Live practice

Substitute the two complex numbers and simplify numerator and denominator.

For any integers \(a,b\), closure under subtraction gives \(a-b\in\mathbb Z\). Thus every ordered pair in \(\mathbb Z\times\mathbb Z\) belongs to \(R\).

A universal set must contain every object under discussion. For either collection, the set of all triangles in the plane is suitable. If both are considered together, the same universal set contains both as subsets.

Conventional current is opposite electron motion, towards the back wall. Using Fleming's left-hand rule with force to the right gives magnetic field vertically upward.

The element is a high-resistance alloy designed to become very hot. The cord is thick copper with very low resistance. Since heat rate is \(I^2R\) and the same current passes through both, far more heat is produced in the element; the cord remains comparatively cool.

A plane mirror always gives an upright image. A convex mirror also always gives a virtual upright image. A concave mirror gives an inverted real image for objects beyond F.

The central pistil contains stigma, style and ovary with ovules. Stamens consist of anthers and filaments around it. Petals attract pollinators; sepals protect the bud. All parts arise from the receptacle attached to the flower stalk.

Dendrites receive signals and conduct them to the cell body. An impulse travels along the axon, which may be insulated by myelin, to terminal branches. Neurotransmitter released at the terminals carries the message across a synapse to another neuron, muscle or gland.

A nephron begins with a cup-shaped Bowman's capsule surrounding a glomerulus. Blood pressure ultrafilters water and small solutes into the capsule while cells and plasma proteins remain in blood. The filtrate passes through the proximal tubule, loop of Henle and distal tubule; useful glucose, amino acids, ions and most water are selectively reabsorbed into capillaries. Additional ions and wastes are secreted into the tubule. The collecting duct reabsorbs water according to the body's needs, and the remaining urine enters the renal pelvis and ureter.

A homologous series is a family of organic compounds with the same functional group and general formula, similar chemical properties and a gradual change in physical properties. Consecutive members differ by \(\ce{-CH2-}\), or 14 u.

For alkanes, \(\ce{C_nH_{2n+2}}\): methane \(\ce{CH4}\), ethane \(\ce{C2H6}\), propane \(\ce{C3H8}\).