 # MATH1040 Mathematical Foundations

## Question:

The equation for the straight line that passes through (x1,y1) & (x2,y2) can be found here

Now, the equation for the straight line that passes through (-4, 20,) and (–2.5, 15.5), is:

Take the first point.

Now, let’s take the first point, i.e. x=-2 and then y=14.

Take x=-1.25 and y=12.5, and you get.

Take x=-1 and then y=11 to get.

As such, the points (-2.14, (-1.5.12.5), and -1.11 are collinear.

L’ = 3x+y-8=0.

For the intersection:

These two intersect at (104/17,11/17)

Plotting of 4*x+ = 5

Plotting of 14x+11y=25

Plotting of 2*x+3*y=5

Let’s solve the 4x+y=5 problem and the 2x+3y=5 problem

Therefore, x=5-3*1)/2=1

You can put x=1 as well as y=1 at 14x+11y-25=0

The system has a unique solution because the three straightlines intersect at a singular point.

The minimum fare for a trip is \$6.20. This is also the yintercept in the graph. Here, the y-axes represent total fare and the x-intercept distance (in kilometers).

So \$6.20 is the cost of sitting in the vehicle.

The straight line intersects the zero-point y-axis, so we can conclude that (0.6.20) is the intersection.

You pay \$5.25 per mile.

\$5.25/km

Accordingly, the equation for the straight line is

where y represents the fare and the distance

This makes the distance 32.0km.

So the total fare for this trip is y=5.25*32 – 6.2 = 174.20 \$

Ans 4.

We have f (x)=x3 – 3*x+ 1

Because the price per kilogram of banana is quadratic we have a function like this.

Now, we have, -eqn1

Equation becomes

The following is the list:

Here we are,

It is generated using Python 3.4

Below is the program.

“””Created at 16:41.25 on Sep 12, 2018

@author: ABHIBASU SEN

“””importnumpy, np

Frommatplotlib import Pyplot as Plt

Get 20% off your first purchase

X
Hi