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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. :)

Oops. Apparently I had no idea what I was talking about.

ds/dt   =  [ 4t^3 - 36t^2 + 56t ] /  50  = 0

(4/50) ( t^3 - 9t^2 + 14t) = 0

(4/50)t [ t^2 - 9t + 14) = 0

t ( t - 7) (t - 2)  = 0

t = 0     t  = 2   or t  =7

Take the second derivative  of  [t^3 - 9t^2 + 14t ]

[3t^2 - 18t + 14 ]

At t = 0...this is positive...so....a rel min  and the height= 8 ft

At t =2 ....this is 0

At t =1, the first derivative is positive

At t =3, the first derivative is negative

So...a t= 2...we have a max.....and the height is  8.64 ft

At t = 7 ....this is 0

At t = 8....the first derivative is positive

So...at t = 7...we have another min  and the height is 1.14 ft

So.....

max =   (2, 8.64)

min = ( 7, 1,14 )

Here's the graph to confirm this : https://www.desmos.com/calculator/rdjmso6wrw

The numbers x^3 and y^3 are inversely proportional. 

This is what that means    

$y^3=\frac{k}{x^3}\\ $

Now sub in x = 2 when y = 15 and solve for k

Once you have k you can plug in x=1 and find the corresponding value of y

Now you can answer yourself  :)

Please no one answer over me.

asdf335    

That is a very good method !     

Using you method you can see straight off that  it will be 

odd+ odd which must be even 

So it has to be divisable by 2   

If I'm reading this right, you just need to put t as 0 and 8.

1 - FV = PV x [1 + R]^N

     FV =2,000 x [1 + 0.05/12]^(3*12)

     FV =2,000 x [1.0041666667]^36

     FV =2,000 x [1.1614722313....]

     FV = $2,322.94 - what Kevin owes his mother after 3 years @ 5% comp.monthly.

2 - FV = PV[1 + R]^N

       $2=$1[1 + R]^6  -             Take the 6th root of both sides

R =~12.25%

9,600 = 300 x  1.1225^N         Divide both sides by 300

    32  = 1.1225^N                    Take the log of both sides

N = log(32) / log(1.1225)

N =~30 - years for $300 to grow to $9,600

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

Hi,

yes I am sorry I did make a mistake when copying the problem  it should be "The numbers x^3 and y^2".

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. :))

∑[- 4(8n - 2005), n, 1, 250] = 1,001,000

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.

1000^2 + 999^2 - 998^2 - 997^2..........etc.

Why did you subtract the first 2 terms?

Every 4 terms form an arithmetic sequence as follows:
7,988, 7,956, 7,924, 7,892........etc., where:
First term =7,988
Common difference = - 32
Number of terms =1,000 / 4 = 250
SUM = N/2 * [2*F + (N - 1)* D]
         =250/2*[2*7,988 + (250 - 1) * - 32]
         =125 * [15,976 + (249 * - 32)]
         =125 * [15,976 - 7,968]
         =125 * [8,008]
         = 1,001,000

you want the max delta y which is (3-0)=3

and the min delta x which is (4-2)=2

So the greatest slope is 3/2

Can you write your answer in simplest radical form?

Let's do this a different way! 
Group the terms in pairs. 
1000² - 999² = (1000+999)(1000-999) = 1999. 
998² - 997² = (998 + 997)(998-997) = 1995. 
. 
. 
. 
2²-1² = (2+1)(2-1) = 3. 

So we have to sum the arithmetic progression 
3 + 7 + ... + (4n-1) 
to 500 terms, since 1999 is the 500th term of 
this progression. 
So, how do we do this? 
Note that 
3 + 1999 = 2002 
7 + 1995 = 2002 
11 + 1991 = 2002 
. 
. 
. 
1999 + 3 = 2002 
Call the sum of each column S 
Then S + S = 500*2002 
S = 500*1001 = 500500.