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1000 = 10^3

So

7.5 x 10^5 x 10^3 =  

7.5 x 10^8 miles

Area of the base x height = volume  ......so....

40 x 10  = 400 cm^3   {assuming that the "10" is in cm  ...}

Let Θ be the angle of elevation.....so we have

tan^-1(25.5 / 34) = Θ =  about 36.87°

We have

sin(45) = d / 6    where  d is the distance from the wall

Rearrange

d = 6sin(45)  =  [6 / √2 ] ft  = about 4.24 ft

y = 2 is just a horizontal line at y = 2

y = -1/2 x    pick two x values - I'll pick 0 and 2

So, when x = 0 , y = 0

And when x = 2, y = -1

So we have the points (0, 0) and (2, -1)......draw a line through both and there's your graph

x - y = 4

This is similar to the last one ...  when  x = 0, y = -4 and  when y = 0, x = 4.

So the points  (0, -4) and ( 4, 0).......draw a line between the two and there's your graph.

We have

sin30 = 1.5 / h    where h is the span of 1/2 of the roof

h = 1.5/sin 30  =  2m

We need to multiply this by 2 to get the span  = 4 m

We can find the longer leg - call it L -  with the Law of Sines

L/sine 52 = 140 / sine 90

L  =140 sine(52) = 110.32 m

And the other leg is

140sin(38) = 86.19m

So the perimeter is

140 + 110.32 + 86.19 = 336.51 m

We have

1 = 100e^(-.18t) divide both sides by 100

.01 = e^(-.18t)    take the log of both sides

ln . 01 =ln e^(-.18t)    and since ln e = 1, we can write

ln .01  = (-.18t)       divide both sides by -.18

ln .01 / (-.18)  = t = about 25.58 hrs.

I think this is supposed to be  .... (y+3)/y = 77/56

Cross-multiply

56(y+ 3)  = 77y    simplify

56y + 168  = 77y     subtract 56y from both sides

168 = 21y    divide by 21 on both sides

8 = y

She makes 60 cents selling each cupcake.

So.....the number sold times the profit on each gives the total profit.

And we have....

.60c ≥ $30   where "c" is the number sold

CPhill, when the 2 and the 1 are in the first two positions, you only have 8 numbers available for the third position and 7 for the fourth, (if the numbers are to be unique, you can't use the 2 or 1 again).

......................................................................................................................

length of rope: 16 ft

length of one side of the square: x

area of square: A_s(x) = x²

length of the "square piece": 4x

length of "circle piece": 16 - 4x

We know that: C = 2 * pi * r   =>    r = C/(2 * pi)

Area of cicle: Ac = pi * r² = pi * [C/(2 * pi)]² = pi * (C²/4 * pi²)

Ac = C²/4pi = (16 - 4x)²/4pi = 4(4 - x)²/4pi

Ac = (4 - x)²/pi

Ac(x) = (4 - x)²/pi

The answer is 3.6 i believe.

twice the sum of a number and 3 is equal to three times the difference of the number and 6. find the number

The number is x:

2(x+3) = 3(x-6)

2x + 6 = 3x -18

x = 18 + 6

x = 24

Pi is always the same number. It is a mathematical constant with the approximate value 3.14. The definition of pi is the ration of a circle's circumference to its diameter. 

It can be done with seven weights, and I would guess that this is the optimum, but apart from it being obvious ????? I don't know how to prove it.

As Heureka points out, weights of 1 and 3 allow us to get to 4. We now need to cater for 5 and this can be done (optimally) with a weight of 9 since the 4 can be used for subtraction. Also by subtraction we can get 6,7 and 8. Moving on from 9, the 1 and 3 allow to get to 13, and the next weight we need to worry about is 14.

Using the subtraction method again, we can get 14 using a weight of 27, (27 in one pan and 1+3+9=13 in the other), and since all weights from 1 to 13 are already available, the other weights from 15 to 26 can be formed. That takes us upto 40, 1+3+9+27=40.

To get 41 a weight of 81 wiil do, (81 in one pan and 40 in the other), and the intervening weights will be covered also.

It seems fairly clear now that we are going up through the powers of 3, in which case in addition to 1, 3, 9, a 27 and 81, we need 243 and 729.

Actually,  I think Melody is a teacher.

yes now its very clear .. 

thank you =) 

Yes, that's correct.

But you now have to shift your result back in terms of x.