# 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` 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:`

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)! 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 + 478.53t=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)` 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`

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` 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 -55f(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`

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` 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+82.1f(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`

`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🏋!

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