CPhill

OK...we have a parabola here, and where it touches the roadway, we can just call that point the "origin," i.e., (0,0)

So...we have this equation 

y = ax²

And we know that when x= 2100, y = 500   .... and we need to solve for "a"

So we have

500 = a (2100)²

a = 500 / (2100)²  = 1 / 8820

So we have , when x = 1000

y = (1 / 8820) (1000)²  ≈ 113 ft.

The "formula" is .......  (1/3) * (Area of the base)  * (Height)

The height is easy.

The area of the base is a little more complicated.

It's given by (√(3)/4)(s²), where s is the side length of the pyramid.

So we have  (1/3) * (√(3)/4)(18²) * (4) = (1/√(3))(324) = (324 / √(3)) ≈ 187.06 cubic units

Just enter it like this........ (2 + 3/4)

Remember that the exponent on the thing on the left is only on "x," not on the 2. So we have...

2/x²   =  1/(2x²)     ???

And this isn't true...

Converting .0005% to a decimal - .0005 -  we have

$${\mathtt{0.000\: \!5}}{\mathtt{\,\times\,}}{\mathtt{234.11}} = {\mathtt{0.117\: \!055}}$$

Yep

The volume of a spere is given by

V = (4/3)  pi (r) ³ 

And...if the diameter is 24 cm, then the radius = 12 cm

So we have

V = (4/3) * pi * (12)³   =

$$\left({\frac{{\mathtt{4}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\left({\mathtt{12}}\right)}^{{\mathtt{3}}} = {\mathtt{7\,238.229\: \!473\: \!870\: \!883\: \!621\: \!4}}$$

And that answer is in cubic centimeters.....

We have .....    Distance / Time = Rate

So......

10 miles / 2 hrs.   =   5 miles / hr =  5 miles per hour

Let's convert each mixed number to an improper fraction ....   we have....

25/3 * 21/5       and we can "cross-cancel" the 25 and 5  and the 21 and 3 giving

5 * 7 = 35    

Hint: It always makes the work of multiplying fractions easier if we can "cancel" before we multiply!!

I assume you have

(2/3)x - 5 + 2x + 6 = 1    Combining like terms, we get

(8/3)x +1 = 1  subtract 1 from each side

(8/3)x = 0   Multiply both sides by (3/8) and we get

x = 0