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in 8 years =  $  800 ( 1 + .03)⁹

top triangle      1/2  16 * 8

left triangle       1/2  6 * 8

rectangle            6 x 16        in²       add together

I saw the problem here at another post.

https://web2.0calc.com/questions/for-each-integer-n-let-f-n-be-the-sum-of-the-elements

But, i do not fully understand it. Does it mean, that... minimum f(n) for n >= 2015, will be $2^{2014} + 1$???

Hello

Can you somehow post a picture of the problem (show the angles all drawn out) so that I can get a better idea of what I am trying to solve?

The Math Whiz

derivative =  2x-4    (this is the slope of the line for any given'x' value)

horizontal line has slope = 0        solve   0 = 2x-4     to find where line is horizontal

                                                                          use the 'x' value in the ORIGINAL equationto calculate the 'y' value

The angle  subtends  an arc  of (360 - 126) °    =  234°

Because it's an inscribed angle it has  half of this measure =  117°

That is what I got! You can also convert it to a mixed number: 1 7/8.

Hello Guest!

Here is the work shown:

We first calculate the area of triangle FAE. 3*4=15. 12/2= 6.

Next, we calculate the area of triangle AEB. 3*6=18. 18/2= 9.

Then, we calculate the area of another triangle made up of D, E, and the point at 5, -3.  6*1=6. 6/2= 3.

Finally, we calculate the area of the rectangle of the points 5, -3, E, B, and C. 6*6=36. 36/2= 18.

Our last step is to add together the bold parts. This gives us the final answer of 36.

Hope this helped!

The Math Whiz

f(x) =    ( x +5)^(1/2)

f ' (x)   = ( 1/2) (x + 5)^(-1/2)

Slope  at  (-1,2)   =   (1/2) (-1 + 5)^(-1/2)  =  (1/2) (4)^(-1/2) =  (1/2) (1/2)  =   1  / 4

$420.69

Ohhh, I should've thought about using the slope to find the intercept, would've been a lot more precise. 

Thanks

=^._.^=

Double sorry      (didn't fix the last equation in my answer:

so line equation is y  = 4x-12      

slope of the equation is gieven by the first derivative....in this case derivative of   x^2-8   is :   2x    

a) 2 (2) = 4 = slope at x = 2

b) tangent line will have this slope       y =4x + b    subbing in the point given     (typo...I put the wrong slope in there ...calculated '4' but I used '2')

                                                           -4 = 4(2) +b    b = -12     so line equation is y  = 2x-12

Here is the graph:

I agree  with catmg...hard  to see

The slope of the line  =   [ 6 - -9 ]  /  [ -4, -1 ]  =  15  / - 5  =   -3

This means  that  when  x  changes  by - 1 , y  rises  by  3

So....I believe the  y intercept should be [  1  -1 , -9 + 3 ]  =  [ 0 ,  -6 ] 

2x-8 isn't correct, I don't know why it's wrong

Is there more of the question?

=^._.^=

The y intercept is when x = 0. 

I can't quite see the numbers, but it looks like that at x = 0, y = -5. 

So our y intercept is -5. 

=^._.^=

Awww, thank you. :))

=^._.^=

We only  need  two points

(0, -6)  and (4, -7)    are  on the  graph

Slope =  m  =    [ -7 -  - 6 ]  /  [ 4 - 0 ] =  [ -7 + 6 ]  / 4   =   -1/4

We can use  either point...I'll use  (0, -6)  = (x1, y1)

y =  (m) * ( x - x1) + y1

y =  (-1/4) ( x - 0) -  6

Don't worry.....you will learn this easily....your math skills won't give you any trouble in Calculus

r =  12sqrt(2)

θ =  arctan ( 12/12)  = arctan (1)  = pi/4

So

(12sqrt 2 * cos (pi/4)  , 12 sqrt (2) , sin (pi/4) )

Also .... add pi to pi/4 = 5pi/4      make  r  negative

(-12sqrt (2) cos ( 5pi/4)  , -12sqrt (2) sin (5pi.4) )

Hello,

If you search this question up on bing, you should find that algebra.com has the answer. I am unfortuanetely not able to get the link for you. Hope this helps!

The Math Whiz

slope of the equation is gieven by the first derivative....in this case derivative of   x^2-8   is :   2x    

a) 2 (2) = 4 = slope at x = 2

b) tangent line will have this slope       y = 2x + b    subbing in the point given 

                                                           -4 = 2(2) +b    b = -8     so line equation is y  = 2x-8

I am very confused rn. 

Hopefully, I'll understand the concept in a few years. :)))

=^._.^=

In simple terms.....the first derivative is a function that  helps  you find the  slope of a  tangent line to a function at any point (if the function is differentiable at that point)....this is the  first derivative.....also used to find velocity

The second derivative is used to find mins and maxes of functions  (if they exist)  and also to calculate acceleration

I hope I've confused you enough, catmg.....LOL!!!!!