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r-ruslan [8.4K]
3 years ago
15

What is the correct ratio of each rational root of the polynomial function

Mathematics
1 answer:
MrRa [10]3 years ago
5 0
According to the Rational Root Theorem, the root of a polynomial is the positive and negative ratios of the constant term and the numerical coefficient of the highest exponent variable. Therefore, the correct ratio of each rational root are:
6/1, 2/1, 3/1 and their negative counterparts
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3 years ago
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The measure of an angle is twenty-four times the measure of its complementary angle. What is the measure of each angle?
Bogdan [553]

Answer:

<h2>         3.6° and 86.4°</h2>

Step-by-step explanation:

24x   - measure of an angle

x      - the measure of a complementary angle

Complementary angles adds to 90°

x + 24x = 90°

25x = 90°

x = 90°÷25

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3 years ago
Please help I don't understand this
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3r^2 = 3 x r^2 = 3 x 1/6^2 = 3 x 1/36 = 3/36 = 1/12

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3 0
2 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
What is the value of x?
Ad libitum [116K]

Answer:

x = 15

Step-by-step explanation:

We are told that a right angle is divided into two parts

A right angle = 90°

Part A = 30°

Part B = 4x

Hence:

30° + 4x = 90°

Collect like terms

4x = 90° - 30°

4x = 60°

4x = 60/4

x = 15

Therefore, the value of x = 15

5 0
2 years ago
Read 2 more answers
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