 ≤ x ≤ 1.




a. 5
14 + e




5
b. 15 + e

5
c. 16 + e

5
d. e



Clear my choice




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