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please help me. im stuck.

2^{2x+3}=14     Take log of both sides

(2x+3) Log 2 = log 14     solve for 'x'

x = (log 14/log2 -3  )/2   =  .403677461        Then 2^x = 1.322876

The radius  is 9in  =  3/4 ft 

The distance that the whell travels in one revolution  is    2pi * (3/4) ft  = (3/2)pi ft = (1.5pi ) ft

The number of feet in a mile  = 5280

So....the number of revolutions it makes is

5280 /[ 1.5pi ]  ≈     1120 revolutions

How many revolutions will a car wheel of diameter 18 in. make as the car travels a distance of one mile? (Round your answer to the nearest whole number.)

Sorry, guest....my bad.....thanx for the better eyesight....LOL!!!!

Thanx..... I realized that soon after I posted it and 'fixed' it!!   D'Oh!

EP:

The first one is SIMPLE interest:

$20,000 x 0.06 x 4 =$4,800 - simple interest for 4 years.

$20,000 x 1.06^4 =25,249.54 - $20,000 =$5,249.54 - This is annual compounded interest @6%.

FV = PV (1+i)^n 

First scenario  

FV = 20,000 (1.06)^4    If compounded annually

  or just  20,000 + 4*(20000*.06)    If only 6% for the entire four years.

Second scenario

FV = 20,000 (1+ .07/4)^16

I'll let you crunch the numbers to compute the differences !

40.

For a parallelogram,  Angle  ABC   +  Angle DAB  =  180

So

64   + 4y  -  12  =  180       

52 + 4y  = 180     subtract 52 from both sides

4y  = 128  divide both sides by 4

y  = 32

Also..for a paralleogram

AE  = EC

3x  - 5  =  16

x  = 21

x  = 7

Since 8 take band AND art ,     17-8 do NOT take art, but only BAND    9

Arc  Length  =  radius *  central angle  (in rads)

So we have

6  = radius  * (2/5)pi

6 (5/2) / pi  =  radius  =   30/pi ≈  9.55 m

y  = x^2  - 5

Let the point on the parabola  be  (x, x^2 - 5)

The distance, D, between this point and the origin can be represented by :

D  = sqrt  [  x^2  +  ( x^2 - 5)^2 ]

D  = sqrt [ x^2 + x^4 - 10x^2 + 25]

D  = [ x^4 - 9x^2 + 25 ]^(1/2)

Take the derivative of this and set to 0

D'  =  [(1/2] [(x^4 - 9x^2 + 25 ]^(-1/2)* (4x^3 - 18x)  = 0

This will equal 0  when  (4x^3 - 18x)  = 0       factor  this

2x (2x^2 - 9)  = 0

Set both factors to 0   and solve for x

2x  =  0                     2x^2  - 9  = 0

x  = 0                         2x^2  =  9

reject                           x^2 = 9/2

So....the distance, D, is

D  = sqrt  [ (9/2)^2 - 9(9/2) + 25 ]  =  sqrt [  81/4 - 81/2 + 25 ] =

sqrt [ 81/ 4 - 162/4  + 100/4]  =

sqrt  [ 81 - 162 + 100]  / 2  =

sqrt  [ 19 ] /2

So....a +  b  =   19 + 2   =  21

Area of a sector = Angle/360 x Pi x r^2

A =115/360 x 3.141592 x 7^2

A =49.2 ft^2 - area of the sector.

We have that

200 = 250(.5)^(12/h)   where h is the half-life in hours

Divide both sides by 250

200/250  = (.5)^(12/h)

.8  = (.5)^(t/h)      take the log of both sides

log (.8)  = log(.5)^(12/h)   

And by a log property we can write

log (.8) =  (12/h) log (.5)

Rearrange to isolate h

h  = 12log(.5) / log(.8)  ≈  37.28 hrs   

200 = 250 x 1/2^(12/t), where t=half-life
0.8 = 1/2^(12/t)            Take the natural log of both sides
-0.22314355 =(12/t) x -0.69314718      Cross multiply
-0.22314355 t =-8.317766                           Divide both sides by -0.22314355
t = 37.275 =~37 hours - the half-life of this material.

Let's work backwards

y  = x^2/4  +  x + 4     subtract 4 from both sides

y - 4  =  x^2/4 + x      factor out the 1/4 on the right side

y - 4   = (1/4)(x^2 + 4x)    complete the square on x within the parentheses

y - 4  = (1/4)(x^2 + 4x  + 4  - 4)   factor the first three terms inside the parentheses

y - 4  = (1/4) [ (x + 2)^2 - 4 ] distibute the 1/4 across the brackets

y - 4  = (1/4)(x + 2)^2  -1     add 1  both sides

(y - 3)  = (1/4) (x + 2)^2       

In the form (y - k) = a(x - h)^2....the vertex is at  ( -2, 3)

Multiply both sides by 4

4(y - 5) = (x + 2)^2

In the form 

4p (y - k)  = (x - h)^2

p  = the focal distance from the vertex

So...in our equation    4  = 4p   ⇒  p  = 1

Since the parabola turns upward....the focus is given by (h, k + p)  = (-2,  3 + 1) =

(-2, 4)

The directrix is given by   y  = k - p   =  3 - 1  =  2

Look at the graph here : https://www.desmos.com/calculator/wixfeughs1

Both functions are exactly the same

The vertex  is  (-2, 3)

The focus is (-2,4)

The directrix  is  y  = 2

10/3.25x5/5=25/8

You're welcome !

Mt Everest was still the tallest mountain in the world....before it was 'discovered'

10/3.2  x 5/5 = 50/16 = 25/8

f(x) =5,000 x 2^(30/10)

f(3) =5,000 x 2^3

f(3) =5,000 x 8

f(3) =$40,000 - the value of $5,000 investment after 30 years.

Yes, as long as you wrote the question right. 

If it was an x instead of a 2, it would have been exponential. 

are you sure?

I think this is linear because it represents a line.

y = 4 * 5 ^ 2

y = 100

This is one straight line.

Thanks for your response. 

I understand now.

For future references, just call me Gavin, to save you from typing gyanggg :)