Prostaglandins in seminal fluid stimulate smooth muscle contractions in the female reproductive tract, aiding sperm movement toward the egg. Oxytocin is a hormone; androgens/testosterone are male sex hormones.

For the parabola $y^2=4\sqrt{5}x$: tangent in slope form is $y=mx+\frac{\sqrt{5}}{m}$.

For the circle $x^2+y^2=5/2$ (radius $\sqrt{5/2}$): distance from origin to tangent $= \frac{|\sqrt{5}/m|}{\sqrt{1+m^2}}=\sqrt{5/2}$

$\frac{5/m^2}{1+m^2}=\frac{5}{2}\Rightarrow\frac{1}{m^2(1+m^2)}=\frac{1}{2}\Rightarrow m^2+m^4=2\Rightarrow m^4+m^2-2=0$

Hmm: $m^4+m^2-2=(m^2+2)(m^2-1)=0$, so $m=\pm1$. Statement II gives $m^4-3m^2+2=0=(m^2-1)(m^2-2)=0$, so $m=\pm1,\pm\sqrt{2}$ — this is different. But $m=\pm1$ works for both. At $m=1$: tangent is $y=x+\sqrt{5}$ ✓. Statement I is true; Statement II is false (wrong equation).

Rate law: Rate = k[A]^1 [B]^2.

• $P_{1} = 35 \text{ psi}$, $T_{1} = 27 + 273 = 300 \text{ K}$
• $P_{2} = 40 \text{ psi}$, $T_{2} = ?$
• $35/300 = 40/T_{2}$
• $T_{2} = (40 \times 300) / 35 \approx 342.8 \text{ K}$
• Converting to Celsius: $342.8 - 273 = 69.8^{\circ}\text{C} \approx 70^{\circ}\text{C}$

Genotype refers to the actual alleles present (e.g., BB, Bb, bb). Phenotype is the physical expression. Karyotype is the chromosome set.