M varies jointly as N and inversely as the square root of R. If M = 35 when N = 7 and R = 9, find the equation connecting M, N and R. Find R when M = 42 and N = 15. Find the percentage change in M whe

M varies jointly as N, so $M \propto N$.
M varies inversely as the square root of R, so $M \propto \frac{1}{\sqrt{R}}$.
Combining these, we get:

Multiply both sides by 3:

Divide by 7:

The equation connecting M, N, and R is $\boxed{M = \frac{15N}{\sqrt{R}}}$.

Simplify the fraction:

The value of R is $\boxed{\frac{5625}{196}}$.

Let the original values be $N_1$ and $R_1$. The original M is $M_1 = \frac{15N_1}{\sqrt{R_1}}$.
N is increased by 25%, so the new N, $N_2$, is:

R is reduced by 36%, so the new R, $R_2$, is:

Substitute $N_2 = 1.25N_1$ and $R_2 = 0.64R_1$:

Rearrange the terms to relate $M_2$ to $M_1$:

Since $M_1 = \frac{15N_1}{\sqrt{R_1}}$:

Calculate the fraction:

So, $M_2 = 1.5625 M_1$.

Percentage change $= \frac{M_2 - M_1}{M_1} \times 100\%$
Percentage change $= \frac{1.5625 M_1 - M_1}{M_1} \times 100\%$
Percentage change $= (1.5625 - 1) \times 100\%$
Percentage change $= 0.5625 \times 100\%$
Percentage change $= 56.25\%$
The percentage change in M is an increase of $\boxed{56.25\%}$.