Solve the equation!3 tan^3θ = tan θ

Answers

Answer 1

Answer: 3 tan³ t(theta) = tan t(theta)
3 tan³ t - tan t = 0
tan t ( 3 tan² t - 1 ) = 0
tan t = 0
t 1 = k π , k ∈ Z
3 tan ² t - 1 = 0
3 tan ² t = 1
tan ² t = 1/3
tan t = +/- √3/3
t 2 = π / 6+ k π
t 3 = - π / 6 + k π , k ∈ Z

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True or False it's possible to build a triangle with side lengths of 5,5, and 10.

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12

Answers

The correctclassification for this triangle is:

obtuse, because 6² + 10² < 12²

Option C is the correct answer.

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine the classification of a triangle based on its sidelengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have a triangle with side lengths of 6 cm, 10 cm, and 12 cm. Checking the sum of the lengths of each pair of sides, we have:

6 + 10 = 16 > 12

6 + 12 = 18 > 10

10 + 12 = 22 > 6

Since all three pairs satisfy the triangleinequalitytheorem, the given side lengths do form a valid triangle.

Next, we can use the lawofcosines to determine the measure of the largest angle in the triangle, which will allow us to classify it.

The lawofcosines states that, for a triangle with side lengths a, b, and c, and the angle opposite c denoted as C, we have:

$c^2 = a^2 + b^2 - 2ab cos(C)$

In this case, the sidelengths are a = 6 cm, b = 10 cm, and c = 12 cm. Substituting these values into the formula and solving for cos(C), we get:

cos(C) = (6² + 10² - 12²) / (2 x 6 x 10)

cos(C) = -1/5

Since the cosinefunction is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.

Therefore,

The correctclassification for this triangle is:

obtuse, because 6² + 10² < 12²

Learn more about triangles here:

brainly.com/question/25950519

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Answer:

Step-by-step explanation:

use Pythagorean theorem

$a^(2)$ + $b^(2)$ = $c^(2)$

c is the longest side

if $a^(2)$ + $b^(2)$ > $c^(2)$ then it's acute (greater than)

if $a^(2)$ + $b^(2)$ < $c^(2)$ then it's obtuse (less than)

if they are equal, then its a right triangle

$6^(2)$ + $10^(2)$ = $12^(2)$

36 + 100 = 144

136 = 144

136 < 144 obtuse

The ratio of the side lengths of two regular hexagons is 3 to 7. If the area of the smaller hexagon is 18 square units, then the area of the larger hexagon is ________.

Answers

$(side_1)/(side_2)=(3)/(7)\n\n(Area_1)/(Area_2)=\left((3)/(7)\right)^2=(9)/(49)\n\n(18)/(Area_2)=(9)/(49)\n\ncross\ multiply\n\n9Area_2=18\cdot49\n\nArea_2=(18\cdot49)/(9)\n\nArea_2=2\cdot49\n\nArea_2=98$

Kay builds a 1/6 scale model of a train. The actual train is 42 1/2 feet long. How long is the model

Answers

7 1/12 feet long..
42 1/2 * 1/6 = 7 1/12

PLEASE HELP ASAP!!!!!

Answers

Answer:

C. Have a good day. :)

Step-by-step explanation:

Let f(x) = 3x2 – x 2 and g(x) = 5x2 – 1. Find f(g(x)). Show each step of your work.

Answers

easy, sub g(x) for x in f(x)

f(g(x))=3(g(x))^2-(g(x))^2

g(x)=5x^2-1
f(g(x))=3(5x^2-1)^2-(5x^2-1)^2=
3(25x^4-10x^2+1)-(25x^4-10x^2)=
2(25x^4-10x^2+1)=
50x^4-20x^2+2

f(g(x))=50x^4-20x^2+2

Find the value of 5.8 ÷ 1.2.
A. 4.6
B. 6.96
C. 5.24
D. 4.83