Find the exact values of the solutions in the interval 0 <= x < 2pi of the following equations without using a calculator. a) 3sec(x) + 2 = 8

Find The Exact Values Of The Solutions In The Interval 0 &lt;= X &lt; 2pi Of The Following Equations

Answers

Answer 1

Answer:

a) [tex]x_{1} = \frac{\pi}{3}\,rad[/tex], [tex]x_{2} = \frac{5\pi}{3}\,rad[/tex], b) [tex]x_{1} = \frac{\pi}{4}\,rad[/tex], [tex]x_{2} = \frac{3\pi}{4}\,rad[/tex], [tex]x_{3} = \frac{5\pi}{4}\,rad[/tex], [tex]x_{4} = \frac{7\pi}{4} \,rad[/tex]

Step-by-step explanation:

a) We proceed to solve the expression by algebraic and trigonometrical means:

1) [tex]3\cdot \sec x + 2 = 8[/tex]

2) [tex]3\cdot \sec x = 6[/tex]

3) [tex]\sec x = 2[/tex]

4) [tex]\frac{1}{\cos x} = 2[/tex]

5) [tex]\cos x = \frac{1}{2}[/tex]

6) [tex]x = \cos^{-1} \frac{1}{2}[/tex]

Cosine has positive values in first and fourth quadrants. Then, we have the following two solutions:

[tex]x_{1} = \frac{\pi}{3}\,rad[/tex], [tex]x_{2} = \frac{5\pi}{3}\,rad[/tex]

b) We proceed to solve the expression by algebraic and trigonometrical means:

1) [tex]6\cdot \cos^{2} x = 3[/tex]

2) [tex]\cos^{2} x = \frac{1}{2}[/tex]

3) [tex]\cos x = \pm\frac{\sqrt{2}}{2}[/tex]

4) [tex]x = \cos^{-1} \left(\pm \frac{\sqrt {2}}{2} \right)[/tex]

There is one solution for each quadrant. That is to say:

[tex]x_{1} = \frac{\pi}{4}\,rad[/tex], [tex]x_{2} = \frac{3\pi}{4}\,rad[/tex], [tex]x_{3} = \frac{5\pi}{4}\,rad[/tex], [tex]x_{4} = \frac{7\pi}{4} \,rad[/tex]


Related Questions

The distance from Cherotich's home to school is
2km 400m. He goes to school in the morning
and returns in the evening daily. What distance
does he cover from Monday to Friday?

Answers

Answer:

24 kilometers

Step-by-step explanation:

Given

Represent the distance with x

[tex]x = 2km\ 400m[/tex]

Required

The distance covered for 5 days (i.e. Monday to Friday)

First, we calculate the distance covered in a day

He covers the same distance when going to school and when coming back from school.

So, the daily distance is:

[tex]Daily = 2 * x[/tex]

[tex]Daily = 2 * (2km\ 400m)[/tex]

[tex]Daily = 4km\ 800m[/tex]

In 5 days, he covers:

[tex]5\ days = 5 * Daily[/tex]

[tex]5\ days = 5 * (4km\ 800m)[/tex]

[tex]5\ days = 5 * (4km+ 800m)[/tex]

Open bracket

[tex]5\ days = 5 * 4km+ 5 * 800m[/tex]

[tex]5\ days = 20km+ 4000m[/tex]

Convert m to km

[tex]5\ days = 20km+ 4km[/tex]

[tex]5\ days = 24km[/tex]

un tren ha recorrido dos tramos de un viaje en 5,12 horas el primer tramo mide 143, 39 kilómetros y el segundo 176,45 kilómetros ¿cuál es la velocidad media con la que el tren recorrido esos dos tramos?

creo que la tarea se trata de operaciones combinadas con decimales
con proceso porfavor​

Answers

Answer:

...

Step-by-step explanation:

Sabes que no estoy muy seguro porque solo hablo un poco de español solo con mi familia, ¿puedes poner esto en inglés?

What are the solutions of this quadratic equation? x2 − 18x + 58 = 0 A. B. C. D.

Answers

Answer:

Step-by-step explanation:

Let's use "completing the square" to solve this quadratic:  x^2 − 18x + 58 = 0

We want to rewrite the terms "x^2 - 18x" in the form '(x - h)^2 - h^2 and leave the terms '58 = 0' as they are:

Taking half of the coefficient of x (which coefficient is -18), we get -9.  We square this -9, obtaining 81, and then rewrite

"x^2 - 18x"   as  "x^2 - 18x" + 81 - 81."  To this we must append '58 = 0":

x^2 - 18x + 81 - 81 + 58, or x^2 - 18x + 81 - 23 = 0

Now the first three terms condense to the expression

(x - 9)^2, which is then followed by "-23":

(x - 9)^2 = 23

Solve this for x.  Taking the square root of both sides, we get

x - 9 = ± √23

so that one root is x = 9 + √23

and the other is x = 9 - √23

Answer: Let's use "completing the square" to solve this quadratic:  x^2 − 18x + 58 = 0

We want to rewrite the terms "x^2 - 18x" in the form '(x - h)^2 - h^2 and leave the terms '58 = 0' as they are:

Taking half of the coefficient of x (which coefficient is -18), we get -9.  We square this -9, obtaining 81, and then rewrite

"x^2 - 18x"   as  "x^2 - 18x" + 81 - 81."  To this we must append '58 = 0":

x^2 - 18x + 81 - 81 + 58, or x^2 - 18x + 81 - 23 = 0

Now the first three terms condense to the expression

(x - 9)^2, which is then followed by "-23":

(x - 9)^2 = 23

Solve this for x.  Taking the square root of both sides, we get

x - 9 = ± √23

so that one root is x = 9 + √23

and the other is x = 9 - √23

Step-by-step explanation: Hope it helps

7(x+4)=-21 help find x plz

Answers

Answer:

x = -7

Step-by-step explanation:

An art teacher is buying clay by the pound. The teacher buys pounds of clay for $7.50. How much will pounds of clay cost? A. $8.25 B. $15.75 C. $9.09 D. $9.90

Answers

Answer:

nnnnnnnnnnnn

Step-by-step explanation:

What is the 35th number in the sequence 4, 7, 12, 19, 28,…?

Answers

Answer:

n²+3. is the nth term

Step-by-step explanation:

Hi! Will someone please help me with expanding and simplifying this?:

5(2p+5) + 4(2p-3)

Thanks!

Answers

10p + 25 + 8p -12. Then it is 18p + 13

16. Solve the inequality -24 < x- 3 - 8x.
O A.X23
OBX 3
OC.X2-9
D. X 2-3

Answers

Answer: The answer is x<3 but I can't really tell what the answer choices are

Step-by-step explanation:

-24<x-3-8x

-21<-7x

x<3

can someone do this for me

Answers

Answer:

Step-by-step explanation:

Someone please help~~~~~~~

Answers

y the ''~~~~~~~~~~~~~~~~''?

What value of x makes the equation below true 6x-7=26

Answers

Answer:

11/2

Step-by-step explanation:

6x−7=26

Step 1: Add 7 to both sides.

6x−7+7=26+7

6x=33

Step 2: Divide both sides by 6.

x= 11/2

6x-7=26
+7 +7
6x=33 (divide both sides by 6)
x= 11/2 or 5.5

2x2 - 8xy - 2y2 for x = 6 and y = 5

Answers

Answer:

-236

Step-by-step explanation:

Step 1 (plug in x and y): [tex](2)(6)(2)-(8)(6)(5)-(2)(5)(2)=[/tex]

Step 2 simplify): [tex](24)-(240)-(20)[/tex]

Step 3 (evaluate): [tex]-236[/tex]

Find the value of each variable.

Answers

Step-by-step explanation:

x=15

y=15√3

sure 100%

welcome

What does 48s, s represents

Answers

Answer:

seconds

Step-by-step explanation:

Answer:

48s= number of scarves

Step-by-step explanation:

48 represents the price of scarf

Thank me later :)

PLEASE HELP ME I WILL GIVE BRAINLIEST

Answers

Answer:65

Step-by-step explanation:

Last year, 12 hydrange bushes had a mean of 14 blooms each, with a standard deviation of 2. The dot plot shows the number of blooms on the same bushes this year after a new plant food is used. What conclusions can you draw about the use of the new plant foor and the number of blooms?​

Answers

Answer: The plant food produces more blooms on average, but the results aren't as consistent as before.

========================================

Explanation:

The dot plot leads to this data set

{8, 12, 12, 17, 17, 18, 18, 18, 19, 19, 20, 23}

Using pencil/paper, or using technology, you should find the following properties of this data set

mean = 16.75sample standard deviation = 4.11

The second value is approximate. Both the mean and standard deviation are larger than their original counterparts (mean = 14 and std dev = 2).

Since the mean is larger, this means the data points have been shifted to the right further. The larger standard deviation tells us that the data is more spread out.

So it appears this new plant food has made the number of blooms increase overall, but it's also made the data more inconsistent. A smaller standard deviation would mean a more narrow set of points and therefore more consistent values (they'd all be clumped around the mean better).

Bags of sugar come in 3 sizes:

Small bag: A 250 g bag costs 85p.
Medium bag: A 500 g bag costs £1.90.
Large bag: A 3 kg bag costs £3.90.

Calculate the cost of 3 kg for the small and medium bags.
Give your answer in pounds to 2 dp.
Write the bag that is the better value in the comments.

Answers

Answer:3kg of small bag costs £10.20 while 3kg of the medium bag costs £11.40. Hence, the bag with better value which is the cheapest is a 3kg of the big bag which costs £3.9

Step-by-step explanation:

can someone please help me?!

Answers

Answer:

x = 119

z = 28

Step-by-step explanation:

To find x: Because of same-side exterior angles, you can add x and 61 together to find 180 degrees.

x + 61 = 180

Subtraction: x = 119

To find z: Use given quantities, not found variables for most accurate answer. Because of opposite exterior angles, you can equal them to each other.

61 = 5z - 79

Addition: 140 = 5z

Division: 140/5 = 5z/5

Final Answer = 28 = z

X = 19
Z = 28
Hope this helps

2. Does the graph show a proportional relationship? Explain. *

Answers

Answer:

Yes

Step-by-step explanation:

The two rules for a proportional relationship are

The line is straight (Check)The line goes though the origin (Check)

Because of that it is a proportional relationship.

Hope this helps :)

HELP PLS LMK IF U CANT READ IT AND I WILL TYPE IT

Answers

Answer:

cant read it type it pls

Step-by-step explanation:

porfavor necesito ayuda cuanto es -14x>-3

Answers

Balslsiksns kalsosijend f mlosoosk

x < 3 / 14        or       x < 0.2143

pleessssssssssssssssssss hellpp i will give you brainlist if you get coreted

Answers

Answer and Step-by-step explanation:

We are told that there is 24 cupcakes, which total up to be 36 dollars.

c will represent One cupcake.

We would do 36 divided by 24 to find the cost of One cupcake.

[tex]\frac{36}{24} = \frac{3}{2} = 1.5[/tex]

Each cupcake (c) is equal to $1.5.

Equations that would get us to this would be:

36/24 = c

36 = 24c

#teamtrees #PAW (Plant And Water)

Answer:

=9

Step-by-step explanation:

11919

Find the solution set of the inequality
5x + 13 > -37.
x ?

Answers

Answer:

x > -10

Step-by-step explanation:

5x + 13 > -37

subtract 13 from each side:

5x > -50

x > -10

Answer:

X >/ -10 (imagine this is more or equal to symbol lol)

Step-by-step explanation:

1. subtract 13 from both sides

5x +13-13 >/ -37 -13

2. Simplify

5x >/ -50

3. solve for x (which means divide by 5)

5x/5 >/ -50/5

x>/ -10

Whats the answer to these? (These are called Proper fractions.)

Jeremiah ran for 3/10 of a mile and then walked another 2/5 of a mile. How far did he travel in all?

Daniel read 4/5 books and Edgar read 1/2 books. How many more books did Daniel read than Edgar?

Jared drove 2/8 miles to the restaurant. He drove another 1/4 miles to the mall. How many miles did he drive in all?​

Answers

Answer to the first question: 7/10ths of a mile

Explaination: When adding fractions, you need to have a common denominator. Since dividing 3/10 by 2 to get a denominator of 5 makes 3 a decimal, it's easier to multiply 2/5 by 2 to get a denominator of 10. You do the same to the top that you do to the bottom: [tex]\frac{2*2}{5*2} = \frac{4}{10}[/tex]. From there, just add 4/10 and 3/10 to get the answer: 7/10ths of a mile.

Answer to the second question: Daniel read three (3/10) more books

Explaination: Since you can't evenly multiply 5 or 2 to get the opposite number, it's easier to multiply to the lowest common multiple. The easiest way to find that is to multiply both denominators (5*2=10). You'll have to multiply the numerator by the same amount you multipled the denominator by. For Daniel, that would mean: [tex]\frac{4*2}{5*2} = \frac{8}{10}[/tex]. For Edgar, that would mean: [tex]\frac{1*5}{2*5} = \frac{5}{10}[/tex]. So, Daniel read 3 more books than Edgar.

Answer to the third question: 2/4 mile (or 1/2 a mile)

Explaination: 2/8 can be simplified, by dividing the top and bottom by 2, resulting in 1/4. Since both fractions have the same denominator (/4), you can add them to get 2/4ths. This can be simplified further to half (1/2) a mile.

Answer and Step-by-step explanation:

1. Convert [tex]\frac{2}{5}[/tex] to have a denominator of 10.

[tex]\frac{2}{5}[/tex] × [tex]\frac{2}{2}[/tex] = [tex]\frac{4}{10}[/tex]

[tex]\frac{3}{10} + \frac{4}{10} = \frac{7}{10}[/tex]

Jeremiah ran [tex]\frac{7}{10}[/tex] of a mile in total.

2. Convert the denominators of all the fractions to have a 10.

[tex]\frac{1}{2}[/tex] × [tex]\frac{5}{5} =\frac{5}{10}[/tex]

[tex]\frac{4}{5}[/tex] × [tex]\frac{2}{2} = \frac{8}{10}[/tex]

Daniel read [tex]\frac{3}{10}[/tex] more books than Edgar, since 8 books is more than 5 books by 3 books.

3. Convert [tex]\frac{1}{4}[/tex] to have a denominator of 8.

[tex]\frac{1}{4}[/tex] × [tex]\frac{2}{2} = \frac{2}{8}[/tex]

[tex]\frac{2}{8} +\frac{2}{8}= \frac{4}{8}, or\frac{1}{2}[/tex]

Jared drove [tex]\frac{4}{8}[/tex], or [tex]\frac{1}{2}[/tex] miles in total.

#teamtrees #PAW (Plant And Water)

Help me lolz i would like it

Answers

Answer:

2/11 you are welcome

# 12 Find the area of the figure below. 121​

Answers

Answer:

120 ft²

Step-by-step explanation:

12(8) + 4(6) = 120

Answer:

96ft

Step-by-step explanation:

First we can find the rectangle which would be

6*12=72

then we can find the triangle, since their are two triangles we can combine them to make a rectnagle so we can just do

6*4=24

then we can add them together

72+24=96

Can I please have brainliest :)

A probability that is computed with the knowledge of additional information is called

Answers

Step-by-step explanation:

according to me it's conditional probability

Answer:

Conditional probability

Step-by-step explanation:

Conditional probability is the probability that is computed with the knowledge of additional information.

What angle measurement do you think goes between 30 degrees and 60 degrees

Answers

Answer:

[tex]45^{o}[/tex]

ifā=r, then which of the following are true statements?
Check all that apply.
O A. n1/r = a
✓ B. = a
c. a1/nur
O D. a' = n.

Answers

Answer:

B. a = rⁿ

C. a¹/ⁿ = r

Step-by-step explanation:

ⁿ√a = r

The above expression can be simplified as follow:

1. ⁿ√a = r

Recall:

ⁿ√a = a¹/ⁿ

Therefore,

a¹/ⁿ = r

2. ⁿ√a = r

Take the n square of both side

(ⁿ√a)ⁿ = rⁿ

(a¹/ⁿ)ⁿ = rⁿ

a = rⁿ

Can somebody help me?

Answers

Answer:

Its the 1st answer: A

Step-by-step explanation:

I already knew this.

Answer:

It should be A

Step-by-step explanation:

I hope this helps

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