CPhill

24 (1.09) = 26.16 mpg

Let's take this by parts

log3² + log 16^1/2 = lg 9 + log 4  = log (9*4)  = log(36)  .... and.....

[log 12 - log 2]   =  log (12/2)  = log (6)

So, the first fraction becomes.....log(36)/log(6) = log(6)² / log(6) = 2log(6)/log(6) = 2

And the numerator of the second fraction is.......

[2 - log 25 + 2log8] = ] 2 - log25 + log 8² ] = [2 - log25 + log64]

Notice, in terms of logs, that 2 can be written as log 100

So we have..

[log100- log25 + log 64] = [ log (100/25) + log64] = [log(4) + log (64)] =

log (4 * 64) = log(256) = log(16)² = 2log(16)

And the denominator is....

log ³√16 = log 16 ^(1/3) = (1/3) log 16

And the second fraction becomes...

[2log(16)] / [(1/3)log(16)]  = 2/(1/3) = 6

So...combining the result of the first fraction and the second fraction, we have

2 + 6  = 8

And there you go.......

The ln of 1 = 0

So, 0 - 7  = -7

We're just adding the x coordinates and the y coordinates to get the result...so we have

(10 + 11, 11 + (- 5))  =  (21, 6) = g + h

Think of it this way...If we are plotting the point (2,3), aren't we really just adding 2 and 3 to the coordinates of the origin, (0, 0) ???

Hope that helps......

There are 100cm in a meter...so, in a cubic meter, there are (100 cm)³

So we have.......

7.73 * (100cm)³  / .27cm  ≈ 28,629,629.6 cm² ≈ 2862.96 m²

-6q + 1.2 = -21.8 - 1.4q

Add 6q to each side

1.2 = 4.6q - 21.8

Add 21.8 to each side

23 = 4.6q    

Divide both sides by 4.6

5 = q

This is just a fancy way of asking..."What is the power (exponent) on "10" when we write this number using scientific notation??"

So we have......

1.178 x 10⁵   

So  "5"  is our answer !!!!

Call the number of tuna pies "x."

Then the number of chicken pies = x + 185

If he sold .6 of the chicken pies, then he had .4 of those left, and if he sold 1/2 = (.5) of the tuna pies he must have had .5 of those left.

So......

.4(x + 185) + .5(x) = 146

.9x + 74 = 146

.9x = 72

x = 72/.9  = 80   and that's the number of tuna pies he started with

So, he sold 1/2 of these = 40

And the number of chicken pies he sold is given by:

.6(80 + 185)  = 159

So the total pies sold =   40 + 159   = 199

This is an old problem from my calculus class days....let me see if I remember how to solve it.

Let x be the distance that the tip of his shadow is from the pole. Let xp be the distance the person is from the pole, and let xs be the length of his shadow.

So......x = xp + xs

We want to determine x' when the person is 6m from the pole.

Note that x'p  = 1m/s

Let's eliminate xs from the above equation.

Using similar triangles, we have

1.8/6 = xs/x = xs/(xp + xs)  so

1.8/6 = xs/(xp + xs)     (  note that 1.8/6   = .3   )

(.3) (xp + xs)  = xs

.3xp = .7xs

xs = (3/7)xp

Now.....substituting back into the original equation, we have

x = xp + (3/7)xp  = (10/7)xp    ....   So.....differentiating both sides, we have....

x' = (10/7)x'p  = (10/7)(1m/s)  = (10/7)m/s

And that's how fast the tip of the shadow is moving away from the pole.

The second part is easy.....we want to find x's when xp = 6

Again, we can use

x = xp + xs      and differentiating, we have

x' = x'p  + x's

But, we know x'p = 1m/s  and x'= (10/7)m/s.....so we have

(10/7)m/s  = 1m/s  + x's

So  x's  =  (3/7)m/s  ....   And that's how fast the length of the shadow is changing!!

Here's a diagram of the problem......

Yep.....that's what I got, too!!!

Good work !!!