Algebra Archive: Questions from October 15, 2023
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5. Find the inverse of \( f \), if possible: \( f(x)=-125(x-7)^{3}-1 \) a) \( f^{-1}(x)=-\frac{1}{5} \sqrt[3]{x+1} \) b) \( f^{-1}(x)=\frac{1}{5} \sqrt[3]{x+1}+7 \) c) \( f^{-1}(x)=-\frac{1}{5} \sqrt[1 answer -
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Given integrand \[ f(x, y)=4 y \cos (y+x) \] and domain \[ R=\left\{(x, y) \mid 0 \leq x \leq \pi, 0 \leq y \leq \frac{4 \pi}{3}\right\}, \] calculate \( \iint_{R} f \mathrm{~d} A \).1 answer -
\( \frac{\left(6 x^{3}+16 x^{2}+17 x-6\right)}{(3 x-2)} \) \( \frac{\left(2 x^{4}-x^{3}+19 x^{2}+18 x+5\right)}{(2 x-5)} \) \( \frac{\left(4 x^{5}+6 x^{4}+5 x^{2}-x-10\right)}{\left(2 x^{2}+3\right)}1 answer -
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Solve the following system: \[ \left\{\begin{array}{l} 2 x-y>2 \\ 2 x-y \geq 0 \end{array}\right. \]1 answer -
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Complete the identity. 19) \( \cos (4 \theta)= \) ? A) \( \cos ^{3} \theta-3 \sin ^{2} \theta \cos \theta \) B) \( 4 \sin \theta \cos ^{3} \theta-4 \sin ^{3} \theta \cos \theta \) C) \( 3 \sin \theta-1 answer -
7. [10 pts] Find the following determinants: (b) \( \left|\begin{array}{ccc}\sin \theta \cos \phi & r \cos \theta \cos \phi & -r \sin \theta \sin \phi \\ \sin \theta \sin \phi & r \cos \theta \sin1 answer