Teacher Emily wrote the following operations on the board. Simplify the operations a)g b)

Pointi ni $A(x_1, y_1) = (0,0)$ na $B(x_2, y_2) = (4,3)$.
Formula ya gradient ni:

Gradient ya mstari unaounganisha pointi A na B ni $\boxed{\frac{3}{4}}$.

:
Ili kurahisisha usemi huu, tutatumia sheria za vipeo (exponents) na kurahisisha namba.

Tumia sheria $a^m \times a^n = a^{m+n}$:

Tumia sheria $\frac{a^m}{a^n} = a^{m-n}$:

Usemi uliorahisishwa ni $\boxed{12x^{11}y^5}$.

:
Ili kukokotoa eneo lililoangaziwa na spotlight, tunahitaji kutumia formula ya eneo la sekta ya duara.

Kipenyo (diameter) $D = 10$ m, hivyo radius $r = \frac{D}{2} = \frac{10}{2} = 5$ m.
Angle ya sekta $\theta = 30^\circ$.

Eneo la sekta $= \frac{\theta}{360^\circ} \times \pi r^2$

Eneo lililoangaziwa na spotlight ni takriban $\boxed{6.54 \text{ m}^2}$ (kwa desimali mbili).