Geogebra 4 Engineer

How to Solve Engineering Problem Using GeoGebra — #Geo4EngineerSeries — Episode #00

In this post we will solve 20 exercises using only GeoGebra.

GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops, tablets and web. Wikipedia

Let’s get it on!

I am assuming that your account for o GeoGebra is up and running!

01#Question —GeoGebra — Derivative Calculation:

Calculate the derivative of: 

GoTo geogebra.org/classic and type:

f(x)= (x^2/2)-4
g(x)=f'(x)
➡ x

Type the function f(x)= (x²/2)-4 and on GeoGebra: g(x)=f’(x) » hit enter and that’s how it’s done! Easy, right? 👉link: https://www.geogebra.org/classic/kgbm5nvq

02#Question — Python— Consumer Price Index — CPI:

Calculate the Bradstreet CPI of the commodities of a building materials store below:

Download Excel file here

Go To this post, and here is the answer:

Solved by Python Jupiter Notebook .👉 link

03#Question — GeoGebra — Polynomial Interpolation:

A store sells basketballs at a price of $59 generating a monthly profit margin of $3500; when the store charged $49 it made a profit of $4000. Knowing that fixed monthly costs are $1000, determine the price that maximizes the store's monthly profit.

GoTo geogebra.org/classic and type:

list = {(0,-1000),(49,4000),(59,3500)}
polynomial(list)
➡ - 2.58x² + 228.31x - 1000
Extremum (f(x))
➡ (44.3, 4056.96)

The ideal price is $44.3 (A)!

Extremum function creates local extremum (44.3, 4056.96) in the given interval and shows it in the graphics [] .👉link:https://www.geogebra.org/classic/upqjv5dj

04#Question —GeoGebra — Linear Regression:

An LED manufacturer knows that the lifetime of a lamp based on this technology is a direct function of the operating temperature. In order to find a function that expresses this useful life, the points shown in the following table were collected, with temperature in Celsius:

Using linear regression in GeoGebra, find the lifetime of the light LED if it is exposed to a temperature of 70°C.

GoTo geogebra.org/classic and type:

A =(10,420)

B =(20,365)
 
C =(30,285)
 
D =(40,220)
 
E =(50,176)
 
F =(60,117)

list = {A,B,C,D,E,F}
FitLine(list)
➡ y = -6.13x + 478.53
t=f(70)
➡ 49.13

Exposed at the 70 °C the LED reaches in 49.13 hours of operations.

👉link: https://www.geogebra.org/classic/fx9nh4pp

05#Question — GeoGebra — Roots of Functions:

Let f(x) = -x² + 9x -18 the function that relates the selling price of a certain product to the profit from the sale of those products. 
Determine what possible prices are such that the profit is greater than zero.

GoTo geogebra.org/classic and type:

f(x) = -x^2 + 9x -18
Roots(f(x))
➡ A = (3,0)
➡ B = (6,0)

In this equation as the function is a parabola with downward concavity, the positive values are between 3 & 6. 👉Link:https://www.geogebra.org/classic/g8ymytka

06#Question — GeoGebra — Linear Regression:

An automobile steering wheel industry produced 2000 units in the third month of the current year and 3000 units in the seventh month. What is the equation of the line that passes through these points?

GoTo geogebra.org/classic and type:

list {(3,2000),(7,3000)}
FitLine(list)
➡ y = 250x + 1250

👉link: https://www.geogebra.org/classic/ysv6qgjm

07#Question — GeoGebra — Solving Simple Equation:

Calculate the value of x in the equation: 12x + 6 = 3x -15

GoTo geogebra.org/classic and type:

eq1 = Solve(12x + 6 = 3x -15)
➡ {x = - 7/13}
or
➡ {x = - 2.33}

👉 Link: https://www.geogebra.org/classic/xzmvwngb

08#Question — GeoGebra — Linear Regression:

The relationship between the first months of the year and the production of an Electric industrial kitchen Oven factory is presented in the table below:

Which line best fits the points and what is the production forecast for the fifth month?

GoTo geogebra.org/classic and type:

list={(1,180), (2,210), (3, 198), (4, 222)}
FitLine(list)
➡ y = 11.4x + 174
f(5)
➡ 231

The expected production for the 5th month is 231 units of Electric industrial kitchen Oven 👉 Link: https://www.geogebra.org/classic/deaqtdjw

09#Question — GeoGebra —Polynomial interpolation:

For a water tank, are different temperatures given, in degrees Celsius, as a function of the depth, in meters, according to the table below:

Find the temperature for a depth of 2.5 meters using the interpolating polynomial.

GoTo geogebra.org/classic and type:

A =(1,66)

B =(2,52)
 
C =(3,18)
 
D =(4,11)
 
E =(5,10)

list = {A,B,C,D,E,F}
Polynomial(list)
➡ -2.83x^4+36.17x^3-156.17x^2+243.83x -55
f(2.5)
➡ 32.97

At the depth of 2.5 meter the temperature of the water tank is at 32.97 °C 👉Link: https://www.geogebra.org/classic/s3peuyau

10#Question — GeoGebra —Polynomial interpolation:

Let C = (0,0)
    D = (10.76,0)
    E = (5.4,1.82)
what is the polynomial function that interpolates these points?

GoTo geogebra.org/classic and type:

C = (0,0)
D = (10.73,0)
E = (5.4,1.82)
list {C,D,E}
Polynomial(list)
➡ -0.06 x² + 0.68 x

👉 Link: https://www.geogebra.org/classic/ucbgjpg8

11#Question — GeoGebra —Polynomial interpolation:

Look at the table below, and get an interpolating polynomial using GeoGebra.

What is the value of f(0.47) in four decimal places?

GoTo geogebra.org/classic and type:

list = {(0.2,0.16),(0.34,0.22),(0.4,0.27),(0.52,0.29),(0.6,0.32),(0.72,0.37)}
Polynomial(list)
➡ -279.34x^5+665.81x^4-610.42 x^3+267.07x^2 -54.81x + 4.35
f(0.47)
➡ 0.2872

Go to Settings > Global > Rounding > 4 Decimals Places, and here is the 👉https://www.geogebra.org/classic/f2rvtzua

12#Question — GeoGebra — Linear Regression:

A butcher shop has the following demands, in kilograms, from Monday to Friday, for the sale of rump.

What is the sales forecast for Saturday?

GoTo geogebra.org/classic and type:

list = {(1,90),(2,98),(3,107),(4,115),(5,122)}
FitLine(list)
➡ y = 8.1x+82.1
f(6)
➡ 130.7

👉 Link: https://www.geogebra.org/classic/rsumg6be

13#Question — GeoGebra — Derivative Calculation:

Calculate the derivative of:

GoTo geogebra.org/classic and type:

f(x)= x^2-2x
g(x)=f'(x)
➡ 2x-2

👉 Link: https://www.geogebra.org/classic/r2b7faqt

14#Question — GeoGebra —Limit — Calculus

Compute the limit:

GoTo geogebra.org/classic and type:

Limit((2–3y²)/(5y²+4y), inf)
➡ -3/5

👉 Link: https://www.geogebra.org/classic/qkdgyhpt

15#Question — GeoGebra — Consumer Price Index — Relatives

The price of a tablet, in 2015, was R$2340. In 2016, it began to be traded for R$2780. What is the relative price, considering 2015 as the base year?

GoTo geogebra.org/classic and type:

[(2780/2340)-1]*100
➡ 18.8

👉 Link: https://www.geogebra.org/classic/xem63pwj

16#Question — GeoGebra —Pearson Coefficient — Linear Regression

Consider the following ordered pairs. 
(1,5),(2,7),(3,6),and (4,10)
What is the person coefficient?

GoTo geogebra.org/classic and type:

list{(1,5),(2,7),(3,6),(4,10)}
CorrelationCoefficient(list)
➡ 0.84

👉 Link: https://www.geogebra.org/classic/zgvdpddd

17#Question — GeoGebra — Linear Regression

The following table records residential electricity consumption, in KWH, in the first 5 months of the current year.

Using GeoGebra find the regression line.

GoTo geogebra.org/classic and type:

list = {(1,180), (2,211),(3,197),(4,233),(5,219)}
FitLine(list)
➡ y = 10x+178

18#Question — GeoGebra — Geometry — Lines & Points

Using GeoGebra find the equation of the line that passes through the points:
A(1,-3)
B(-4,2)

Then calculate the value of this function for coordinate 3

GoTo geogebra.org/classic and type:

A = (1,-3)
B = (-4,2)
Line(A,B)
➡ -x - y = 2
f(3)
➡ -5

👉 Link: https://www.geogebra.org/classic/cqmxqazg

19#Question — GeoGebra — Polynomial interpolation:

Let the points be: (1,7),(3,5), (4,9)(6,9), and (7,3)
what is the polynomial function that interpolates these points?

GoTo geogebra.org/classic and type:

list={(1,7),(3,5),(4,9),(6,9),(7,3)}
Polinomial(list)
➡ 0.07x^4-1.61x^3+11.31X^2-28.17x+25.4

👉 Link: https://www.geogebra.org/classic/s2bksrv5

20#Question— GeoGebra — Quadratic Equation:

Considering that the relationship between profit and price of a certain product is given by the equation:
L = -x^2 + 65x - 550 
For what values of x do we have L>0?

GoTo geogebra.org/classic and type:

-x^2+65x-550
Root(f(x))
➡ A = (10,0)
➡ B = (55,0)

the ideal price is between 10 and 55. 👉 Link: https://www.geogebra.org/classic/errknxeh

That’s all Folks!

Hope it’ll help someone…

Bye!

Credits & References

Thank you, Mr. Ricardo A. Deckmann Zanardini — You are an Awesome Teacher! o/; Text edited while I’m studying Computer Engineer at Escola Superior Politécnica Uninter🏋!

How to find a Derivative in GeoGebra by Phil Clark

Operating temperature effects on LED lifetime by ledrise