A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Eric conducted an experiment in his science class and recorded the data in a table.

Eric’s science experiment, time (seconds), 3, 6, 9, 12, 15, 18, distance (ft), 18, 36, 54, 72, 90, 108.

Let x be the time and y be the distance.

Let the distance and time be linear to each other. Then the linear equation is given as

y - 36 = [(36 - 18) / (6 - 3)] (x - 6)

y - 36 = 6 (x - 6)

y = 36 + 6x - 36

y = 6x

Then the constant of proportionality that relates the distance traveled to the elapsed time represented by this data will be 6.

More about the linear system link is given below.

brainly.com/question/20379472

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4 0

2 years ago

0,5.<img src="https://tex.z-dn.net/?f=%5Csqrt%7B0%2C09%7D" id="TexFormula1" title="\sqrt{0,09}" alt="\sqrt{0,09}" align="absmidd

Komok [63]

Answer:

0.21

Step-by-step explanation:

The given expression is :

$0.5\times \sqrt{0.09}-2\sqrt{0.05}+\sqrt \frac{1}{4}$

We need to solve it.

We know that,

$\sqrt{0.09}=0.3\ and\ \sqrt{0.05}=0.223$

So,

$0.5\times \sqrt{0.09}-2\sqrt{0.05}+\sqrt \frac{1}{4}=0.5\times 0.3-2\times 0.22+0.5\\\\=0.21$

$=\dfrac{21}{100}$

So, the value of the given expression is equal to 0.21.

8 0

3 years ago

Solving a trigonometric equation involving an angle multiplied by a constant

PIT_PIT [208]

In these questions, we need to follow the steps:

1 - solve for the trigonometric function

2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.

3 - Complete these angles with the complete round repetition, by adding

$2k\pi,k\in\Z$

4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.

1 - To solve, we just use algebraic operations:

$\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}$

2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:

The value for the angle that give positive

$+\frac{\sqrt[]{3}}{3}$

is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of

$-\frac{\sqrt[]{3}}{3}$

Are:

$\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}$

3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:

$\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}$

Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:

$\theta=\frac{5\pi}{6}+k\pi,k\in\Z$

4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:

$\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}$

So, the solutions are:

$x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z$

4 0

1 year ago