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New Zealand Homework Resources

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New Zealand
1 The displacement of an oscillating mechanism (in \( m \) ) at any time ( \( t \) seconds) is given by \( y=-30 \cos (3 \pi t-0.35) \).
Calculus Oct 21, 2024
1.2 The angle of elevation of the top of a building, sighted from a point 150 m horizontally from its base, is \( 30^{\circ} \). What is the height of the building? Round your answer to the nearest 10 cm .
Trigonometry Oct 21, 2024
If a body is said to move according to the formula \( s=500 t-24 t^{2} \) where \( s \) is the distance in metres travelled in time \( t \) seconds, find: 5.1 the distance from the origin at time \( t=0 \) and after 3 seconds.
Physics Oct 21, 2024
If \( y=f(x)=4 x^{3}-3 x^{2}+1 x+9 \), find \( f^{\prime}(x) \)
Calculus Oct 21, 2024
3. There is a firework show. You see the firework for several seconds before you hear the explosion. Knowing light travels at \( 3 \times 10^{8} \mathrm{~ms}^{-1} \), explain why is this so.
Physics Oct 21, 2024
A teacher suspects that a bottle of butan-1-ol has become accidentally contaminated with some butanal. Describe a chemical test to confirm this suspicion. Your answer should include: - the reagent and reaction conditions - observations - structural formulae of any organic product(s).
Chemistry Oct 21, 2024
6) \( \left\{\begin{array}{l}x=2 y-4 \\ x-y=0\end{array}\right. \)
Algebra Oct 21, 2024
(5) \( \left\{\begin{array}{l}x=y-3 \\ x+4 y=7\end{array}\right. \)
Algebra Oct 21, 2024
2) Decrease \( \$ 840 \) by \( 15 \% \)
Arithmetic Oct 21, 2024
Increase \( \$ 1500 \) by 35\%
Economics Oct 21, 2024
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