We can use the subtraction property of logs to expand the right side of the equation:

log(1/H*) = log(1) - log(H*)

No matter what base we’re using, log(1) = 0, so this simplifies to -log(H*). We’re also given a pH value of 3.6, so we can substitute this value into the original equation along with -log(H*) to get

3.6 = -log(H*)

Multiplying by -1 on both sides:

-3.6 = log(H*)

And rewriting in exponential form:

H* = 10^(-3.6) = 0.0003 (rounded to the nearest ten thousandth)

6 0

2 years ago

For a cone, if the radius was quadrupled and the slant height was reduced to 1/6 of its original size what would be the formula

Paladinen [302]

Let $r$ be the radius of the cone's base and $\ell$ the slant height.

The surface area of a cone is

$A=\pi r^2+\pi r\ell$

If the radius is quadrupled ( $r\to4r$ ) and the slant height scaled by a factor of $\dfrac16$ , then the new area is

$A=\pi(4r)^2+\pi (4r)\left(\dfrac\ell6\right)$
$A=16\pi r^2+\dfrac23\pi r\ell$

7 0

3 years ago