solve the equation on the interval [0,2pi] 5sec(x)+7=-3

Answers

Answer 1

Answer:

Hello,

[tex]x\in \bigg\{\dfrac{2\pi}{3} ,\dfrac{4\pi}{3}\bigg\}\\[/tex]

Step-by-step explanation:

[tex]5*sec(x)+7=-3\\\\sec(x)=\dfrac{-10}{5} \\\\\dfrac{1}{cos(x)} =-2\\\\cos(x)=-\dfrac{1}{2} \\\\x=120^o\ or\ x=240^o\\[/tex]

Answer 2

Answer:

[tex]\sf \boxed{\sf x = \dfrac{2\pi}{3},\dfrac{4\pi}{3}}[/tex]

Step-by-step explanation:

A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]

The given equation is ,

[tex]\sf\longrightarrow 5 sec\ x +7 = -3[/tex]

Add -7 to both sides ,

[tex]\sf\longrightarrow 5sec\ x = -10 [/tex]

Divide both sides by 5 ,

[tex]\sf\longrightarrow sec \ x =\dfrac{-10}{5} [/tex]

Simplify ,

[tex]\sf\longrightarrow sec \ x =-2 [/tex]

Now solve for x ,

[tex]\sf\longrightarrow x = sec^{-1}(-2) [/tex]

Simplify ,

[tex]\sf\longrightarrow x = \dfrac{2\pi}{3}[/tex]

The secant function is negative in the second and third quadrants. Subtracting the reference angle from 2π to find the solution in the third quadrant to find the solution second solution.

[tex]\sf\longrightarrow x = 2\pi -\dfrac{2\pi}{3}[/tex]

Simplify ,

[tex]\sf\longrightarrow x = \dfrac{4\pi}{3}[/tex]

Now here the period of sec x is 2π . Therefore ,

[tex]\sf\longrightarrow x = \dfrac{2\pi}{3} +2\pi n , \dfrac{4\pi}{3}+2\pi n , \textsf{ for any integer n } . [/tex]

Therefore all the possible solutions are ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{2\pi}{3},\dfrac{4\pi}{3}}} [/tex]

Hence the required answer is 2π/3 and 4π/3.


Related Questions

Geometry, please answer question ASAP

Answers

9514 1404 393

Answer:

  C.  16

Step-by-step explanation:

UV is a diameter of the circle. If it is perpendicular to the chord XS, then it bisects that chord. This means ...

  XT = TS

  3b -1 = b +5

  2b = 6

  b = 3

  TS = b +5 = 8

The chord length is 2·TS = 2·8 = 16 units.

Answer:

C,XS=16

Step-by-step explanation:

3b-1=b+5

3b-b=5+1

2b=6

b=6/2=3

TS=b+5=3+5=8

XS=2 TS=2×8=16

what is the answer the / is division/divided? t+d/8-6

Answers

Answer:

t+d/2

Step-by-step explanation:

The width of a rectangle measures (2h-6) centimeters, and its length measures (7h+8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answers

Answer:

18h +4

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)  where l is the length and w is the width

  =2( 7h+8 + 2h-6)

Combine like terms

  = 2( 9h+2)

Distribute

   = 18h +4

Belinda is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for three years: Number of years 1 2 3 House 1 (value in dollars) 186,160 193,606.40 201,350.66 House 2 (value in dollars) 190,000 201,000 212,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points) Part C: Belinda wants to purchase a house that would have the greatest value in 30 years. Will there be any significant difference in the value of either house after 30 years? Explain your answer, and show the value of each house after 30 years. (4 points)

Answers

Answer:

A) both functions are linear

B) f(x) = 7446.4x + 178713.6 and f(x) = 11000x + 179000

C) House 2 will value $106894.4 more than house 1.

Step-by-step explanation:

A) Value Increase from year 1 to year 2:

House 1: 193,606.40 - 186,160 = 7446.4

House 2: 201,000 - 190,000 = 11000

Value Increase from year 2 to year 3:

House 1: 201,350.66 - 193,606.40 = 7744.26

House 2: 212,000 - 201,000 = 11000

This means that a constant increament in x variable gives a constant increament in both houses vales. Then, both functions are linear.

B) The slope is the same as the value increment from one year to the next one.

slope (m) of House 1: 7446.4

slope (m) of House 2: 11000

General formula of a line:

f(x) = mx+b

Replacing with a known point:

House 1

186,160 = 7446.4(1) + b

b = 186,160 - 7446.4 = 178713.6

equation: f(x) = 7446.4x + 178713.6

House 2

190,000 = 11000(1) + b

b = 190,000 - 11000 = 179000

equation: f(x) = 11000x + 179000

C) Replacing x = 30 into each equaiton:

Value of House 1 after 30 years

f(x) = 7446.4(30) + 178713.6 = 402105.6

Value of House 2 after 30 years

f(30) = 11000(30) + 179000 = 509000

Then, house 2 will value 509000 - 402105.6 = $106894.4 more than house 1.

Can you guys helppppppppppppp

Answers

Step-by-step explanation:

to find this angle you can use the sin ratio seeing that the opposite has been given which is 35 and the hypotenuse which is 48.so the solution will be

sin?=opposite/hypotenuse

sin?=35/48

sin?=0.729

?=sin inverse of 0.729

?=46.8 rounded off to 47°

I hope this helps

Hi

in application of sinus formula : ( must learn your trigonimetric formulas by heart !)

value of ? is sin^(-1) = (35/48) = 46,8. so 47 when rounded to the nearest degree

Find the missing side lengths

Answers

Answer:

u is 172 and v is 17

Step-by-step explanation:

To find u:

[tex]{ \bf{ \sin( \theta) = \frac{opposite}{hypotenuse} }}[/tex]

feed in the terms:

[tex] \sin(45 \degree) = \frac{17}{u} \\ \\ u = \frac{17}{ \sin(45 \degree) } \\ \\ u = 17 \sqrt{2} [/tex]

To find v:

[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

feed in the terms:

[tex] \cos(45) = \frac{v}{u} \\ \\ v = u. \cos(45) \\ v = (17 \sqrt{2} )÷( \sqrt{2} ) \\ v = 17[/tex]

What are the solutions to the equation StartFraction w Over 2 w minus 3 EndFraction = StartFraction 4 Over w EndFraction? w = –6 and w = –2 w = 0, w = 2, and w = 6 w = 0 and w = Three-halves w = 2 and w = 6​

Answers

Answer:

Hope it will helps you

.

.

Answer:

and w = –2 w = 0, w = 2, and w = 6 w = 0 and w = Three-halves w = 2 and w = 6

hope it's help you...!!!

#rishu

1. Find the sum of csc230° and cot2 45°.​

Answers

Answer:

5

Step-by-step explanation:

Based on the given conditions, formulate

Evaluate the expression:

Calculate the power:

Calculate the first two terms:

Answer:

Find the principle that yields and interest of Rs.2240 at the rate of 10% p.a. in a years 6 months.​

Answers

Step-by-step explanation:

I=PRT/100

p=I/RT×100

p=2240/10×2×100

p=11200

divide the numbers 1 to 8 by 9. observe the decimal and discuss your observation of non terminating recurring decimal

Answers

Answer:

When dividing the numbers 1-8 by 9, we get whatever number was divided as a decimal in repeating form. For example, 2/9 = 0.22222...

Brainliest, please! I'm almost an Ace!

Step-by-step explanation:

1/9 = 0.11111...

2/9 = 0.22222...

3/9 = 0.33333...

4/9 = 0.44444...

5/9 = 0.55555...

6/9 = 0.66666...

7/9 = 0.77777...

8/9 = 0.88888...

what is the external angle of a polygon where the corresponding interior angle equals 105 degrees

Answers

Answer:

75 degrees maybe.......

Answer:

75 degrees

Step-by-step explanation:

the external angle is between the outside of one of the sides of the angle and the continued line of the second side of the angle.

and because it is measured against a line, where we have a total of 180 degrees for angles, we have

exterior angle = 180 - interval angle = 180-105 = 75

Would be grateful if I get help

Answers

[tex]\\ \sf\longmapsto 72^{\frac{3}{4}}[/tex]

[tex]\\ \sf\longmapsto 72^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}[/tex]

[tex]\\ \sf\longmapsto 2.91+2.91+2.91[/tex]

[tex]\\ \sf\longmapsto 3.73[/tex]

Click on the sentence that represents the following equation.
m - 15 = 22
A. The difference of a number and 15 is equal to 22.
B. A number plus 15 is equal to 22.
C. A number increased by 15 is equal to 22.

Answers

Answer:

A.

Step-by-step explanation:

'The difference' means minus or subtraction. 'plus' and 'increased' are both for addition.

Brainliest please!

Simplify (square root 3)(^5 square root 3)

Answers

Answer:

[tex]3^{\frac{7}{10} }[/tex]

Step-by-step explanation:

[tex]\sqrt{3} *\sqrt[5]{3}[/tex] = 3^1/2 x 3^1/5 = 3^(1/2 +1/5) = 3^7/10

Answer:

Step-by-step explanation:

Exponent law: [tex]a^{m}*a^{n}=a^{m+n}[/tex]

[tex](\sqrt{3} ) )*(\sqrt[5]{3})= 3^{\frac{1}{2}}*(3^{\frac{1}{5}})\\\\=3^{\frac{1}{2}+\frac{1}{5}}\\\\=3^{\frac{1*5}{2*5}+\frac{1*2}{5*2}}\\\\= 3^{\frac{5}{10}+\frac{2}{10}}\\\\=3^{\frac{5+2}{10}}\\\\=3^{\frac{7}{10}}[/tex]


Describe fully the single transformation that maps shape A onto shape B.

Answers

B is an upside down image of A and is 2 units below A.

The image of A is mirrored across the y axis at y = 2.

Answer: A was mirrored across y= 2 to form B.

martin is filling his bathtub, but he left the drain partially open. martin knows that it takes 8 minutes to fill his 40 gallon tub. the equation v = 2.5t represents the volume, v , of water that drains out of the tub in t minutes. if martin leaves the water on, will the tub ever overflow ?

please someone help ​​

Answers

Answer:

Yes, it will overflow after 16 minutes..

Step-by-step explanation:

The tub fills at a rate of 5 gallons every minute, but it drains at a rate of 2.5 gallons every minute. This means that it fills twice as fast as it drains, so it would take 16 minutes for the tub to overflow. If you subtract the rate of draining from the rate of filling then the net rate of water going up is 2.5 gallons a minute.

please help me with this

Answers

Answer:

a) 10

b) 2.5

Step-by-step explanation:

2^n = 1024

2^n = 2^10

n = 10

4^(2n-3) = 16

4^(2n-3) = 4^2

2n-3 = 2

2n = 5

n = 2.5

Solution:-1:-

[tex]\\ \sf\longmapsto 2^n=1024[/tex]

Equal the bases

[tex]\\ \sf\longmapsto 2^n=2^10[/tex]

[tex]\\ \sf\longmapsto n=10[/tex]

Solution:-2:-

[tex]\\ \sf\longmapsto 4^{2n-3}=16[/tex]

[tex]\\ \sf\longmapsto 4^{2n-3}=4^2[/tex]

[tex]\\ \sf\longmapsto 2n-3=2[/tex]

[tex]\\ \sf\longmapsto 2n=2+3[/tex]

[tex]\\ \sf\longmapsto 2n=5[/tex]

[tex]\\ \sf\longmapsto n=\dfrac{5}{2}[/tex]

[tex]\\ \sf\longmapsto n=2.5[/tex]

25 points please help me

Answers

Answer:

I can help you with C and I tis non-linear because to make it linear it needs to be a straight line and shouldn't have any curves.

Step-by-step explanation:

please help with number 9!!!

Answers

Answer:

2 + sqrt(3)

Step-by-step explanation:

Roots that contain square roots come in pairs

If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)

2 -sqrt(3) means there is a root 2 + sqrt(3)

The sets A and L are given below.
A = (a, b, e}
L={c, k,j}
Find the intersection of A and L.
Find the union of A and L.
Write your answer using notation (in roster form)
Help plzzz

Answers

Step-by-step explanation:

A n L =null

A U L= a,b,c,e,k,j

Which line is parallel to the line given below?
x - 3y = 24
a. y = -x + 3
b. y = -3x - 1
c. y = 3x + 8
d. y=-x-4

Answers

Answer:

x - 3y = 24

B. y = -3x - 1

Step-by-step explanation:

Hope it helped.

° ° °

PLEASE HURRY

1 Your dad asks you to go to the grocery store and buy at least 3 pounds of grapes. Write an inequality for this scenario.

Answers

Answer:

X ≥ 3

Step-by-step explanation:

Let the number of grapes you'll buy be X, you need to buy at leaF 3 pounds so:

X ≥ 3

Answered by Gauthmath

Factor the polynomial expression 4x3 - 4.

Answers

Answer:  4(x - 1)(x^2 + x + 1)

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

Work Shown:

4x^3 - 4

4(x^3 - 1)

4(x - 1)(x^2 + x + 1)

In the last step, I used the difference of cubes factoring formula which is

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

If i work in a week 2 days cleaning and i will work 4 hours in a day and in 1 hour is 8$ how much will it be in a year

Answers

Answer:

$3072

Step-by-step explanation:

It is given that :

I work for 4 hours everyday, working 2 days a week.

And in 1 hour , I get $8.

Therefore,

1 hour = $8

4 hours = 4 x  8

             = $32

So, in 1 day working for 4 hours, I get $32.

∴ Working 2 days = 32 x 2

                              = $64

In 1 month, there are 4 weeks

So, in 4 weeks (or 1 month), I work for = 4 x 2

                                                               =  8 days

Therefore, in 8 days, I get = 8 x 32

                                            = $256

Now there are 12 months in a year.

So, in 12 months , I will get = 12 x 256

                                            = $3072

Therefore, in 1 year , I will get $3072.

prove that root 3 + root 7 is irrational

Answers

Answer:

√3+√7 is irrational.

Step-by-step explanation:

Let us assume that √3+√7 is rational.

That is , we can find coprimes a and b (b≠0) such that \sqrt{3}+\sqrt{7}=\sqrt{a}{b}

3

+

7

=

a

b

Therefore,

\sqrt{7}=\frac{a}{b}-\sqrt{3}

7

=

b

a

3

Squaring on both sides ,we get

7=\frac{a^{2}}{b^{2}}+3-2\times \frac{a}{b}\times \sqrt{3}7=

b

2

a

2

+3−2×

b

a

×

3

Rearranging the terms ,

\begin{gathered}2\times \frac{a}{b}\times \sqrt{3}=\frac{a^{2}}{b^{2}}+3-7\\=\frac{a^{2}}{b^{2}}-4\end{gathered}

b

a

×

3

=

b

2

a

2

+3−7

=

b

2

a

2

−4

\implies 2\times \frac{a}{b}\times \sqrt{3}=\frac{a^{2}-4b^{2}}{b^{2}}⟹2×

b

a

×

3

=

b

2

a

2

−4b

2

\begin{gathered}\implies \sqrt{3}=\frac{a^{2}-4b^{2}}{b^{2}}\times \frac{b}{2a}\\=\frac{a^{2}-4b^{2}}{2ab}\end{gathered}

3

=

b

2

a

2

−4b

2

×

2a

b

=

2ab

a

2

−4b

2

Since, a and b are integers , \frac{(a^{2}-4b^{2})}{2ab}

2ab

(a

2

−4b

2

)

is rational ,and so √3 also rational.

But this contradicts the fact that √3 is irrational.

This contradiction has arisen because of our incorrect assumption that √3+√7 is rational.

Hence, √3+√7 is irrational.

38) Paula is making a pair of drapes for her dining room. Each of the four drapery panels, when completed, measures 8 feetlang by 4 feet wide. What is the total area of the four drapery panels?




pls help if I see a off topic answer or a silly joke I will report and make sure u get in trouble so do not joke around.​

Answers

Answer:

128 ft^2

Step-by-step explanation:

each drapery has an area of 8*4 feet^2 and there are four panes so the total area is 8*4*4= 128

if three less than one half a number is equal to one-third of the same number, find the number​

Answers

Answer: The number would be 18

Step-by-step explanation:

18/2=9 9-3=6 6*3=18

The equation be (x/2) - 3 = x/3 then, the number of x = 18.

How to estimate the value of x?

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let x be the number

From the given information, we get

(x/2) - 3 = x/3

The set all the fractions on one side and constants on another side

(x/2) - (x/3) = 3

Multiply by LCM

3x - 18 = 2x

Add 18 to both sides

3x - 18 + 18 = 2x + 18

simplify

3x = 2x + 18

Subtract 2x from both sides

3x - 2x = 2x + 18 - 2x

x =18.

Therefore, the number is x = 18.

To learn more about algebraic expression refer to:

https://brainly.com/question/4541471

#SPJ2

Can you guys help me ?

Answers

The answer is -6.5

Have a good day!

Answer:

6.5

Step-by-step explanation:

you just take whats between the numbers

The average age of a preschool class is 4.5 years old. If there is one 3-year-old, five 5-year-olds, and two other children both of the same age, what is the age, in years, of the other two children?

Answers

Answer:

3.1

Step-by-step explanation:

5 x5 =25

25+3=28

the other children are 4 years old

Selling frozen yogurt at a fair, you make $565 and use 250 cones. A single-scoop cone cost $2 and a double-scoop cone cost $2.50. How many of each type of cone did you sell?

Answers

The seller sold 120 single-scoop cones and 130 double-scoop cones to make $565.

250 cones were used while selling yogurt and made $565.

There are two types of cones:

Single-scoop cone that cost $2.

Double-scoop cone that cost $2.50.

We need to know how many cones of each type were used while selling yogurt that made $565.

This is a system of linear equations problem.

We will have to make two linear equations using the given statements and apply the substitution method to get our answer.

Consider,

x = single-scoop cone.

y = double-scoop cone.

Now, we can make two linear equations:

x + y = 250............(A)

2x + 2.50y = 565...............(B)

Apply substitution method.

From (A) we get,

x = 250 - y...............(C)

And putting x = 250 - y in (B) we get,

2 ( 250 - y ) + 2.50y = 565

500 - 2y + 2.50y = 565

0.50y = 565 - 500

0.50y = 65

y = 65 / 0.50
y = 6500 / 50

y = 130

Putting y = 50 in (C) we get,

x = 250 - 130

x = 120

We have,

x = 120 and y = 130

We see that we need 120 single-scoop cones and 130 double-scoop cones to make $565.

Learn more about the system of the linear equations here:

https://brainly.com/question/8062932

#SPJ2

Other Questions
Let a=(1,2,3,4), b=(4,3,2,1) and c=(1,1,1,1) be vectors in R4. Part (a) [4 points]: Find (a2c)b+||3c||a. Part (b) [6 points]: Find two perpendicular vectors p and q in R4 such that their sum is the vector b and such that p is parallel to a. Part (c) [3 points]: If T(1,1,2,2) is the terminal point of the vector a, then what is its initial point? Part (d) [2 points]: Find a vector in R4 that is perpendicular to b. Why did most women want to keep working after the war A company claims that its soup vending machines deliver exactly 8 ounces of soup to every customer. You do not want the vending machines to deliver too much or too little soup. How would you formulate this properly in hypothesis testing?a) H0 : >8b) H0 : =8c) H0 > 8d) None of these What are 3 reasons why government spending should be increased? SOMEONE HELP ME PLEASE qual foi o objetivo da implantao da zona franca de manaus ? The particles of a substance stay close together but slide past one another as they move. When thermal energy is removed from the substance, the particles are forced into fixed positions by their attraction to one another. What change in state has occurred? O A. Gas to solid O B. Liquid to solidO C. Solid to liquidO D. Gas to liquid in how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively By reporting only p-values, many scientific publications provide an incomplete story of their findings.a. Trueb. False A tall plant has been found, but its zygosity is unknown. Tall is dominant over short height. The following can be done to determine its zygosity: _________.a. Let it self fertilize then analyze the progeny b. Cross to a true breeding short plant c. Cross to a heterozygous tall plant d. Cross to a true breeding tall plant PLEASE HELP WILL NAME BRAINLYEST Question 2(Multiple Choice Worth 1 points)(06.04 HC)Listen, look at the images, read, and choose the option with the correct image to answer the question.Based on the audio, what clothing item or items is the person missing?A pair of bootsA sweatshirtA t-shirt Which object has potential energy but not kinetic energy?A.A battery in a pair of headphonesB.A person riding an elevator upwardC.A person climbing a ladderD.A car that is slowing down Solve the triangle ,find m Based on your observations in question 7, what general conclusion can you draw about any line that is parallel to one side of a triangle and intersects the other two sides?(question 7. Now check the boxes for Show Segment Parallel to AC and Show Segment Parallel to AB. Find the ratio of BF to FC and the ratio of GB to AG. Then find the ratio of IC to BI and the ratio of HC to AH. (If you want to move , select point F, and if you want to move , select point H.) What can you say about the relationship between the pairs of lengths in each case? (The ratio of BF to FC is proportional to the ratio of GB to AG. Similarly, the ratio of IC to BI is proportional to the ratio of HC to AH.)) What is a second-generation Japanese American called?isseiniseidesuossuTHE ANSWER IS B) NIESEI I JUST DIDNT SEE IT ON HERE SO IM ADDING IT HELP PLEASE!!! The expected value of a random variable X is 35. The variable is transformedby multiplying X by 4 and then adding 1 to it. Find the expected value (mean)of the transformed variable. A. 135 B.117 C. 154 D.141 (A) superstar such as Angelina Jolie, who reportedly is paid $15 million or more per movie overpaid? Find the reference angle for -200 Find the circumference.Use 3.14 for t.r= 2 mC = [?] mC=Td What is government ? Two types of government.