Numerade

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Find the bases that make the following equations true and show all the necessary calculations: 21ₐ = 25ᵇ

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At time t = 0, a particle is located at the point (6,6,1). It travels in a straight line to the point (2,4,7), has speed 3 at (6,6,1) and constant acceleration -4i - 2j + 6k. Find an equation for the position vector r(t) of the particle at time t. The equation for the position vector r(t) of the particle at time t is r(t) = (Type exact answers, using radicals as needed.)

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Current Attempt in Progress Propose an efficient synthesis for the following transformation: SH OH The transformation above can be performed with some regent or combination of the reagents listed below. Give the necessary reagents in the correct order, as a string of letters (without spaces or punctuation, such as "EBF"). If there is more than one correct solution, provide just one answer. A. MCPBA (RCO$_3$H) B. 1) NaSH; 2) H$_3$O$^+$ C. 1) LiAlH$_4$; 2) H$_2$O D. Na$_2$Cr$_2$O$_7$, H$_2$SO$_4$, H$_2$O E. KMnO$_4$ F. Br$_2$, hv G. H$_3$O$^+$ H. 1) NaSMe; 2) H$_3$O$^+$ I. H$_2$S, H$_2$SO$_4$

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What are the rights of non-controlling interest and how are noncontrolling interest reported on financial statements?

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1. List and describe all of the physical changes that adolescents experience in their teenage years. What role does nutrition and exercise play with these changes? What influences positive health outcomes in this age group? 2. What is juvenile delinquency? What factors lead to juvenile delinquency? Is it common? What are some ways to reduce juvenile delinquency? What role does the parent play in juvenile delinquency?

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2 (a) The linearity property of Laplace transform states that to find the Laplace transform of a sum of functions one can, alternatively, sum the Laplace transforms of the individual functions. The linearity property of the Laplace transform can be expressed as follows: $\mathcal{L}\{f(t) + g(t)\} = \mathcal{L}\{f(t)\} + \mathcal{L}\{g(t)\} $\mathcal{L}\{kf(t)\} = k\mathcal{L}\{f(t)\} where $f(t)$ and $g(t)$ are two functions of $t$ and $k$ is a constant. (2.a.1) Use the linearity property of the Laplace transform and the attached table of Laplace transforms to find the Laplace transform for each of the two functions below: (i) $5\cos3t + 2\sin5t - 6t^3$ [5 marks] (ii) $5t^2 - 2e^t$ [5 marks] (b) The first shifting theorem of the Laplace transform is detailed below: If $\mathcal{L}\{f(t)\} = F(s)$ then $\mathcal{L}\{e^{-at}f(t)\} = F(s + a)$ where $a$ is constant (2.b.1) Assume that the Laplace transform of the function $f(t)$ is given as: $F(s) = \frac{2s+1}{s(s+1)}$ (2.b.2) Use the first shifting theorem of the Laplace transform and the Laplace representation of $f(s)$ that has been provided in Eq. (8.b.2) to derive the Laplace transform for each of the two functions below: (i) $e^{-2t}f(t)$ [5 marks] (ii) $e^{3t}f(t)$ [5 marks] [20 marks] Page 2 of 11

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An analog source produces a baseband voltage signal x t( ) with bandwidth equal to 10 kHz. Assume that sample functions of x t( ) follow a probability density given by: 1 2 0 2 0 otherwise , ( ) , x X e x f x ? ? ? > = ? ? ? The source output is quantized according to the rule: 0 5 1 for 1 5 60 50 6 i i i xi i y x i ? ? ?? <

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$\lim_{x \to \infty} e^{-x} \cos x$

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Solve the linear system \begin{cases} x + y - z + w = 1 \\ 2x + 3y + z = 1 \\ 3x + 4y + z + 2w = 2 \\ y + 3z - 2w = -1 \end{cases}

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3. A rectangular tank measuring 90 cm by 25 cm by 80 cm is filled with water to a height of 30 cm. How much more water is needed to fill up the tank completely?

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miranda b.