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How many 220 V, 10 W lamps can operate in parallel if total allowed current is 5 A?
Maximum total power \[\begin{aligned}P &= VI\\&= 220(5)\\&= 1100\end{aligned}\] W. Number \(=\frac{1100}{10}=110\).
110 lamps.
Of five listed employees, choose a spokesperson at random. Find the probability that the person is male or older than 35.
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.
For the ellipse \(4x^2+9y^2=36\Rightarrow\frac{x^2}{9}+\frac{y^2}{4}=1\), 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 line through (−2,3) parallel to 3x−4y+2=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.
If the pth, qth and rth terms of a geometric progression are a, b and c, prove aᑫ⁻ʳbʳ⁻ᵖcᵖ⁻ᑫ=1.
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.
Complete every requested part of miscellaneous exercise, question 10: 5 (2x – 7) – 3 (2x + 3) ≤ 0 , 2x + 19 ≤ 6x + 47 .
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.
Prove \(\dfrac{\cos(\pi+x)\cos(-x)}{\sin(\pi-x)\cos(\frac\pi2+x)}=\cot^2x\) wherever both sides are defined.
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.
Let \(A=\{9,10,11,12,13\}\) and \(f(n)\) be the greatest prime factor of \(n\). Find the range.
\[\begin{aligned}9 &= 3^2\Rightarrow f(9)\\&= 3\end{aligned}\]; \[\begin{aligned}10 &= 2\cdot5\Rightarrow f(10)\\&= 5\end{aligned}\]; \(f(11)=11\); \[\begin{aligned}12 &= 2^2\cdot3\Rightarrow f(12)\\&= 3\end{aligned}\]; \(f(13)=13\). Distinct images form the range.
\(\{3,5,11,13\}\).
In CH₂=CH–CH₂–CH₂–C≡CH, identify the hybrid orbitals forming the C₂–C₃ bond.
C₂ is part of C=C and is sp²; C₃ is saturated and is sp³. Their sigma bond forms by head-on overlap.
sp²–sp³ overlap.
Identify which of the followings are Lewis acids? H2O, BF3, H+, and NH4+
A Lewis acid accepts an electron pair. BF₃ has an incomplete octet, H⁺ accepts a pair directly, and NH₄⁺ can donate H⁺; water normally donates a lone pair and acts as a Lewis base.
BF₃, H⁺ and NH₄⁺ are Lewis acids.