find the 6th term of 14,84,504

Answer:

cos ([tex]\frac{7\pi}{8}[/tex]) = [tex]-\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos [tex]\frac{7\pi}{8}[/tex] = cos [tex](\pi-\frac{\pi}{8})[/tex] = −cos [tex]\frac{\pi }{8}[/tex]

Now using half angle formula, cos(x) = 2 cos²([tex]\frac{\pi }{2}[/tex]) − 1, we can write cos [tex]\frac{\pi }{4}[/tex] = 2

cos²([tex]\frac{\pi }{8}[/tex]) − 1

This means [tex]\frac{1}{\sqrt{2}}[/tex] + 1 = 2 cos²([tex]\frac{\pi }{8}[/tex])

2 cos²([tex]\frac{\pi }{8}[/tex]) = [tex]\frac{\sqrt{2}+1}{\sqrt{2}}[/tex]

cos²([tex]\frac{\pi }{8}[/tex]) = [tex]\frac{\sqrt{2}+1}{2\sqrt{2}}[/tex]

cos([tex]\frac{\pi }{8}[/tex]) = [tex]\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}[/tex]

Simplify,

[tex]\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}[/tex] = [tex]\sqrt{\frac{2+\sqrt{2}}{4}[/tex] = [tex]\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

Hence,

cos ([tex]\frac{7\pi}{8}[/tex]) = −cos ([tex]\frac{\pi }{8}[/tex]) = [tex]-\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

The exact value of cos(7pi/8) is [tex]\rm -\dfrac{\sqrt{2+\sqrt{2}} }{2 }[/tex] and this can be determined by using the trigonometric properties.

Given :

Expression  -- [tex]\rm cos(\dfrac{7\pi}{8})[/tex]

The following steps can be used to determine the exact value of the given expression:

Step 1 - Write the given expression.

[tex]=\rm cos(\dfrac{7\pi}{8})[/tex]

Step 2 - Rewrite the above expression.

[tex]= \rm cos(\dfrac{8\pi - \pi}{8})[/tex]

Step 3 - The above expression is reduced to:

[tex]= \rm -cos(\dfrac{ \pi}{8})[/tex]    --- (1)

Step 4 - According to the trigonometric properties:

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

Step 5 - Substitute the value of x = [tex]\pi[/tex]/4 in the above expression.

[tex]\rm cos(\frac{\pi}{4}) = 2 cos^2(\frac{\pi}{8})-1[/tex]

Step 6 - Simplify the above expression.

[tex]\rm cos(\frac{\pi}{8})=\sqrt{\dfrac{\dfrac{1}{\sqrt{2}} +1}{2}}[/tex]

[tex]\rm cos(\frac{\pi}{8})=\sqrt{\dfrac{1+\sqrt{2} }{2\sqrt{2} }[/tex]

[tex]\rm cos(\frac{\pi}{8})=\dfrac{\sqrt{2+\sqrt{2}} }{2 }[/tex]

Step 7 - Substitute the value of cos([tex]\pi[/tex]/8) in the expression (1).

[tex]\rm -cos(\frac{\pi}{8})=-\dfrac{\sqrt{2+\sqrt{2}} }{2 }[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17081568

Answer:

yes it is great job

Step-by-step explanation:

Answer:

Step-by-step explanation:

Q2

Q3

The line is proportional relationship y = kx

Using point (8, 40), we can find the value of k:

Roland earns $5 per hour

Correct option is A

Answer:

11 17/21 :)

Step-by-step explanation:

Example for Table 1:

y = x + 6

So if X=-8

1st Row -8+6=-2

2nd Row -4+6=2

3rd Row -2+ 6=4

4th Row -9+6=-3

5th Row 2+6=8

So for any table, the X in the table rule is the X that you are working on.

Answer:

i got you:

1) -2, 2, 4, -3, 8

2) 37, -3, 29, -67, -75

3) -36, 4, -4, -20, -12

4) -10, 6, -4, 8, 4

5) -2, 18, -16, 6, -10

6) -4, -15, 2, 0, -6

7) -25, 23, 5, 29, 11

8) 24, 38, -60, 3, 10

9) 2, 4, 9, -1, -3

10) -14, -8, -15, -10, -16

11) 9, 18, -21, -3, -24

12) -10, 35, -73, 71, -19

hope that helps

Step-by-step explanation:

With the given coordinates it doesn't form a rectangle the correct set of the coordinates should be (2, 2), (1, 2), (1, -2), and (2,-2).

Answer:

The perimeter of the given rectangle that is formed by the given coordinates is 30miles.

Step-by-step explanation:

We are given the Rectangular coordinates such as

(2,2) , (1,2) ,(1,-2) (2,-2)

we will mark these  point on the cartesian planes to understand the rectangle

We can apply the distance formula or we can just look on the cartesian plane to simply get the distance between two points

we get

[(2,2) ,(1,2) ] and [(1,-2) ,(2,-2) ] are two units apart each pair as they are parallel so our width is

W = 2 units

similarly

we now need the length

(1,2) and (1,-2) are four units apart

so our length will be four units

L= 4 units

we need the perimeter

Perimeter of the rectangle = 2( L+W)

                                          = 2( 2 + 4)

                                          = 2* 6 = 12units

Now we are given that 1 unit is equal to 2.5 miles so 12 units will be  

             = 12* 2.5 = 30 miles

Therefore The perimeter of the given rectangle that is formed by the given coordinates is 30miles.

Answer:

31 degrees

Step-by-step explanation:

Answer:

31 Degrees

Step-by-step explanation:

Since this is a right angle, it will equal 90 degrees.

Take 90 and subtract 59 to get g.

g = 31 degrees

Answer:

B

Step-by-step explanation:

Answer:

3[tex]x^{4}[/tex] - 10x³ - x² - 11x + 6

Step-by-step explanation:

Each term on the upper row is multiplied by each term on the lower row.

This can be expressed as

3x²(x² - 5x + 2) + 2x(x² - 5x + 2) + 3(x² - 5x + 2) ← distribute parenthesis

= 3[tex]x^{4}[/tex] - 15x³ + 6x² + 2x³ - 10x² + 4x + 3x² - 15x + 6 ← collect like terms

= 3[tex]x^{4}[/tex] - 10x³ - x² - 11x + 6

Answer:

a = 8

Step-by-step explanation:

Pythagoras

hypotenuse² = Attitude ² + Base²

10² = a² + 6²

100 = a² +36

change side ; a² = 100-36

a² = 64

a = √64

a = 8 (Positive number only. not minus number)

so a = 8

hope it helps ☺️

Answer:

2/7

Step-by-step explanation:

7x/7=2/7

Simplify:Cancel terms that are both the numerator and denominator

Solution: 2/7

Answer:

13.7 years

Step-by-step explanation:

The equation of the line of the best fit is N = 62t + 35

where

N is the number of enrollments

t is years after the  year 2006

If the actual enrollment is 885 students. Put N = 885 in the given equation.

885 = 62t + 35

or

885 -35 = 62t

850 = 62t

t = 13.7 years

So, the required answer is 13.7 years.

Answer:

1 and 2

Step-by-step explanation:

slope is 1

y intercept is 2

basically base it off the equation y = mx + b

the m is the slope, but since in this case there is no number before x, you just put 1, since 1 times x is just x and thats why its left out

the b is the y intercept, so in this case its 2

Answer:

[tex]y=3(x-2)^2[/tex]

Step-by-step explanation:

The vertex form of the quadratic function has the following equation:

[tex]y=a(x-h)^2+k[/tex]

Where (h, k) is the vertex of the parabola, and a is a coefficient different from zero.

We are given the vertex located at (2,0). The equation is now:

[tex]y=a(x-2)^2+0[/tex]

[tex]y=a(x-2)^2[/tex]

Since we know the point (1,3) is on the parabola:

[tex]3=a(1-2)^2[/tex]

3=a(1)

a = 3

Finally, the quadratic equation is:

[tex]\mathbf{y=3(x-2)^2}[/tex]

Answer: -ab - 11a^2 - 3b + 3a

Step-by-step explanation:

i think this is what you're wanting? if not just comment what you need and i'll retry it!

Answer:

After 10 years , the number of residents in the community = 100,007.45

Step-by-step explanation:

Let P be the population of a farming community.

As we know that,

Exponential Growth model is :

P(t) = P₀[tex]e^{kt}[/tex]      ........(1)

where P₀ is the initial state , k is the growth constant.

As given,

A farming community begins with one resident.

⇒At t = 0 , P(t) = 1

∴ Put t = 0 in equation (1), we get

1 = P₀[tex]e^{0}[/tex]

⇒1 = P₀

∴  equation (1) becomes

P(t) = [tex]e^{kt}[/tex]    ......(2)

As given, every year, the number of residents multiplies by 10

⇒At t = 1 , P(t) = 10

∴ Put t = 1 in equation (2), we get

10 = [tex]e^{k}[/tex]

Taking ln both side we get

ln(10) = ln([tex]e^{k}[/tex] )

⇒2.3026 = k

∴  equation (2) becomes

P(t) = [tex]e^{2.3026t }[/tex]

Now, we have to find the population at t = 5

⇒P(5) = [tex]e^{5(2.3026} = e^{11.513} = 100,007.45[/tex]

So, we get

After 10 years , the number of residents in the community = 100,007.45

Answer:

295 is the answer... god bless

Answer25

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

3 (4 - n) + 8

When n = 3:

3 (4 - 3) + 8

3 (1) + 8

3 + 8

11

Answer:

11

Step-by-step explanation:

Answer:

-12.6

Step-by-step explanation:

Answer:

12.6 this is the answer

Step-by-step explanation:

sporting get up in subtracting numbers

Answer:

brackets

Step-by-step explanation:

Ya ave to use BIDMAS nd the B in BIDMAS stands for brackets

Answer:

it's c

Step-by-step explanation:

4 times 10 times 6 is 240 and you use volume because its by 3 values.

hope this helped!

Answer:

9

Step-by-step explanation:

Answer:

4x/5-2

Step-by-step explanation:

k(6)=0

#pglubestiehere

Answer: 0

Step-by-step explanation:

1) Go to x-value (6)

2) Locate the point

3) Identify the y -value

4) k(6) = 0

Answer:

-2x+18+25=14-3x

collect like terms

-2x+3x=14-25-18

x=29

Answer: a and b only are similar

Step-by-step explanation:

Ad/ab= de/bc similar triangles have proportional sides

Answer:

The true answer below

Step-by-step explanation: