asdf335

What you coudl do is draw an octagon and find the intersection points. When I did this with on octagon, it made more points forming another octagon, and there were 49 of them. So I think both answers are off. :)

The symbols are not relevant; f(a, b) was just an example. It wasn't part of the question. 

Now I think you can just plug in the stuff to get 2b - 27 + 7 = 90 => b = 55. :)

You could try to find it by not using calculus, but it might be bashier.

a)

Let's first find the points that are on y = f(x). This means the y coordinates are 4 and -4, so the x's are -4 and 4, respectively. Because it is on the graph of f(2x), the 2x halves the values, giving a = -2 and b = 2.

b)

Since I can't draw it out, I will tell you how to draw it. 

f(2x) will need a half as small x value to have the same effect. Here's an example: f(2 * 3) = f(6). So, we just have to "squish" the graph in towards the linex = 0 so that each x coordinate is half as much, but the y coordinates are the same.

c)

We know that the x's are -4 and 4 (from (a)). So, we set 2x - 8 equal to -4 and 4, getting c = 2 and d = 6.

d)

It has the same coefficient of x, so you can just draw graph b with the same shape but have (2, 4) and (-4, 6) and on the graph in the same spots that (-2, 4) and (2, -4) were in the graph of f(2x).

1)

3 years is 36 months, so the amount he owes is 2000 dollars * (1 + 5%) ^ 36, which, using a calculator, is approximately 11583.63.

2)

We are given that it takes 6 years to double. Because the same percentage applies with the same properties, after 6 years, the 300 dollars turns into 600, then 1200, then 2400, then 4800, then 9600. This doubles 5 times, which is 5 * 6 = 30 years.

Here's my work: https://snag.gy/SgLJCu.jpg

(It's my own writing with a mouse, so it's not pretty. :))

I will answer this again, taking into account that you said radical form.

As a note, you may have copied your question incorrectly as I know a question similar to this one but instead, one of them is x^2 and y^3 or x^3 and y^2. So, if you did miswrite it, please rewrite it and I will solve it correctly. :)

Inversely proportional means that the product stays constant. If x^3y^3 stays constant, then taking the cube root maens xy stays constant, so xy = 2*15 = 30, so when x = 1, y = 30. No radicals needed. :)

You could probably simplify that stuff... I don't know. Googling it may help.

Let's first go over some definitions:

Supplementary angles are when the angles sum to 180 degrees.

Complementary angles are when the angles sum to 90 degrees. 

So, we can calculate 180 - 82 and 90 - 82 to get 98 degrees and 8 degrees, respectively.

10)

Assuming t is a time unit.

The initial amount is when t = 0, so it is 250 * 1 = 250. The growth rate is how much the amount goes up by for every increase of 1 in t. This is 1.2, because that is the part being affected by t. So, it is 120% factor or an increase of 20% each time.

11)

Using the same logic, we plug in 0 for t to get 9.8 as the initial amount. The growth rate is just 135% factor, or 35% more each time, because 1.35 is the base of the exponent.