1. A sine function has the following key features:
Frequency = 18π
Amplitude = 6
Midline: y = 3
y-intercept: (0, 3)
We have the following form
y = Asin (Bx) + C
The A is the amplitude = 6
To find B...we need to realize that the frequency is 1 / period...so....
Period = 1 / [ 18 pi ]
And B = 2pi / period = 2pi / (1/18 pi) = 36
And C = the midline value = 3
So.....the function is
y = 6sin (36x) + 3
See the graph here : https://www.desmos.com/calculator/whvopdsf3l
The function will have a vertical asymptote at x = 2 ....this value makes the denominator of the first fraction 0
Looking at the first fraction, we have a lower power polynomial over a higher power poynomial....this would give us a horizontal asymptote at y = 0....however, the " + 9 " actually shifts this up 9 units
So....the asymptotes are
x = 2 and y = 9
The domain includes all real numbers except x = 0 [ this value makes the denominator = 0 ]
Domain = (- inf, 0 ) U (0, inf)
For the range....we have a lower power polynomial over a higher power polynomial.....when this is the case, we will have a horizontal asymptote at y =0
So,the range is the same as the domain (-inf, 0) U ( 0, inf)
2[L + W] =22
L*W = 28
W = 28/L sub this in the first equation
Solve for L:
2 (L + 28/L) = 22
Divide both sides by a constant to simplify the equation.
Divide both sides by 2:
L + 28/L = 11
Write the left hand side as a single fraction.
Bring L + 28/L together using the common denominator L:
(L^2 + 28)/L = 11
Multiply both sides by a polynomial to clear fractions.
Multiply both sides by L:
L^2 + 28 = 11 L
Move everything to the left hand side.
Subtract 11 L from both sides:
L^2 - 11 L + 28 = 0
Factor the left hand side.
The left hand side factors into a product with two terms:
(L - 7) (L - 4) = 0
Find the roots of each term in the product separately.
Split into two equations:
L - 7 = 0 or L - 4 = 0
Look at the first equation: Solve for L.
Add 7 to both sides:
L = 7 or L - 4 = 0
Look at the second equation: Solve for L.
Add 4 to both sides:
L = 7 or L = 4 and W=4 or W = 7
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Thanks very much Alan :)
I looked at Matlab by Mathworks. It is $219 in Australia.
But then they say that to buy Simulink and add ons they are $65 each.
So this means I do not really know how much it will cost as I don't know if I need these extras.
The videos you sent have been written in Python programming language which appears to be a free download. In the very distance past I was relatively proficient at FORTRAN so I have some of the basic concepts and may be able to learn this language. I will admit though that getting my head around the logic could be a major problem for me these days.
I also looked at a Matlab video. It was showing many fabulous practical applications but I know I will never master any of those. At this instant in time I am only interested in running MonteCarlo simulations so that i can check my own probability answers.
I do not think I am interested in learning to do this in EXCEL. I think it would be super clumsy.
So this has led me to 3 options:
1) Get Matlab and learn to use it.
2) Download Python and learn to use it.
3) Keep asking you to check my answer :))
Do you have any input for me?
y = Asin(Bx + C )
A = the amplitude = [ difference in high/low/point ] / 2 = 6 / 2 = 3
The period is 20sec...so B =
2pi / period = 2pi / 20 = pi / 10
Since the sine graph starts at its highest position...the is a shift of pi/2 units to the left....thus C = pi/2
The function is :
y = 3sin ((pi/10) x + pi/2 )
The only question I have about this one is at the beginning of the observation, x = 0 and the weight will be at its highest point......thus.....the graph's first point will not be at the midline......that occurs 5 seconds later....
1. Freq = 1 / [ 6pi]
The frequency is 1 / period....so the period is 6pi....
In the form y = Asin (Bx) + C
Amplitude = 2 = A
Midline .....y = 3 = C
To find B
B = 2pi/ period = 2pi / 6pi = 1/3
y -intercept = (0, 3)
The function is :
y = 2sin ( (1/3) x) + 3
Here's the graph : https://www.desmos.com/calculator/8hza0yorxy
f(x) = 3 (x - 5)^2 + 9
1. f(x) is shifted 6 units to right to obtain function g(x). What is the equation of g(x) in terms of f(x)?
g(x) = f(x - 6)
2. What is the equation of g(x) in terms of x?
g(x) = 3 (x - 11)^2 + 9
3. Then, g(x) is shifted 7 units down to obtain function j( x) . What is the equation of j(x) in terms of
j(x) = f(x - 6) - 7
4. What is the equation of j(x) in terms of x?
j(x) = 3 (x - 11)^2 + 2
EDIT to correct a previious omission....
For...the second.....the bisected apex angle GEH sets up the following proportion :
GD / GE = DH / HE
x + 4 / 44.8 = 35 / 56 multiply both sides by 44.8
x + 4 = 44.8 * 35 / 56 simplify
x + 4 = 28 subtract 4 from both sides
x = 24
Check for youself that GD / GE = DH / HE = 5/8
Hope that helped......!!!!
The first and third one use the fact that a line segment drawn parallel to a base splits the sides proportionally
So on the first
MA = 46.2 - 14 = 32.2
And we have the following proportion :
MA / MN = MB / MP
32.2 / 46.2 = MB / 72.6 multiply both sides by 72.6
72.6 * 32.2 / 46.2 = MB = x = 50.6
For the third one
5x + 10 / 10 = 121 / 11
5x + 10 / 10 = 11 multiply both sides by 10
5x + 10 = 110 subtract 10 from both sides
5x = 100 divide both sides by 5
x = 20 CORRECT!!!
You don’t necessarily need expensive software to do Monte Carlo simulations (though it depends what you classify as “expensive”!).
You can do MC simulations using Excel (though I’m not a fan of Excel!).
I use an old version of Mathcad (unfortunately, PTC, who own Mathcad, now insist on an annual subscription for newer versions – and you can’t buy the older versions alone!).
I also use a home version of MATLAB - price ~ £100 (100 UK pounds) – made by the Mathworks.
There are lots of You Tube examples of MC simulation. A simple example is shown at https://www.youtube.com/watch?v=VJTFfIqO4TU for example.