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How many 176 Ω resistors in parallel draw total 5 A from 220 V?
Required equivalent \[\begin{aligned}R &= \frac{220}{5}\\&= 44\end{aligned}\] Ω. For n equal parallel resistors, \(R_{eq}=\frac{176}{n}\); hence \[\begin{aligned}n &= \frac{176}{44}\\&= 4\end{aligned}\].
4 resistors.
Differentiate transport by xylem and by phloem.
Xylem transports water and minerals, mainly upward, through dead vessels/tracheids; transpiration pull supplies most energy. Phloem transports organic food from sources to sinks in either direction through living sieve tubes and companion cells; loading and unloading require ATP and drive pressure flow.
Xylem: water/minerals, mainly upward, mostly passive. Phloem: food, source-to-sink in either direction, energy-dependent.
Define a neutralisation reaction and support the definition with two balanced examples.
Neutralisation is the reaction of an acid with a base to form salt and water. The essential ionic change is:
Examples:
Three letters are inserted randomly into three addressed envelopes. Find the probability that at least one reaches its proper envelope.
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 \(36x^2+4y^2=144\Rightarrow\frac{x^2}{4}+\frac{y^2}{36}=1\), 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.
The two geometric progressions are a, ar, …, arⁿ⁻¹ and A, AR, …, ARⁿ⁻¹. Prove that their corresponding products form a geometric progression and state its ratio.
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.
Form a seven-member committee from nine boys and four girls. Count committees with (i) exactly three girls(ii) at least three girls(iii) at most three girls.
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 8: 2 (x – 1) < x + 5, 3 (x + 2) > 2 – x
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.
Prove \(\cos(\frac\pi4-x)\cos(\frac\pi4-y)-\sin(\frac\pi4-x)\sin(\frac\pi4-y)=\sin(x+y)\).
Proceed from the given expression and keep every transformation explicit.
The last line satisfies the required domain and establishes the result.
For \(A=\{1,2,3,4\}\), \(B=\{1,5,9,11,15,16\}\), and \(f=\{(1,5),(2,9),(3,1),(4,5),(2,11)\}\), decide whether \(f\) is (i) a relation from \(A\) to \(B\)(ii) a function from \(A\) to \(B\).
Every first coordinate lies in \(A\) and every second coordinate in \(B\), so \(f\subset A\times B\) and is a relation. It is not a function because input 2 has two distinct images, 9 and 11.
(i) Yes, a relation. (ii) No, not a function.