CPhill

Subtract x from both sides and add z to both sides.....this gives

3x = z      divide by 3 on both sides

x = z/3

No...the graph of g(x) is continous. The graph of f(x) will look similar to g(x), except there will be a "hole" at x = 4. The reason for this is that "4" makes the denominator of f(x) = 0......and that's not allowed.....

I'm not sure what you mean by "standard" form

5,183,700  is in "standard" form (as far as I know)

In scientific notation it would be

5.1837 x 10⁶      (this would be the "standard" engineering form, as well)

Maybe there is some other "standard" form of which I'm unaware.......

I approached this one a little differently from Melody, but I think we end up with the same solution.

Like her, since x= 2 and x=7 are "zeroes," the x coordinate (because of symmetry) must be at x = 4.5.

And the vertex is given by (4.5, 25)...so.....in "vertex" form, we have...

y = a(x - 4.5)^2 + 25     and we need to find "a"

And we know that when x = 7, y = 0....so we have

0 = a(7 - 4.5)^2 + 25    subtract 25 from both sides

-25 = a(6.25)     divide both sides by 6.25

a = -4       and this should be correct, since the parabola turns "downward"

So, our function is

y = -4(x - 4.5)^2 + 25

The slant height of the cone is the hypoteneuse of a 7 - 24 - 25 right triangle

The "formula" for a cone's surface area is   SA = pi(R² + R*L)  where R is the radius and L is the slant height

So we have

Sa = pi[7²+(7)(25)] = pi [49 + 175] = 224pi

2.5 = 25/10      "of" means "multiply...so...

1/4 x 25/10  =  25/40 = 5/8 lbs.

Ella can actually type faster than a jiffy.......but only if she's in a jam and kneads more bread.

What Alan describes is known as the "method of exhaustion" employed by Atchimedes. He might have been close to discovering Calculus centuries before it was actually discovered. Unfortunately, he was killed by a Roman soldier. But as the saying goes, 'The brutes win in the short term, but the brains prevail in the long term." And Archimedes was one of the brainiest.

7/16 = 0.4375

67.5% = .675

30.5% = .305

.675/.305 = about 2.213