Mth101 Assignment No. 1 solution

Mth101 GDB Solution

With the name of Almighty, dears we’re to discuss the calculus application in the field of our practical life.

First me have to say that “Calculus” is that branch which deals with the integral calculus e.g. calculation area under the curve and the deferential calculus that deals with the motion calculation, and that all are the part of our practical life. Calculus is deeply integrated with the physical science and such as physics and Bio science, so now we can say that it is more important in every aspects of life some of them we’ll here discuss.

It is found in computer science, statistics, and engineering; in economics, business, and medicine. Modern developments such as architecture, aviation, and other technologies all make use of what calculus can offer. Graph visualization are also based on that, we can easily graph the function with the help of it. Finding average of function one example is the path of an airplane. Using calculus you can calculate its average cruising altitude, velocity and acceleration.

So at the end that branch cover a lot of area of our practical life to overcome them we’d have good knowledge of it.

Another:

"Why do we study calculus,write its at least three applications"

Graded Moderate Discussion will be open on Calculus is Latin for stone, and the ancient Romans used stones for counting and arithmetic. In its most basic sense, calculus is just that a form of counting. After advanced algebra and geometry, it is the next step in higher mathematics, and is used for solving complex problems that regular mathematics cannot complete.

Calculus is the mathematics of change, of calculating problems that are continually evolving. This is possible by breaking such problems into infinitesimal steps, solving each of those steps, and adding all the results. Rather than doing each step individually, calculus allows these computations to be done simultaneously.

Calculus is useful for solving non-linear equations. For example, say you were looking for the area inside a flat rectangle.

Calculus is deeply integrated in every branch of the physical sciences, such as physics and biology. It is found in computer science, statistics, and engineering; in economics, business, and medicine. Modern developments such as architecture, aviation, and other technologies all make use of what calculus can offer. This page is designed to out line some of the applications of calculus and give you some idea of why calculus is so important and useful.

Calculus can give us a generalized method of finding the slope of a curve. The slope of a line is fairly elementary, using some basic algebra it can be found. Although we do have standard methods to calculate the area of some shapes, calculus allows us to do much more. A function can represent many things. One example is the path of an airplane. Using calculus you can calculate its average cruising altitude, velocity and acceleration.

MTH302 GDB Solution

Total Marks 5

Starting Date : Thursday, January 27, 2011

Closing Date : Friday, January 28, 2011

Construct a real world business problem and then apply simple linear regression analysis.

Question:-

Suppose that 4 randomly chosen plots were treated with various level of fertilizer in the following yield of corn:-

Fertilizer(kg/Acre) X 100 200 400 500

Production(Bushels/Acre) Y 70 70 80 100

Estimate the Linear Regression of production Y on fertilizer X.

Solution:-

X Y XY X2

100 70 7000 10000

200 70 14000 40000

400 80 32000 160000

500 100 5000 250000

å = 1200 å = 320 å =103000 å = 460000

Byx = nåXY – åXåY / nåX2 - (åX) 2

Byx = 4(103000)-((1200)(320)) / 4(460000)-(1200) 2

Byx = 0.07

ayx = y - Byx X

= ((åY/n) – ((0.07) (åX/n))

=(320/4) – (0.07)(1200/4)

= 59

y = 59 + 0.07 X is required regression equation.

MTH001 Assignment No. 2 Solution

Assignment # 2 (Lecture# 17 - 24) Of MTH001 (FALL 2010)

Maximum Marks: 30

Due Date:

January 24, 2011

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Question: 01 Marks: 10

Ali decides to invest a certain sum of money in business at the end of each year in the form of an annuity. He wants to get a sum of Rs.40, 000 after 20 years. If the payments accumulate at expected profit of 8% compound annually, how much should he start investing annually?

Question: 02 Marks: 10

Find the unknown values of , , and if and are multiplicative inverses of each other. Where .

Question: 03 Marks: 10

If and are the means for the two sets and respectively and related by and . Then find the values of ‘ ’ and ‘ ’.

.................

Solution 1):

This is a Future Value of an Ordinary Annuity problem.

Future Value is 40,000. Number of periods is 20. Annual rate is 8%

From TVM table for FV of an Annuity, the Factor is 45.7625

The FV = Annuity x Factor. We know the FV is 40,000, so divide it by the factor of 45.7625 to determine the Annuity amount of 874.08

The formula is ((1+ r)^n - 1) / r, or ((1.08)^20 - 1) / .08, or 4.661 - 1 = 3.661 / .08 = 45.7625

Mth302 Assignment No. 2 Announced

Assignment # 2

MTH302 (Fall 2010)
Total marks: 10
Lecture # 22 to 33
Due date: January 17, 2011

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• There are 5 questions in the assignment but only one question will be graded.


Question 1: (Non-graded)

Find a linear regression line y = ax + b (where a is the slope and b is the y-intercept)
for values of x and y given below.


y x

7 3
10 5
11 7
15 9

Question 2: (Non-graded)

Find Quartile Deviation of the following data.

1,2,8,7,10,11,15,20,18,25

Question 3: (Graded) Marks 10

The table below shows the demand for a particular item in a shop for the last nine months.

Month Demand

1 10
2 12
3 13
4 17
5 15
6 19
7 20
8 21
9 20

Calculate a three month moving average. What would be your forecast for the demand in month ten?

Question 4: (Non-graded)

Calculate the coefficient of variation for data given below.
10, 12, 14, 16, 18, 20

Question 5: (Non-graded)
Calculate the mean, median, mode and range of the data given below.
0, 1, 2, 5, 9, 8, 3, 2, 6

Mth202 Assignment No. 4 Solution

Assignment 4 Of MTH202 (Fall 2010)

Maximum Marks: 15

Due Date: January 11, 2011

Q-1:

How many bit strings of length 10 have

a) Exactly three 0’s?

b) The same number of 0’s as 1’s?

Q:2

Prove by mathematical induction that for all positive integral values of n, x²ⁿ-1 is divisible by x +1 ;( x¹1)

Q:3

Use the Euclidean algorithm to find gcd (1331, 1001)

Question#2 solution

Using Mathematical Induction

Step 1: First we will prove that for n =1 it is true

thus x^2n-1 = x^2-1 = (x-1)*(x+1)

clearly since it has factor of x+1 we can say that x^2n-1 is divisible by x-1

Step 2: let assume that for n = k it is true thus

x^2k-1 is divisible by x+1

thus we can write as x^2k-1 = P (x+1) P is quotient

now we have to prove that it is true for n=k+1

Step 3: now let n = k+1 thus

x^2(k+1) - 1 = x^(2k+2) - 1 = x^2k*x^2 -1 = (x^2k-1+1)x^2 - 1

(x^2k-1)*x^2 + (x^2-1)

for step 2 we can write above equation as

P (x+1)*x^2 + (x+1)*(x-1) = (x+1)* (Px^2+x-1)

which contain factor of x+1 thus divisible by x+1

thus even it is proved for n=k+1

according to mathematical induction given is true for all integral values of n


Question 3; Marks: 03
Use the Euclidean algorithm to find gcd (1331, 1001)
Solution
gcd(1331, 1001) = gcd(1001, 330)
= gcd(330, 11)
= gcd(11, 0)
= 11


How many bit strings of length 10 have

a) Exactly three 0’s?

is ka answer hai 10C3 =120

b) The same number of 0’s as 1’s?
is ka answer hai 10 C 5 = 152