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Connect three 6 Ω resistors to obtain (i) 9 Ω(ii) 4 Ω.
(i) Put two in parallel to obtain 3 Ω, then in series with the third: 9 Ω. (ii) Put two in series to obtain 12 Ω, then parallel with the third: \(12\parallel6=4\) Ω.
(i) (6∥6)+6(ii) (6+6)∥6.
Compare alveoli and nephrons in
Both occur in very large numbers, have thin walls, large surface areas and intimate capillary networks. These features allow rapid selective exchange.
Alveoli exchange gases by diffusion: oxygen enters blood and carbon dioxide leaves. Nephrons ultrafilter blood under pressure and then selectively reabsorb useful substances and water while secreting wastes, thereby forming urine and regulating composition of blood.
State two important uses each of washing soda and baking soda.
Washing soda, \(\ce{Na2CO3.10H2O}\):
Baking soda, \(\ce{NaHCO3}\):
Washing soda: water softening and industry/cleaning. Baking soda: baking powder and antacid/fire extinguisher.
Given P(A)=0.54, P(B)=0.69 and P(A∩B)=0.35, find four stated union, complement and difference probabilities.
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.
Find the derivative of f(x)=99x at x=100.
Apply the definition or the stated differentiation rules term by term.
Substitution into the original expression verifies the stated domain and final value.
For the ellipse \(16x^2+y^2=16\Rightarrow x^2+\frac{y^2}{16}=1\), determine its foci, vertices, axis lengths, eccentricity, and latus-rectum length.
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.
Find the separations of (i) 15x+8y−34=0 and 15x+8y+31=0(ii) l(x+y)+p=0 and l(x+y)−r=0.
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.
Find four geometric-progression terms such that the third exceeds the first by 9 and the second exceeds the fourth by 18.
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.
All distinct arrangements of EXAMINATION are placed in dictionary order. Count those appearing before the first arrangement beginning with E.
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.
Complete every requested part of miscellaneous exercise, question 9: 3x – 7 > 2 (x – 6) , 6 – x > 11 – 2x
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.