CPhill

So I assume you're here.........

log₅ X  ≤ -1

This says that 

X  ≤  5^-1

X  ≤ 1/5

(1/2)x + (4/5)x =2   simplify

5/10x + 8/10x = 2

13/10x  = 2    multiply both sides by 10/13

x = 20/13

Nice pic, Melody......you have something in common with Picasso.......you're both into "cubism"....

We need to find the radius.....

The volume is given by

Vcylinder = (4/3) pi r^(3)   ....so we have

3600pi^3  = (4/3)pi r^3      .....multiply by (3/4) and divide by pi

(3/4)3600pi^2  = r^3

2700pi^2  = r^3       take the cube root of each side

r = 29.87

To find the surface area (inckuding the top amd bottom), we have

Sa = 2pi (r * h + r^2)     where r is the radius and h is the height

Sa = 2pi( 29.87 * 16 + 29.87^2)  =  8608.82 cubic inches

What is the "net" of the pyramid???

Can you provide a pic of this, Melody??

The domain of this function is all x's except x =3......that would make the denominator 0

This function has a horizontal asymptote at y = 1

Thus, the range is (-∞, 1) u (1,∞)

The first one asks..... to what power do we raise .6 to obtain .36.....the answer is 2

We can evalute the other two by using the "change of base" rule

It says that  log_a b   =  log b/ log a

So the second one is

log₈ .0039  =  log.0039 / log 8  =    about  -2.67

I'll let you do the last one.....

We have

80 = ab^5  →    a = 80/b^5

And

64 = ab^7  →  a = 64/b^7

Setting  the "a's" equal, we have

80/b^5 = 64/b^7

b^2 = 64/80  = 4/5  = .8

b = √.8 = .894

And solving for "a" we have

80 = a(.894)^5

80 = a(.571)

a = 80/.571 = 140.1

So...our function is

f(x) = 140.1 (.894)^x

The area will increase as the square of the scale factor

So

140 x (1.5) ^2 =

140 x 2.25 =

315 in ^2

P(1600) = P(x) = 70√1600 − 0.5(1600) − 500 =

70*40 - 800 - 500 =

2800 - 800 - 500 =

2300 - 500 =

1800

P(4900)  is evaluted in a similar manner