Live practice

Translate every condition into an equation and retain exact values throughout the ellipse calculation.

The last line satisfies the original conditions and supplies every requested part.

Insert the conversion formula in the compound inequality.

For \((A\cup B)'\), shade only the region outside both circles; the same region represents \(A'\cap B'\). For \((A\cap B)'\), shade every part of the universal set except the overlap; the same region represents \(A'\cup B'\).

The matching shaded regions also provide a visual verification of De Morgan's laws.

(i) \[\begin{aligned}I &= \frac{6}{3}\\&= 2\end{aligned}\] A, so \[\begin{aligned}P_2 &= I^2R\\&= 8.00\end{aligned}\] W. (ii) 2 Ω has full 4 V, so \[\begin{aligned}P_2 &= \frac{V^2}{R}\\&= \frac{16}{2}\\&= 8.00\end{aligned}\] W. Powers are equal.

Define the sample space and count each favourable outcome once.

The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.

Apply the definition or the stated differentiation rules term by term.

Substitution into the original expression verifies the stated domain and final value.

Translate every condition into an equation and retain exact values throughout the ellipse calculation.

The last line satisfies the original conditions and supplies every requested part.

Translate every condition into an equation and retain exact values throughout the straight-line calculation.

The last line satisfies the original conditions and supplies every requested part.

Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.

The displayed substitutions cover every requested part and verify the result against the original data.

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.