Question

1. lire lénoncé

clara et victor possèdent chacun une terrain de loisir. ils engagent le même entrepreneur pour aménager leur terrain. voici les infos à connaître :

lentrepreneur propose deux types daménagements : un véranda ou une peinture

les trois semaines sont carrées, mais de tailles différentes.

la véranda

la surface du terrain carrée de clara est donnée par la fonction f définie par :

f(x) = 8,8 x²

(i) hauteur (en m) des côtés de la véranda, en mètres.
(ii) coût de lapplication du vernis en dollars ?

la peinture

pour une terrasse carrée, la fonction g permet de calculer le coût de lapplication de la peinture. elle est définie par :

g(x) = x²

où :

• x : mesure (en m) des côtés de la peinture, en mètres.
• g(x) : coût de lapplication de la peinture, en dollars.

• le coût de lapplication du vernis sur la terrasse de clara est de 176,0 $
• le coût de lapplication de la peinture sur la terrasse de victor est de 201,35 $
• le coût de lapplication de la peinture sur la terrasse de clara est de 143,06 $
• chaque côté de la terrasse de victor mesure 1,8 m de plus que celui de la terrasse de clara.

quel est le coût de lapplication du vernis sur la terrasse de victor ?

Explanation:

To solve the problem of finding the application cost of the wind turbine on Victor's plot, we follow these steps:

Step 1: Determine the function for the application cost of the wind turbine

We know that for Clara, the application cost of the wind turbine is given by \( f(x) = kx^2 \), where \( x \) is the width of the plot (in meters) and \( k \) is a constant. We are given that for Clara, \( x = 1.7 \, \text{m} \) and \( f(1.7) = 176.20 \, \text{€} \). We first need to find the value of \( k \).

Substitute \( x = 1.7 \) and \( f(1.7) = 176.20 \) into the function \( f(x) = kx^2 \):
\[
176.20 = k \times (1.7)^2
\]

Calculate \( (1.7)^2 \):
\[
(1.7)^2 = 2.89
\]

Now solve for \( k \):
\[
k = \frac{176.20}{2.89}
\]
\[
k = 61
\]

So the function for the application cost of the wind turbine is \( f(x) = 61x^2 \).

Step 2: Determine the width of Victor's plot

We are told that the width of Victor's plot is \( 1.8 \, \text{m} \) (since the width of Clara's plot is \( 1.7 \, \text{m} \) and Victor's plot is \( 1.8 \, \text{m} \) wide).

Step 3: Calculate the application cost for Victor's plot

Now we use the function \( f(x) = 61x^2 \) with \( x = 1.8 \, \text{m} \):
\[
f(1.8) = 61 \times (1.8)^2
\]

First, calculate \( (1.8)^2 \):
\[
(1.8)^2 = 3.24
\]

Then multiply by \( 61 \):
\[
f(1.8) = 61 \times 3.24
\]
\[
f(1.8) = 197.64
\]

The application cost of the wind turbine on Victor's plot is \(\boldsymbol{197.64 \, \text{€}}\).

Answer:

To solve the problem of finding the application cost of the wind turbine on Victor's plot, we follow these steps:

Step 1: Determine the function for the application cost of the wind turbine

We know that for Clara, the application cost of the wind turbine is given by \( f(x) = kx^2 \), where \( x \) is the width of the plot (in meters) and \( k \) is a constant. We are given that for Clara, \( x = 1.7 \, \text{m} \) and \( f(1.7) = 176.20 \, \text{€} \). We first need to find the value of \( k \).

Substitute \( x = 1.7 \) and \( f(1.7) = 176.20 \) into the function \( f(x) = kx^2 \):
\[
176.20 = k \times (1.7)^2
\]

Calculate \( (1.7)^2 \):
\[
(1.7)^2 = 2.89
\]

Now solve for \( k \):
\[
k = \frac{176.20}{2.89}
\]
\[
k = 61
\]

So the function for the application cost of the wind turbine is \( f(x) = 61x^2 \).

Step 2: Determine the width of Victor's plot

We are told that the width of Victor's plot is \( 1.8 \, \text{m} \) (since the width of Clara's plot is \( 1.7 \, \text{m} \) and Victor's plot is \( 1.8 \, \text{m} \) wide).

Step 3: Calculate the application cost for Victor's plot

Now we use the function \( f(x) = 61x^2 \) with \( x = 1.8 \, \text{m} \):
\[
f(1.8) = 61 \times (1.8)^2
\]

First, calculate \( (1.8)^2 \):
\[
(1.8)^2 = 3.24
\]

Then multiply by \( 61 \):
\[
f(1.8) = 61 \times 3.24
\]
\[
f(1.8) = 197.64
\]

The application cost of the wind turbine on Victor's plot is \(\boldsymbol{197.64 \, \text{€}}\).