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Given that abc = -37 + 36i; b = -2 + 3i; c = 1 + 2i, what is a?

Substituting the given values for b and c into the equation for abc , a (-2 + 3i)(1 + 2i) = -37 + 36i Multiplying out the terms in brackets, a (-2 - 4i + 3i - 6) = -37 + 36i Collecting like terms and multipl...
AS
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How can I distinguish when to use the verbs "ser" or "estar"?

Both these verbs are translates as "to be", however they are used in different circumstances. the verb "ser" is used to express permanent states of being, such as characteristics of ident...
HC
Answered by Hannah C. • Spanish tutor
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Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

y = e 2x (x 2 +1) 5/2 The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation: y = uv where u = e 2x and v = (x 2 +1) 5/2 . We now diffe...
AS
Answered by Adam S. • Maths tutor
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Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).

De Moivre's Theorem states that if z = cos(q)+isin(q), then z n = (cos(q)+isin(q)) n = cos(nq)+isin(nq) But then z -n = cos(-nq)+isin(-nq). Now, cos(-p)=cos(p), as cosine is a symmetric (even) function, and ...
DA
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Two lines have equations r = (1,4,1)+s(-1,2,2) and r = (2,8,2)+t(1,3,5). Show that these lines are skew.

Recall that for two lines to be skew they must satisfy two conditions: 1) They must not be parallel. 2) They must not intersect. We shall check each condition individually. Condition 1 The general vector equ...
DA
Answered by Dorian A. • Maths tutor
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