geno3141

a) Graph it, either byhand or by calculator.

b) The h-intercept represent the height of the log.

c) The maximum height occurs at about 0.0765 secs. The maximum height is about 14.87 cm. These are the coordinates of the vertex of the funtion.

d) The spider lands after approximately 0.251 seconds.

e) Appropriate domain: [0, 0.251]    Appropriate range:  [0, 14.87]

f) Replace t with  0.05 to get 14.525  cm. 

When you have an exponent to an exponent, multiply the exponents together.

25^(1/10)  =  (5^2)^(1/10)  =  5^(1/5)

36^(-1/10)  =   (6^2)^(-1/10)  =  6^(-1/5)

[5^(1/5)·6^(-1/5)]^5  = [5·(1/6)]  =  5/6

If this is the problem:  (4x + 6) x 0.5

Distribute the 0.5          0.5(4x) + 0.5(6)

                                           2x + 3            

Simplifying:  3x + 10 + x + 10  =  180

                                   4x + 20  =  180

                                            4x  =  160

                                              x  =  40

If we do not assume any interest added to her account:

First friday:  $100.00 - $10.00  =  $90.00

Second friday:  $90.00 - $9.00  =  $81.00            

Third friday:      $81.00 - $8.10  =  $72.90

Fourth friday:   $72.90 - $7.29  =  $65.61

etc.

I'll let you finish this; but there will be money left in the account after 10 withdrawals because, even though the account gets smaller, every week a smaller and smaller amount will be withdrawn.

From the first equation, x = 2.Substituting 2 into the second equation, y = 3.

The value of z?  Who knows?

(x/7) + 1 ≠ (x/7)  

The left side is always 1 larger than the right side.

Since (x² - 16) / (x - 4) can be factored to be:  [ (x + 4)(x - 4) ] / (x - 4)  =  x + 4 providing that x ≠ 4.

So, the equation is almost true, but not exactly true.

How you approach this depend upon whether or not you use a calculator.

1)  The domain of the function is:  -∞ < x < ∞

2)  If you have to do this by hand, you may want to complete the square:

       d(x)  =  0.0125(x² - 80x + 1600) - 20

        d(x)  =  0.0125(x - 40)² - 20  

      This shows that the vertex occurs at (40, -20).

      Substituting 0 for x gives you the point (0, 0).

      Substituting 80 for x gives you the point (80, 0).

      The parabola passes through these points.

3)  The maximum depth of the dish occurs at the vertex; the depth will be 20 cm.

      This is the minimum of the function, not the maximum.

4)  Range:  -20 ≤ y < ∞

5)  Substituting 25 for x, d(x)  =  -17.1875.  

     Distance from vertex:  20 - 17.1875  =  2.8125; distance from top of dish:  17.1875 cm.

1/2, 1/3, 1/4, 1/5, 1/6, ...

2/3, 2/5, 2/7, 2/9, 2/11, ...

3/4, 3/5, 3/7, 3/8, 3/11, ...

4/5, 4/7, 4/9, 4/11, 4/13, ...

...,  ...,   ...,   ...,     ...,  ...