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Home Question Bank Other Archive 2024 December 15

Other Questions from Dec 15,2024

Browse the Other Q&A Archive for Dec 15,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Decompose \( \mathbf{v} \) into two vectors \( \mathbf{v}_{1} \) and \( \mathbf{v}_{2} \), where \( \mathbf{v}_{1} \) is parallel to \( \mathbf{w} \) and \( \mathbf{v}_{2} \) is orthogonal to \( \mathbf{w} \). \( \mathbf{v}=4 \mathbf{i}-6 \mathbf{j} \) and \( \mathbf{w}=\mathbf{i}+\mathbf{j} \) Write the expression in rectangular form, \( x+y i \), and in exponential form, \( \mathrm{r} e^{i \theta} \) \( (-1-i)^{3} \) Find \( z w \) and \( \frac{z}{w} \). Write each answer in polar form and in exponential form. \( \begin{array}{l}z=4+4 i \\ w=\sqrt{3}+i\end{array} \) Write the expression in rectangular form, \( x+y i \), and in exponential form, \( e^{i \theta} \). \( (-1-i)^{3} \) 15 Considera gli enunciati aperti: \( A(x) \) : « \( x \) è numero naturale minore di \( 9 » \); \( B(x): 《 x \) è numero primo minore di \( 20 » \). Scegli un insieme universo \( U \) e rappresenta con un diagramma di Venn l'insieme di verità degli enunciati \( A(x), B(x), A(x) \wedge B(x), A(x) \vee B(x) \). For the linear transformation \( L: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3} \) given by \[ L((x, y))=(x+2 y,-x, 0) \] find the matrix \( A_{B C} \) for \( L \) with respect to the bases \[ B=\{(1,3),(-2,4)\}, C=\{(1,1,1),(2,2,0),(3,0,0)\} \] For the linear transformation \( L: \mathbf{R}^{4} \rightarrow \mathbf{R}^{3} \) \( L\left(x_{1}, x_{2}, x_{3}, x_{4}\right)=\left(4 x_{1}+x_{2}-2 x_{3}-3 x_{4}, 2 x_{1}+x_{2}+x_{3}-4 x_{4}, 6 x_{1}-9 x_{3}+9 x_{4}\right) \) find a basis for \( \operatorname{ker}(L) \) and a basis for \( \operatorname{range}(L) \) its) Let \( v=(-5,8,-5) \in \mathbf{R}^{\circ} \). Let \( B \) and \( C \) be bases of \( \mathbf{R}^{\circ} \) \( B=\{(2,1,1),(2,-1,1),(1,2,1)\}, C=\{(3,1,-5),(1,1,-3),(-1,0,2)\} \) Find the coordinates \( [v]_{B} \) of vector \( v \) with respect to \( B \). Find the transition matrix \( P \) from \( B \) to \( C \). Using \( [v]_{B} \) and \( P \) find \( [v]_{C} \). \( v_{1}=(-8,2,-3,2), v_{2}=(4,1,-5,-4), v_{3}=(-3,-1,4,3), v_{4}=(2,-1 \) form a basis of \( R^{4} \) ? Answer this question by using 3.1 Simplified Span Method (Andrilli p.232) 3.2 Independence test method (Andrilli p.242) 6. ( 8 points) Determine whether the set \( S=\left\{\left(x_{1}, x_{2}\right)^{T} \mid x_{1}=2 x_{2}\right\} \). forms a subspace of \( R^{2}=\left\{(a, b)^{T} \mid a, b\right. \) are real numbers \( \} \) specific steps should be part of the task analysis, then follow the developed task analysis to see if any critical steps have been omitted (similar to the "make a pea- nut butter and jelly sandwich" activity children often experience in school). Prior to implementation, the interventionist(s) should decide whether additional inter- ventions should be used (e.g., photographs for each step, a prompting procedure) and ifforward or backward chaining will be used. Delivery of the task analysis intervention usually includes forward or back- ward chaining. Forward chaining involves teaching the person the first step in the task analysis until mastery and supporting them through the remaining steps (or doing the remaining steps with and for the learner). Backward chaining involves teaching the person the final step in the task analysis until mastery is achieved and supporting him or her through the initial steps (or doing them with and for the learner). Prompting procedures usually are integrated in all steps, with specific attention on fading the prompt for the current step being targeted for independence. Data are collected to determine whether the intervention is sufficiently effective (i.e., whether steps in the task analysis are being mastered at or above the expected rate).
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