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We can find the common ratio, r,  by

Ratio  of   :  2nd term / 1st   term   =

6 / 9   =   2/3

So.....the explicit formula  is

a_n  = 9 (2/3)^{n- 1}

The period of the first graph is 5 seconds

The second graph  can be modeled by

y = 6sin (  2pi * x / 1.5    -  pi / 2)   +  6

Here's the graph : https://www.desmos.com/calculator/1hzzmtin1z

At..  x  = .75 s....we have

2pi * (.75) / 1.5   - pi.2   =

pi  - pi/2   =  pi/2    =  90°

a₁   = 10

a_n  =  -8 a_n-1

No need to work it. I have it.

I have figured out this question and got it right, thank you. No need to work it. I do need help on my other questions, though.

I've drawn the pic but not answered the question yet  

2.)  

a)  The profit of a company was $10 million in 2006 and $20.6 million in 2012. Find a linear model to represent the profit P of the company (in millions of dollars) in function of t . Variable t represents the number of year after 2004.

b)  Interpret the meaning of the model’s slope in the context of the problem. Include units in your interpretation. 

a)  We have the points   [ 2, 10]  and [ 8, 20.6]

The slope is    [ 20.6 - 10 ]  / [ 8 - 2 ]  =  10.6 / 6   =  53/30

The linear model is

y = (53/30) ( t - 2) + 10

y = (53/30)t  -  53/15  + 10

y =  (53/30)t + 97/ 15

b)  The slope, (53/30)  indicates the profit is increasing by  ≈  $ 1.76 M    per year

Chris you are better at these than I am, why don't you give it a go?

Here is the pic but I don't have an answer yet.

We need to find the x coordinate  of A, thusly

20 =  (-1/2)x^2 - x + 30

Subtract 20 from both sides  and rearrange

(-1/2)x^2 - x + 10  =  0       multiply through by -2

x^2  + 2x - 20  =  0

Using the quadratic formula to find the solutions  of this and taking the negative value, we have that

x  =  -1 - √21

So     ( -1 - √21, 20) is one point on the line

And to find the y values associated with B we have

(-1/2)(5)^2 - 5 + 30   =  -25/2 + 25   =   12.5

So   the point (5, 12.5)  is also on the graph

So  the slope is   [ 20 - 12.5 ]  / [  -1 - √21 - 5 ]  =  [ -7.5] / [ 6 + √21 ] 

So......the equation of the line  is

y  =  (  [ -7.5] / [ 6 + √21 ] )  ( x - 5)  + 12.5

OK.....good-bye!   G'day !

OK.....but only if you can find the surface area of THIS, first......

Mmmmmmm....I just tried it.....worked fine.....try it again....

The area is

(1/2) (15)^2 sin (32°)   ≈  59.6  units^2

Note the  pattern

8, 12, 16, 20........  =

4(2), 4(3), 4(4), 4(5)......  =

4 + 4, 4 + 4 + 4, 4 + 4 + 4 + 4, 4 + 4 + 4 + 4 + 4......  =

4(1) + 4, 4(2) + 4, 4(3) + 4, 4(4) + 4

So.......the explicit rule is

a_n  = 4_n + 4

a_n = a_n-1 + 6,  a1  = 39

Note that the terms are

39, 45, 51, 55.......

So....we can write

6(1) + 33, 6(2) + 33, 6(3) + 33 , 6(4) + 33

So...the explicit rule is

a_n  = 6_n + 33

Hectictar's Web2 anniversary - posted by GingerAle  7/2/18

a_n  =  a_n-1  - 9  ,  a₁  =  5

2.In rhombus ABCD, points E, F, G and H are the midpoints of AB, BC, CD, DA and  respectively. Quadrilateral EFGH has area 14 and perimeter 16. Find the side length for rhombus ABCD.

The side length will = the diagonal length of the quadrilateral

So

Area  of quadrilateral LW  = 14    (1)

Perimeter  of quadrilateral =  16  = 2(L + W)  ⇒ 8 = L + W ⇒  L = 8 - W    (2)

Sub (2)  into (1)

(8 - W) W =  14   simplify  and rearrange

W^2  - 8W  + 14  = 0

Solving this for W  gives us both dimensions  of

4 + √2  units    and  4  - √2  units

And the length of a side of the rhombus is

√  [  ( 4 + √2)^2 +  ( 4 - √2)^2 ]   =

√  [  16 + 2 + 16 + 2 ]  = √36    =   6 units

simplify  [x^2y^(-2/3)] / [x^0y^(-1/3)]

[x^2*y^-2/3] / [x^0* y^(-1/3)]

x^2 / [1 * y^(-1/3) * y^(2/3)]

x^2 / [y^(-1/3 +2/3)]

x^2 / y^1/3

Yep.....hectictar has been a valuable asset on here........happy anniversary!!!!

122.68115942

or

122  47/69

If January is 0 , then June would be x= 5      put 5 in as the value of x to get

F degrees = 43.4 degrees   (using RADIANS)

Room temp problem will need how many hours the experiment is running.

That is an equation for a line of the form   y = mx+b     where m (3 in this case) is the slope and 'b' is the y-axis intercept.