CPhill

1000x^3  + 27       can be factored as a sum of cubes thusly :

(10x + 3) ( 100x^2  - 30x + 9) 

So

a  = 0 , b  = 10, c = 3, d = 100, e = -30  and f = 9

So

(0)^2 + 10^2  + 3^2  + 100^2 + (-30)^2 + 9^2  =  11090

CORRECTED ANSWER>>>>Thanks, Alan for catching my error  !!!

We have six interest periods within a year....so we have  5 * 6  =  30 interest compoundings

So....after 5 years we have

24000(1.01)^(5 * 6)   =  24000(1.01)^30 ≈  $32,348

3 + 2l 9 + xl  ≤  -1      subtract  3 from both sides

2 l 9 + x l  ≤  -4          divide both sides by 2

l 9 + x l  ≤   -2 

Since the result of an absolte value is either  positive or zero, then the result of the absolute value on the left cannot be ≤ -2

-1 + 4 l 6x l   >  -97     add 1 to both sides

4 l 6x l >  -96                divide both sides by 4

l 6x l  >   -24

For the same reason as the first......the minimum value of  the absolute value for any real number x will  = 0

And 0  > -24    is always true

2)

The lead term  is   -2x^4

Sign on lead term   =  negative

Power on lead term  =  even

Based on my previous answer, do you you see the correct answers  ???

First one....the first term, 4x^11 will determine the limits in both directions

When x is some large negative, i.e., x approaches negative infinity, 4(-x)^11  = -4x^11 and the function approaches negative infinity

When x is some large positive, i.e., x approaches positive infinity, 4x^11  approaches positive infinity

So...both statements are False

Here's an easy way to remember the end behavior

Sign  on Lead Term            Power  on lead term         Behavior at both ends           

         +                                       even                          up  [ approaches infinity on both ends]

         +                                       odd                             down on the left, up on the right 

         -                                        even                            down on both sides

         -                                        odd                             up on the left, down on the right

To see this.....look at the following graphs  of    

4x^2 ,  https://www.desmos.com/calculator/c9hunr1imw

4x^3,  https://www.desmos.com/calculator/vvd4oqehol

-4x^2, https://www.desmos.com/calculator/p7b3iqjxpk

-4x^3, https://www.desmos.com/calculator/dyayuiza6y

Thanks, CU  and Tom  !!!

I get four sets

{5  1   9}

{5  2   8}

{5  3   7}

{5  4   6}

{5, 5, 5}  not possible

(5, 6, 4} repeat set

(5, 7, 3}  repeat set

(5, 8, 2} repeat set

(5, 9 , 1} repeat set

BTW...I'm not an expert on sig figs....but.....here's a site that might help :

https://people.uwec.edu/carneymj/Adobe%20handouts/Significant%20Figures.pdf

In multiplication...the number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation.

70.50   = 4 sig figs

10.3   =  3 sig figs

3.00  =  3 sig figs

F  =  mv^2 / r     =    [70.50 kg ] * [3.00 m/s]^2  / [10.3m]   =  61.6  N

3.15  =  3 sig figs

2.006  = 4 sig figs

3.15  * 2.006  = 6.3189  =  6.32 m^2

The trick is to try to get the bases the same

Note  64  =  4^3

So   we have

(4^3)^(x + 7)  =  (4)^(5x - 3)

4^(3x + 21)  = (4)^(5x - 3)       we  have the bases alike.....solve for the exponents

3x + 21  = 5x  - 3    

24  =  2x

x  = 12