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Solve for x:sinx+sin2x+sin3x=cosx+cos2x+cos3x in the interval 0≤x≤2π.

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We write the given equation as

(sinx+sin3x)+sin2x=(cosx+cos3x)+cos2x

or 2sin2xcosx+sin2x=2cos2xcosx+cos2x

or sin2x(2cosx+1)=cos2x(2cosx+1)

or (sin2x−cos2x)(2cosx+1)=0

∴sin2x−cos2x=0 or 2cosx+1=0

If sin2x−cos2x=0, then tan2x=1,

Hence 2x=nπ+π/4

or x=(4n+1)

8

π

.(1)

If 2cosx+1=0, then cosx=−1/2 (2)

∴x=2nπ±

3

2π

or x=

3

6n±2

π

We seek values of x in the interval 0≤x≤2π

In this interval (1) gives

x=π/8,5π/8,9π/8,13π/8. (n=0,1,2,3)

and (2) gives x=2π/3,4π/3. (for n=0,1)

Thus we get the answer

x=π/8,5π/8,2π/3,9π/8,4π/3,13π/8.

Answer:

8:3

Step-by-step explanation:

Answer:

3:8 or 8:3, im leaning towards 3:8 more but i dunno

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function

a) Complete the table. Find the values of f(x) or y:

b) Plot the points:

c. The domain the the set of x- values. Since we connect the points, the domain covers the interval between the endpoints:

Domain: {x | -1 ≤ x ≤ 1}

a) The domain is the set of x- values (first number in ordered pairs):

The range is the set of y- values (second in pairs):

b) Graph by plotting the points:

c) The graph is NOT linear as you don't get a straight line if you connect the points

Applying the theorem of congruent triangles, since FG = 6 units and FG and KL are congruent, therefore:

KL = 6 units

Recall:

Given that:

[tex]\triangle EFG \cong \triangle JKL[/tex],

EF = JK

FG = KL, and

EG = JL

Thus, since FG = 6 units and FG and KL are congruent, therefore:

KL = 6 units

Learn more here:

https://brainly.com/question/9795907

Answer:

Step-by-step explanation:

[tex] \large\underline{\sf{Solution-}}[/tex]

Given that,

[tex]\rm \longmapsto\: {(x + iy)}^{3} = y + iv[/tex]

[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}(iy) + 3x {(iy)}^{2} + {(iy)}^{3} = y + iv[/tex]

[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}yi + 3x {i}^{2} {y}^{2} + {i}^{3} {y}^{3} = y + iv[/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1 \: \: \: and \: \: \: {i}^{3} = - i }}} \\ [/tex]

So, using this, we get

[tex]\rm :\longmapsto\: {x}^{3} + 3 {x}^{2}yi - 3x{y}^{2} - i{y}^{3} = y + iv[/tex]

[tex]\rm \longmapsto\: ({x}^{3} - 3x {y}^{2}) + i(3{x}^{2}y- {y}^{3})= y + iv[/tex]

On comparing real and Imaginary parts, we get

[tex]\rm \longmapsto\:y = {x}^{3} - 3 {xy}^{2} [/tex]

and

[tex]\rm \longmapsto\:v = {3x}^{2}y - {y}^{3} [/tex]

Now, Consider

[tex]\rm \longmapsto\:\dfrac{y}{x} + \dfrac{v}{y} [/tex]

[tex]\rm \:  =  \: \dfrac{ {x}^{3} - {3xy}^{2}}{x} + \dfrac{ {3yx}^{2} - {y}^{3} }{y} [/tex]

[tex]\rm \:  =  \: \dfrac{ x({x}^{2} - {3y}^{2})}{x} + \dfrac{y({3x}^{2} - {y}^{2})}{y} [/tex]

[tex]\rm \:  =  \: {x}^{2} - {3y}^{2} + {3x}^{2} - {y}^{2} [/tex]

[tex]\rm \:  =  \: 4{x}^{2} - {4y}^{2}[/tex]

[tex]\rm \:  =  \: 4({x}^{2} - {y}^{2})[/tex]

Hence, Proved

Answer:

see explanation

Step-by-step explanation:

xyz + 1 ← has 2 terms

xyz is one term and the other is the constant term + 1

Answer:

z=9.6

Step-by-step explanation:

Because you know 17 is one of the values in the model, you do:

65-17=48

Then, because you have 5 z values, you do:

48/5=9.6

z=9.6

Answer:

-32

Step-by-step explanation:

To find w(-7) we have to substitute x with -7

w(x)=4x-4

w(x = -7) = 4(-7) -4

w(-7) = -28-4

w(-7) = -32

Answer:

Yes.

Step-by-step explanation:

Set the equations equal to each other to determine their equality.

-4[3(x - 7)] = 6(14 - 2x)

Distribute the 3 and the 6 into their respective parenthesis.

-4[3x - 21] = 84 - 12x

Distribute the -4 into the brackets.

-12x + 84

Rearrange the equations.

84 - 12x = 84 - 12x

Since the equations come out to be the same thing on both sides so that any value satisfies it, the equations are equivalent.

To find the time Jack takes to cross Swan Lake, his average speed is required:

The time it will take Jack to cross Swam Lake is 0.5 hours

Reason:

Time it took Jack to paddle 6.4 km upstream, t = 2 hours

Distance Jack paddled, d = 6.4 km

The given speed of the Black River, v₂ = 1.8 km/h

The width of the lake, w = 2.5 km

The time it will take Jack to cross Swan Lake

Let v₁, represents Jack's speed, we have;

[tex]v_1 - v_2 = \dfrac{d}{t}[/tex]

Therefore;

[tex]v_1 - 1.8 = \dfrac{6.4}{2} = 3.2[/tex]

v₁ = 3.2 + 1.8 = 5

[tex]Time \ to \ cross \ the \ lake , \ t_S = \dfrac{w}{v_1}[/tex]

[tex]t_S = \dfrac{2.5 \, km}{5 \, km/h} = 0.5 \, hr.[/tex]

The time it will take Jack to cross Swan Lake, [tex]t_S[/tex] = 0.5 hours

Learn more here:

https://brainly.com/question/17168275

Answer:

B) Danni walked farther than Wendi.

Step-by-step explanation:

a mile is 5,280 feet. 5,280 + 5280 = 10,560

Similar shapes may or may not be congruent

The length of DE is 42 units

The given parameters are:

[tex]\mathbf{AC = 84}[/tex]

[tex]\mathbf{BA = 2BD}[/tex] --- Because DE is at the midpoint

The equivalent ratio is then represented as:

[tex]\mathbf{BD : DE = BA : AC}[/tex]

Substitute [tex]\mathbf{BA = 2BD}[/tex]

[tex]\mathbf{BD : DE = 2BD : AC}[/tex]

Express as fraction

[tex]\mathbf{\frac{DE}{BD }= \frac{AC}{2BD }}[/tex]

Make DE the subject

[tex]\mathbf{DE= \frac{AC}{2BD } \times BD}[/tex]

[tex]\mathbf{DE= \frac{AC}{2 }}[/tex]

Substitute 84 for AC

[tex]\mathbf{DE= \frac{84}{2 }}[/tex]

[tex]\mathbf{DE= 42}[/tex]

Hence, the length of DE is 42 units

Read more about similar shapes at:

https://brainly.com/question/20536565

Answer:

mab-2

mbc1/2

mcd-3/4

mad-3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

If binomial (3x+2) is  a factor of some polynomial, then number  is this polynomial's root. Check all polynomials:

6x^3+3x^2+4x+2

Answer:

B. [tex]12x^2+15x+8x+10[/tex]

Step-by-step explanation: I did this assignment on edge.

Answer:

Flour: 18.76 Tablespoons

56.28 Teaspoons

1.17 U.S. Cups

Baking Powder: 0.35 Tablespoons

1.04 Teaspoons

0.02 U.S. Cups  

Sugar: 0.80 Tablespoons

2.40 Teaspoons

0.05 U.S. Cups

Butter: 2.82 Tablespoons

8.46 Teaspoons

0.18 U.S. Cups

Maple Syrup:

0.127 Cups

2.029 Tablespoons

6.087 Teaspoons

Milk:

0.169 Cups

2.705 Tablespoons

8.115 Teaspoons

Hope this helps!!

Have A Blessed Day <333

Answer:

From 25 to 47 is an increase of 88%.

Step-by-step explanation:

From 25 to 47 is an increase (jump) of 22.  Write the ratio 22/25 and then multiply the result by 100%:

(22/25)*100% = 0.88(100%) = 88%

From 25 to 47 is an increase of 88%.

Answer:

X = 80°

Step-by-step explanation:

The total number of degrees in a triangle is 180°.

70° + 30° = 100°

180° - 100° = 80°

Answer:

d=4.5t

Step-by-step explanation:

in two hours, Francine went 9 miles

9/2=4.5

the distance equals 4.5 times each cycling time.

d=4.5t

Answer:

there are 400 meters in a track

400 times 12 = 4800

4800 divided by 1600 =3

Joyce ran 3 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2.3 is ur answer

Step-by-step explanation:

Answer:

2.3

Step-by-step explanation:

the interweb said so

Answer:

a.(-2,-1)

b.(-3,0) and (-1,0)

Step-by-step explanation:

the roots are 2

        You were close, and have the right idea, but I think you did it a bit backwards! You want to "flip" it over the y=x line (picture attached below)

       To solve for the inverse, you will find the equation of the original, switch the x and y, then solve for y.

      We can (mostly, I think?) tell the equation for f(x) is as follows, so we switch the y and x for the steps following to solve for y:

[f(x)] y = -2x + 2

[switch] x = -2y + 2

[subtract 2 from both sides / flip equation] -2y = x - 2

[divide both sides by -2] y = -2x -4

So our equation for g(x) will be about y = 2x -4

(inverse so the negative is weird)

Photos:

- first is y=x

- second is the general idea of the inverse for what g(x) should look like

- third is kinda what the graph will look like (digitally)

I know this isn't a *perfect* answer, but I hope it explains it some and helps. Good luck! :D

Answer:

49/4 inches

Step-by-step explanation:

Inches below ground=  3 1/2 inches

Plant's full  height=15 3/4 inches

Height above ground = 15 3/4 inches -3 1/2 inches

63/4 - 7/2

63-14/4

49/4 inches

Answer:

To solve this, make d the subject from the eqn.

[tex]b = - \frac{1}{c} da[/tex]

[tex]d = - \frac{cb}{a} [/tex]

Answer:

The difference of seven and two tenths and a number is more than twenty nine.

7.2 -n >29

Choice A

Step-by-step explanation:

[tex]x=16\\m<P=73\\m<Q=67\\m<R=40[/tex]

Answer:

x=42,

Step-by-step explanation:

sorry i don't know the rest but hope this helps u don't need to mark me brianlest i just wanted to help

Answer:

m∠1 = 63

m∠2 = 49

m∠3 = 87

m∠4 = 44

Step-by-step explanation:

Angle 2 and 49 are similar

Angle 2 = 49

Angle 1 + 49 + 68 = 180

180 - 49 - 68 = Angle 1

180 - 49 - 68 = 63

Angle 1 = 63

Angle 3 + 93 = 180

180 - 93 = Angle 3

180 - 93 = 87

Angle 3 = 87

Angle 4 + 49 + 87 = 180

180 - 49 - 87 = Angle 4

180 - 49 - 87 = 44

Angle 4 = 44

Step-by-step explanation:

A straight angle measures 180°.

m∠3 = 180 - 93

m∠3 = 87

The sum of the three angles of any triangle is equal to 180°.

m∠4 = 180 - (49 + 87)

m∠4 = 180 - 136 = 44

The vertically opposite angle.

so m∠2 = 49

The sum of the three angles of any triangle is equal to 180°.

m∠1 = 180 - (68 + 49)

m∠1 = 180 - 117 = 63

please give me a brainliest answer