QuestionFind the value of $\mathrm{c}$ if the line $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ passes through the origin.

Studdy Solution

STEP 1

Assumptions1. The function $f \mathbb{R} \longrightarrow \mathbb{R}$ is represented by the straight line $f(\chi)= \chi+3 \mathrm{c}^{3}$ . The line passes through the origin point (0,0)

STEP 2

Since the line passes through the origin point (0,0), we can substitute these values into the equation of the line.
f(0) =2 \cdot0 +c^

STEP 3

implify the equation by multiplying2 by0.
$f(0) =0 +3c^3$

STEP 4

Since the line passes through the origin, $f(0)$ should equal0. So we set the equation equal to0.
$0 =3c^3$

STEP 5

To solve for $c$ , divide both sides of the equation by3.
$0 = c^3$

STEP 6

To find the value of $c$ , we take the cube root of both sides of the equation.
$c = \sqrt[3]{0}$

STEP 7

Calculate the value of $c$ .
$c =0$ So, $c =0$ is the solution.

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QuestionFind the value of $\mathrm{c}$ if the line $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ passes through the origin.

Studdy Solution

STEP 1

Assumptions1. The function $f \mathbb{R} \longrightarrow \mathbb{R}$ is represented by the straight line $f(\chi)= \chi+3 \mathrm{c}^{3}$ . The line passes through the origin point (0,0)

STEP 2

Since the line passes through the origin point (0,0), we can substitute these values into the equation of the line.
f(0) =2 \cdot0 +c^

STEP 3

implify the equation by multiplying2 by0.
$f(0) =0 +3c^3$

STEP 4

Since the line passes through the origin, $f(0)$ should equal0. So we set the equation equal to0.
$0 =3c^3$

STEP 5

To solve for $c$ , divide both sides of the equation by3.
$0 = c^3$

STEP 6

To find the value of $c$ , we take the cube root of both sides of the equation.
$c = \sqrt[3]{0}$

STEP 7

Calculate the value of $c$ .
$c =0$ So, $c =0$ is the solution.

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QuestionFind the value of c\mathrm{c}c if the line f(χ)=2χ+3c3f(\chi)=2 \chi+3 \mathrm{c}^{3}f(χ)=2χ+3c3 passes through the origin.

Studdy Solution

STEP 1

Assumptions1. The function fR⟶Rf \mathbb{R} \longrightarrow \mathbb{R}fR⟶R is represented by the straight line f(χ)=χ+3c3f(\chi)= \chi+3 \mathrm{c}^{3}f(χ)=χ+3c3 . The line passes through the origin point (0,0)

STEP 2

Since the line passes through the origin point (0,0), we can substitute these values into the equation of the line.f(0) =2 \cdot0 +c^

STEP 3

implify the equation by multiplying2 by0.f(0)=0+3c3f(0) =0 +3c^3f(0)=0+3c3

STEP 4

Since the line passes through the origin, f(0)f(0)f(0) should equal0. So we set the equation equal to0.0=3c30 =3c^30=3c3

STEP 5

To solve for ccc, divide both sides of the equation by3.0=c30 = c^30=c3

STEP 6

To find the value of ccc, we take the cube root of both sides of the equation.c=03c = \sqrt[3]{0}c=30​

STEP 7

Calculate the value of ccc.c=0c =0c=0So, c=0c =0c=0 is the solution.

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QuestionFind the value of $\mathrm{c}$ if the line $f(\chi)=2 \chi+3 \mathrm{c}^{3}$ passes through the origin.

Assumptions1. The function $f \mathbb{R} \longrightarrow \mathbb{R}$ is represented by the straight line $f(\chi)= \chi+3 \mathrm{c}^{3}$ . The line passes through the origin point (0,0)

Since the line passes through the origin point (0,0), we can substitute these values into the equation of the line.
f(0) =2 \cdot0 +c^

implify the equation by multiplying2 by0.
$f(0) =0 +3c^3$

Since the line passes through the origin, $f(0)$ should equal0. So we set the equation equal to0.
$0 =3c^3$

To solve for $c$ , divide both sides of the equation by3.
$0 = c^3$

To find the value of $c$ , we take the cube root of both sides of the equation.
$c = \sqrt[3]{0}$

Calculate the value of $c$ .
$c =0$ So, $c =0$ is the solution.