Numerade

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(1 point) Evaluate $$\int_0^2 f(x) dx$$, where $$f(x) = \begin{cases} 5x^7, & 0 < x < 1 \\ 6x^4, & 1 \le x \le 2 \end{cases}$$

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Multiple Choice 1 point When a neurotransmitter binds to a receptor and increases the permeability of the post-synaptic neuron to potassium the membrane will become permeable to sodium. an inhibitory postsynaptic potential (IPSP) will result. more chloride ions will diffuse out of the cell. the neuron depolarizes moving it closer to threshold. Clear my selection

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are unspoken rules for how group members should behave - including what behaviors are acceptable, right, rewarded - and what is inappropriate, wrong, and/or punished.

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The human body is made up of different systems that work together to carry out the functions needed for life. One of these necessary functions is breathing. The following systems help move air in and out of the body. Apply what you've learned about the organization of the human body to order these systems from the simplest to the most complex. simplest system respiratory system, which brings oxygen into the bloodstream and removes carbon dioxide lungs, which expand and contract to move air in and out human, which is made up of multiple interacting organ systems epithelial cell, which helps form the lining of the lungs epithelial tissue, which protects the lungs from pollutants most complex system Submit

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What is the primary industrial application of reverse osmosis beyond water treatment? A) Concentration of fruit juices B) Recovery of precious metals C) Production of pharmaceuticals D) Gas separation processes

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1. Which form must be completed for employee employment eligibility verification within three days of being hired? FICA I-9 1040 ERISA

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Compare and contrast firewalls and intrusion prevention systems in terms of purpose, functionality, granularity and use cases.

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Using Nodal Analysis calculate v1, v2, and i1, i2, i3, i4, i5 and i6.

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Evaluate the inverse Fourier transform $f(t) = (2\pi)^{-1/2} \int_{-\infty}^{\infty} F(\omega)e^{-i\omega t} d\omega$ of the Lorentz distribution \\ $F(\omega) = \frac{\gamma}{\pi} \frac{1}{\omega^2 + \gamma^2}$. \\ You will need to treat the cases $t < 0$ and $t > 0$ differently when evaluating the integral by residues.

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1. (30%) Let $A$ be an $n \times n$ matrix and $c_{ij}$ is the corresponding cofactor of $A_{ij}$. (a) (10%) Starting from the fact that if two rows of $A$ are identical, the determinant of $A$ is 0. Prove $A_{i1}c_{j1} + A_{i2}c_{j2} + \dots + A_{in}c_{jn} = \begin{cases} det(A) & \text{if } i = j\\ 0 & \text{if } i \neq j \end{cases}$ (b) (10%) Following (a), if we define a new matrix called the adjoint of $A$ by $A = \begin{pmatrix} A_{11} & A_{12} & \dots & A_{1n} \\ A_{21} & A_{22} & \dots & A_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ A_{n1} & A_{n2} & \dots & A_{nn} \end{pmatrix}$, $adj \ A = \begin{pmatrix} c_{11} & c_{21} & \dots & c_{n1} \\ c_{12} & c_{22} & \dots & c_{n2} \\ \vdots & \vdots & \ddots & \vdots \\ c_{1n} & c_{2n} & \dots & c_{nn} \end{pmatrix}$ Please show that $A(adj \ A) = det(A)I_n$. (c) (5%) Following (b), please prove that $A^{-1} = \frac{1}{det(A)}(adj \ A)$ whenever $det(A) \neq 0$. (d) (5%) Using (c), please calculate the inverse matrix of $A = \begin{pmatrix} 2 & 1 & 2 \\ 3 & 2 & 2 \\ 1 & 2 & 3 \end{pmatrix}$.

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tara h.