CPhill

Hey, Mellie.....good to see you  !!!!

a. 4f(x)  = 4 ( l 4 - 3x^2 l )   =   4 l 4 - 3x^2 l

b. 2g (x - 3)  =   2 [ 3(4)^x-3 ]  = 6(4)^x-3

c. h(x + 3) + 4   =    log₃ ( [x + 3] - 5) + 4   = log₃ (x - 2) + 4

C.     h(x)  =   f(x) * g(x) /   x   =   

[ x^4 - 2x^2 ] * [ x^5 + x ] / [2x ]  =

x^2 * [ x^2 -2] * x  * [ x^4 + 1 ]  / [ 2x] =

x^2 * [ x^2 - 2] * [ x^4 + 1 ] / 2  =

[ x^4 - 2x^2 ] [ x^4 + 1 ] / 2 =

[x^8 - 2x^6 + x^4 - 2x^2] /2.....notice that this is an even function because replacing x  with  -x   gives back the same function

Also.....the graph is symmetric with the y axis which is a characteristic of even  functions...here"s the graph :

https://www.desmos.com/calculator/setikvzes3

x/60=((3950-x)/45)+8.1

Multiply through by the common denominator of 45, 60  =  180

So we have

3x  = 4(3950 - x)  + 1458     simplify

3x  =  15800 -  4x + 1458     add 4x to both sides and simplify the right side

7x  = 17528    divide both sides by 7

x ≈ 2465.43

I'm unsure of your exact question.....did you leave something out  ???

(b) (c) (d)  on the first part...these are all cones....

Volume of cone  = (1/3)( pi) (radius of base)^2 * height of cone

Here's  (b)......see if you can do  (c)  and (d)...if not...let me know

Volume  = (1/3) (pi) (11^2) ( 16)   ≈  2027.37 in^3

For  (b)  (c) (d)  on the second part

All of these are cylinders

Volume of  cylinder =  pi * (base radius)^2 * (cylinder height)

So

(b)  [ the radius  = 22/ 2  = 11 ]

Volume =   pi * (11^2) ( 9)    = 3421.19 ft^3

See if you can  do (c)  and (d), based on this.....

10 )  21k^3  + 18k^2  + 56k + 48

GCF  of 21k^3  and 18k^2 = 3k^2

GCF of 56k and 48  = 8

So we have

3k^2 ( 7k + 6) + 8 (7k + 6)  =

(7k + 6) (3k^2 + 8)

11) 42x^3  + 49x^2 - 36x - 42

GCF of 42x^3 and 49x^2  = 7x^2

GCF of  -36x and -42  = -6

So we have

7x^2 ( 6x + 7)  - 6(6x +7)  =

(6x + 7)(7x^2 - 6 )

12)  p^3 + 6p^2 - 3p - 18

GCF of  p^3  and 6p^2 =  p^2

GCF of -3p  and  - 18  = -3

So we have

p^2 ( p + 6)  - 3(p + 6)  =

(p + 6) ( p^2 - 3 )

x^2+bx +c   ...  b  = c + 1  ....so....

x^2 + (c + 1)x + c

If this has one real root, the discriminant  = 0

So

(c + 1)^2  - 4(1)(c)  = 0  simplify

c^2 + 2c + 1  - 4c   = 0

c^2 - 2c + 1  = 0    this factors as

(c - 1)^2  = 0      take the square root

c - 1  = 0    ⇒   c  =  1

We can divide the parallelogram into 2 equal triangles by drawing a diagonal

The  area  is  2 (1/2) (6 * 8) / √2  = 48 / √2  =  24√2 ≈   33.94 units^2

Note....There are  ≈ 39.37 inches to one meter

So we have

4000   =  2 * pi^2 * (.59 * 39.37) * r^2

( 4000 / [ 2 * pi^2 * (.59 * 39.37) ] )  = r^2    take the square root of both sides

2.95  in ≈  r

And there are ≈ 2.54 cm to  one in

So....radius  ≈  2.54 * 2.95   ≈  7.493 cm