Mathematics High School

6 tan(2x) − 6 cot(x) = 0 ; [0, 2π)

Answers

Answer 1

9514 1404 393

Answer:

  x ∈ {π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6}

Step-by-step explanation:

We can divide by 6 and use some identities to rewrite this as ...

  2tan(x)/(1-tan(x)²) -1/tan(x) = 0

  2tan(x)² -(1 -tan(x)²) = 0 . . . . . . . . . multiply* by tan(x)(1 -tan(x)²)

  3tan(x)² = 1

  tan(x) = ±1/√3   ⇒   x = {π/6, 5π/6, 7π/6, 11π/6}

__

Interestingly, if we use different identities, we can rewrite it as ...

  2cot(x)/(cot(x)² -1) -cot(x) = 0

  cot(x)(3 -cot(x)²) = 0 . . . . . . . multiply by (cot(x)² -1)

In addition to the zeros found above, this equation also has solutions where cot(x) = 0. That is ...

  x = {π/2, 3π/2}

_____

Usually, the first method shown would give all the solutions. Fortunately, we had a graph of the function, so we could see that the first set of solutions found was not complete. (This is one reason I like to use a graphing calculator for guidance on problems like this.)

_____

* In the first solution, we multiplied by the denominator tan(x)(1 -tan(x)²). It was multiplying by tan(x) that made the π/2, 3π/2 solutions disappear. Had we kept 1/tan(x) as a numerator factor of cot(x), we would have had the same result as seen in the second approach.

6 Tan(2x) 6 Cot(x) = 0 ; [0, 2)

Related Questions

PLS HELP ME WITH 7 AND 6 PLSLSLSLSLS PLS PLS I BEG U PLS

Answers

Answer: 7= D, 26 units

Step-by-step explanation:

Take the length. 0,0 to 0,9  the length is 9  Next take the width 0,9 to 4,9 the width is 4  L+Wx2 13x2=26

Solve the following system of equations algebraically:
y=x^2-3x+10
y=x+10

Answers

good luckkkkkkkkkkkk
Hope this helps
Answer:
(0,10) , (4,14)

QUICKKKKKKKKKK I NEED THIS ANSWER
IF WRONG REPORTED

Answers

Answer:

D

Step-by-step explanation:

. How many minutes is it from 23:35 today to 01:15 tomorrow?
A 100
B 110
C 120
D 130
E 140

Answers

Answer:

A (100)

Step-by-step explanation:

If 2 hours pass starting at 23:35 today, then tomorrow the time will be 1:35. The difference between 1:35 and 1:15 is 20 (minutes) Because there are 120 minutes in 2 hours (60 minutes per hour), This means we do 120 minutes minus 20 minutes. This gives us an answer is A, 100 :)

I NEED HELP WITH THIS!!!

Answers

Answer:

they all are correct

Step-by-step explanation:

A toy company has 6 different heights of its best-selling action figure, labeled versions 1 through 6. Each version is modeled from clay molding of the action figure. Version 1 is 125% taller than the clay molding of the action figure. The heights of action figure versions 2 through 6 are each 125% taller than the previous version of the action figure. The clay molding of the action figure is 4 inches tall. Which function can be used to find the height in inches of each version of action figure, where 1 ≤ v ≤ 6?
h(v) = 1.25(v+ 4)

h(v) = 4(1.25)v

h(v) = 1.25(4)v

h(v) = 4(v + 1.25)

Answers

Answer:

a

Step-by-step explanation:

a

The line segment shown is translated down 4 units, what are the new coordinates of B?
(0.3)

Answers

Answer:

(0, - 1 )

Step-by-step explanation:

A translation down means subtracting 4 from the y- coordinate of the point, that is

B(0, 3 ) → B'(0, 3 - 4 ) → B'(0, - 1 )

Question 1
Construct two expressions that are equivalent to 27x^12.

I’m in a test need an answer ASAP please

Answers

One example is (3x^4)^3 and another is (3x^6)(9x^6)

What is the median value of the data set shown on the line plot?

Enter your answer in the box.

Answers

The median would be 32 due to the xs because you must count 2 to the right every time

Answer:

Its actually 30

Step-by-step explanation:

what’s the slope of the line bellow

Answers

The answer is C. 1/2

(100 points) Give a step by step explanation on how you solved this problem

y = 3x + 3
y = x − 1

Answers

Use substitution
Given both y values, you know that they have to be equal

3x + 3 = x - 1
2x + 3 = -1
2x = -4, divide by 2
x = -2
Now plug x value into any of the equation to find y value
y = 3(-2) + 3
y = -6 + 3, y = -3

Solution: x = -2, y = -3

Answer:

Step-by-step explanation:

Well you have to solve for X to find Y simplified.

Since both equations equal Y you can plug them together

3x+3=x-1

-x          -x

2x+3=-1

-3         -3

2x=-4

Divide -4 by 2 and you get X = -2 then plug X into both equations and boom

y= -3

Which function decreases faster please help

Answers

Answer:

Step-by-step explanation:

which of the following is an odd function?

Answers

Answer: I beleve it is a hope this helpes

Step-by-step explanation:

pleas make brainly

The triangles shown below must be congruent. Help please

Answers

True is the correct answer

You are given that cos(A)=−45, with A in Quadrant III, and cos(B)=15/17, with B in Quadrant I. Find cos(A+B). Give your answer as a fraction.

Answers

Answer:

con you be more organized on how you post the question will answer if fixed

Step-by-step explanation:

What ia the Lcm of 99 and 24

Answers

Step-by-step explanation:

792

........

........

........

.......

........

...

The LCM of 24 and 99 is 794

How many restaurants have a excellent rating that seat over 100. A) 182 , B) 159, C)180 OR D) 311

Answers

Answer:  I don't know if this is possible to solve https://youtu.be/dQw4w9WgXcQ

Step-by-step explanation:

Select ALL the right triangles, given the
lengths of the sides


Answers

The right triangles are A and E

Someone plz help 50 points and brainliest if correct!!!

Answers

Answer:

Ratio of one dimension:

k = R/r = 12/3 = 4

Ratio of the volumes:

k³ = 4³ = 64

Smaller volume given:

97 cm³

Larger volume:

97*64 = 6208 cm³

Answer:

6208 cm³

hope it helps

please mark Brainliest

Use the distributive property with factoring to find the equivalent expression. 24n + 32w = (3n + w)

Answers

Answer:

Step-by-step explanation:

24n + 32w = (3n + w)

We're asked to use distributive property, this means that we have to find a way that the given expression on the left hand side is equal to the given incomplete exresssion on the right hand side. In so doing, we're fulfilling the distributive property tag.

Given 3n, 3 factorises 24 into 8, and at the same time, factorises 32 into 4. Thus, we can then conclude that

24n + 32w = 8(3n + 4w)

help me please lol i don’t understand this

Answers

Answer:

a-88 degrees give me brainiest

If m∠3 is 124° and m∠4 = 8x + 40, what is the value of x?

Answers

Answer:

10.5

Step-by-step explanation:

M«3 =M«4

124°=8x+40

124°-40=8x+40-40

84=8x

84/8=8x/8

10.5=x

y+-16=70

please help​

Answers

Answer:

[tex]y + - 16 = 70 \\ y = 70 + 16 \\ y = 86[/tex]

Hope it helps!!

PLEASE HELP ME ANSWER!

Answers

Answer:

dsg

Step-by-step explanation:

srg

Answer:

x= 110

Step-by-step explanation:

vertical angles

set up :

6x + 115 = 7x +5 (subtract 6x from both sides)

115 = x +5 (subtract 5 from both sides)

110 = x (your answer)

CHECK:

6(110) + 115 = 775

7(110) + 5 = 775

Can someone help me with this

Answers

Answer:

I believe it is 30 toy planes

Hope this helps.

Step-by-step explanation:

toy cars - 2 = 12

toy planes - 5 = 30

total - 7 = 42

Select all of the expressions that are equal to 8 × 35 . A. 8 × ( 30 + 5 ) B. 5 + 3 × 35 C. ( 8 × 30 ) + ( 8 × 5 ) D. ( 8 + 30 ) × ( 8 + 5 ) E. 8 × ( 20 + 15 )

Answers

Answer:

A,C,E

Step-by-step explanation:

Answer:

A,C,E

Sryy if wrong but im pretty sure its right

Step-by-step explanation:

A bag of candy contains 5 different types of colored candies; red, green, blue, yellow, and orange. According to the manufacturer, bags should contain an equal number of each color. Students in a statistics class decided to use a chi-square procedure to test the manufacturer’s claim. They opened a bag of candy and recorded the number of candies of each color. The results are shown in the following table.
Red Green Blue Yellow Orange
17 24 20 25 14
Which color contributes most to the chi-square test statistic?

Answers

Answer:

Orange

Step-by-step explanation:

just took the test

The color which contributes most to the chi-square test statistic for the bag of candy is orange color.

What is Chi-square test?

Chi-square test is the statistical test, which is used to examine, the difference between the expected frequency and the observed frequency.

[tex]x^2=\dfrac{(o_i-E_i)^2}{E_i}[/tex]

A bag of candy contains 5 different types of colored candies; red, green, blue, yellow, and orange. Students in a statistics class decided to use a chi-square procedure to test the manufacturer’s claim.

They opened a bag of candy and recorded the number of candies of each color.  The results are shown in the following table-

Red  Green  Blue  Yellow  Orange

 17      24       20       25         14

The average of the all the values is 20.

Now, according to the manufacturer, bags should contain an equal number of each color. Thus, the expected value for the bag of candy are,

Red  Green  Blue  Yellow  Orange

 20     20       20       20         20

Form, the above formula the color which has less values of observed, and more value of expected, contributes most to the chi-square test statistic.  

Here, the orange color has the less value of observed frequency. Therefore, the color which contributes most to the chi-square test statistic for the bag of candy is orange color.

Learn more about the chi-square test here;

https://brainly.com/question/4543358

Choose the number that can be labelled as a natural number.
99, 2, 10, 0.33, -2, 56, 17, -22

Answers

Answer:

99, 2, 10, 56, 17

Step-by-step explanation:

hope it helps you ❤️❤️

help pleaseeeeeeeeeeeee

Answers

Answer:

B

Step-by-step explanation:

-2 is greater than -3

Answer:

The answer is b

Step-by-step explanation:

Please answer, no jokes or fakes or report ​

Answers

Answer:

375.2887 ft is the answer

Answer:

375.3 ft

Step-by-step explanation:

What we need to do first is divide 175 by the sine of 25°.

175/sin(25°)

175/0.422618

175/1 * 500000/211309

25/1 * 500000/30187

12500000/30187

414.085534 = length of hypotenuse.

Now, find the square root of the difference between c² & a².

b = √414.09² - 175²

b = √171470.528 - 30625

b = √140845.528

b = 375.293922

b ≈ 375.3

The horizontal distance between the technician and the base of the telephone pole is 375.3 ft.

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