# 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)-4g(x)=f'(x)➡x

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

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

Go To this post, and here is the answer:

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 - 1000Extremum (f(x))➡(44.3, 4056.96)

The ideal price is **$44.3 **(A)!

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 + 478.53t=f(70)➡49.13

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

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 -18Roots(f(x))➡ A = (3,0)

➡ B = (6,0)

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

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}

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 + 174f(5)➡231

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 -55f(2.5)➡32.97

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

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 + 4.35f(0.47)➡0.2872

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+82.1f(6)➡130.7

13#Question — GeoGebra — **Derivative Calculation:**

`Calculate the derivative of:`

GoTo **geogebra**.org/**classic** and type:

f(x)= x^2-2xg(x)=f'(x)➡2x-2

14#Question — GeoGebra —**Limit — Calculus**

`Compute the limit:`

GoTo **geogebra**.org/**classic** and type:

Limit((2–3y²)/(5y²+4y), inf)➡-3/5

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

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

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 = 2f(3)➡-5

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

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-550Root(f(x))➡ A = (10,0)

➡ B = (55,0)

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🏋!