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Note....one min point occurs at  -pi/4

The next min occurs at   (pi + pi/2) /2  =    (3pi /2) * (1/2)  = 3pi/4

So.....the period is

(3pi/4   -   - pi/4)  =   4pi/4  =   pi

can’t click on the link 

got the answer 216 cm^2 <-----

We have the form

y = Asin (Bx) 

The amplitude, A, is  [ difference between highest and lowest points ] / 2  = 10/2 =  5

The period is 12 sec

B  =   2pi / period   =  2pi/ 12  =  pi/6

So.....the equation of the function is

y = 5sin [ ( pi / 6) x  ]

Here's the graph : https://www.desmos.com/calculator/6ejfoskflu

Very nice, Rom....I like this problem.....!!!!

s    and r  are both perpendicular to t

So....they must be parallel

So

s ll  r

In the form   f(x) = Acos (Bx) + D

B =   pi  = the number of periods in 2pi

So

B = 2pi / period

pi  =  2pi / period        rearrange  as

period =  2pi / pi    =  2

And the frequency  =   1 /period  =   1/2

Equation of midline  ...  y =  [ max value of function + min value of function ]  / 2

Note that the max value of the cosine = 1    and the min value  = -1

So....max value of function =  3(1) - 2.5  =   .5

And the min value of the function is  3(-1) - 2.5 = -5.5

So the equation of the midline is

y =   [ .5  +    -5.5] / 2   =  [ -5  ] / 2   =   - 2.5

See the graph here :  https://www.desmos.com/calculator/lesls9edag

Partial sums when n=10
0.5, 0.5, 0.375, 0.25, 0.15625, 0.09375, 0.05468 75, 0.03125, 0.01757 8125, 0.00976 5625=1.98828......etc.
When n = 25
0.5, 0.5, 0.375, 0.25, 0.15625, 0.09375, 0.05468 75, 0.03125, 0.01757 8125, 0.00976 5625, 0.00537 10937 5, 0.00292 96875, 0.00158 69140 63, 0.00085 44921 875, 0.00045 77636 719, 0.00024 41406 25, 0.00012 96997 07, 0.00006 86645 5078, 0.00003 62396 2402, 0.00001 90734 8633, 0.00001 00135 8032, 0.00000 52452 0874, 0.00000 27418 1366, 0.00000 14305 11475, 0.00000 07450 58059 7=1.999999......etc.
∑[(n*1/(2^n)), n, 1, ∞] = 2

The midline is the y value that runs straight through the middle of the wave.If you can picture the standard sine function graph.  f(x) = Sin(x) reaches a maximum y = 1 and minimum y = -1 so the midline is y =0. This equation is shifted up 6 so the midline is shifted up 6y = 6 is equation for midline

I managed to solve it on my own but thanks anyways

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(2)  Population growth model

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We have the form

g(x)  = Asin (x) + D

A = the vertical stretch = 2

D = the shift up

So...the equation is

g(x) = 2sin (x) + 3

We have the form

y = A sin (Bx + C ) + D

A = the amplitude =  4

B =  the number of periods in 2pi....so    ...B =   2pi / period  =  2pi/pi   = 2

C is the phase shift....there is none....so....C = 0

D = the shift up / down   =  -3

So.....the equation is

y = 4sin (2x) - 3

Here is the graph :  https://www.desmos.com/calculator/67jvpq3xip

Period = 4pi

T = 4pib = 2pi/T = 2pi/(4pi) = 1/2 = 0.5

Amplitude = 2a = 2

Midline: y = 3

d = 3

y-intercept: (0,3)

The function is a reflection of its parent function over the x-axis, so 'a' is negative meaning a = -2 instead of a = 2

The function is

y = a*sin(bx-c)+d

y = -2*sin(0.5x-0)+3

y = -2*sin(0.5x)+3

Peri

Answer: -5.5

Look at one of the lowest points (there are infinitely many). The y coordinate of each of these valley points is y = -5.5. This is the smallest that y can get, therefore its the function min.

Thanks, Mclovin.....here's another way...

5x ^2 - 3x = 25     divide through by 5

x^2  - (3/5)x  =  5         

Take (1/2) of (3/5) = 3/10....square it = 9/100.....add to both sides

x^2 - (3/5)x + 9/100 =  5 + 9/100      factor the right side

(x - 3/10)^2 =   509/100    take both roots

x - 3/10 =  ±√ [509/100]

x - 3/10 = ±√(509) /10     add 3/10 to both sides

x =     [ 3 ±√509 ] / 10

Given that Megan's tax rates were as follows:
No tax one the first £11000 of earnings Earnings in excess of £11000 and up to £43000 taxed at a rate of 20%

Earning in excess of 43000 and up to £150000 taxed at a rate of 40%

Earnings over £150000 taxed at a rate of 45% If Megan earned £158900 before tax last year,

the amount of tax she paid in total is given as follows:

First £11000 = £0 tax

Balance after first £11000 = £158900 - £11000 = £147900Next (£43000 - £11000 = £32000) = 20% of £32000 = 0.2 x £32000 = £6400 tax

Balance after next £32000 = £147900 - £32000 = £115000Next (£150000 - £43000 = £107000) = 40% of £107000 = 0.4 x £107000 = £42800 tax

Balance after next £107000 = £115000 - £107000 = £8000Remaiming £8000 = 45% of £8000 = 0.45 x £8000 = £3600 tax

Total tax = £6400 + £42800 + £3600 = £52800Therefore, she paid a total of £52800 in tax last year.

Last year Carys earned £4 600 before tax.As given the tax rate in the question 

As the Carys earned £45 600 before tax is lies in the category of the earnings in excess of £43 000 and up to £150 000 taxed at a rate of 40%.

thus 40% tax rate is paid by the Carys.40% is written in the decimal form

.= 0.40Tax Carys paid = 0.40 × 45600                         

= £18240 Therefore the tax paid by the Carys be £18240.

8/4=2

2*3=6

8-6=2

answer is 2 because I correctly followed PEMDAS 

Very nice, Melody!!!!

I didn't see this one, at all....!!!!

1. Put all terms with variable on one side and the constants on the other side.5x^2 - 3x = 252.

Factor out the coefficient of the x^2 term

.5(x^2 - 3x/5) = 253.

Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation.

In this case we add 9/100 and on the other  side we add 9/20.5(x^2 - 3x/5 + 9/100) = 25 + 9/204.

We simplify as follows:

5(x^2 - 3x/5 + 9/100) = 25 + 9/205(x - 3/10)^2 = 509/20(x - 3/10)^2 = 509/100x1 = √(509) /100 + 3/10x2  = -√(509) /100 + 3/10