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Home Question Bank Other Archive 2025 January 07

Other Questions from Jan 07,2025

Browse the Other Q&A Archive for Jan 07,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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12. Find the square roots of the complex number , leaving your answer in rectangular form 11. Find the square roots of the complex number , leaving your answer in rectangular form. (Hint: Solve , where and and are real numbers.) Suppose the firm uses two inputs to produce its output: capital (K) and labor (L). The firm's production function is . Suppose that in the short run capital (K) is fixed at 27. If the wage is and the rental rate on capital is , 1. Does the production function display decreasing, constant, or increasing returns to scale? Explain 2. What is the short run total cost equation (function with )? 3. What is the level of output (q) that minimizes the total cost? Suppose the firm uses two inputs to produce its output: capital (K) and labor (L). The firm's production function is . Suppose that in the short run capital (K) is fixed at 27. If the wage is and the rental rate on capital is , 1. Does the production function display decreasing, constant, or increasing returns to scale? Explain 2. What is the short run total cost equation (function with ? 3. What is the level of output (q) that minimizes the total cost? - Calculate the components and the magnitude of the vectors and . - Determine the unit vectors carried by the veetors and . - calculate the dot product and cross product of vectors et . Fxercice 08: we consider three vectors: , 1- Show that the vectors and are orthogonal. 2- Détermine and so that the vectors and are parallel. 3- Determine the direction (cosines) of the vector . 4. We suppose that and . Calculate the area of the parallelogram constructed by the vectors and . 10. If and , find one element in set B . II. If all even numbers less than 10 and (all multiples of 3 less than 10, list the elements in A and B and draw a enn diagram showing the relationship B. 12. If \{all positive numbers less than 8 and all multiples of 3 less than 10, list the elenents in the sets (i) (ii) . e) Given that Determine : (i) the rank of A (ii) the null space of A (iii) if the vectors and span (e) Given that Determine : (i) the rank of A (ii) the null space of A (iii) if the vectors and span EsERcizio 1 Provare che le seguenti applicazioni non sono forme bilineari: (X) tale che (L) tale che ; (Ni) tale che (iv) tale che ; (v) tale che . SVOLGIMENTO (i) Si trova , pertanto non può essere una forma bilineare. (i) Abbiamo . (if) La funzione determinante non ci permette di portare fuori le costanti moltiplicative. Per esempio sia . Allora mentre (iv) Abbiamo che .
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