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Determine $\mathcal{L}^{-1}\{F\}$. $s^2F(s)-sF(s)-30F(s) = \frac{2s^2+5}{s^2+4s}$ Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. $\mathcal{L}^{-1}\{F\} = \boxed{}$

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research and determine the composition of egg shells and describe them below

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Casey is going to wear a gray sportcoat and is trying to decide what tie he should wear to work. In his closet, he has 27 ties, 10 of which he feets go well with the sportcoat if Casey selects one tie at random, determine the probabity and the odds of the tie going well or not going well with the sportcoat. The probability the tie goes well with the jacket is \( \square \) (Simplify your answer. Type an integer or a fraction ) The probability the tie will not go well with the jacket is \( \square \) . (Simplify your answer. Type an integer or a fraction.) The odds against the tie going well with the jacket is \( \square \) . (Simplify your answer. Type a ratio using a colon.) The odds in favor of the tie going well with the jacket is \( \square \) . (Simplify your answer. Type a ratio using a colon.)

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A 14 y/o female with no significant risk factors is seeing you to develop an exercise program. She is competitive soccer player and wants to improve her agility and power. What type of testing modality and protocol would give you the best data to use to evaluate her fitness level?

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A green car is trailing a yellow car in an adjacent lane while moving down a highway at a constant speed of 75.1 mi/hr. The separation distance between the two cars is 35.8 ft. The yellow car slams on the brakes and decelerates at a rate of -8.82 m/s/s. After a reaction of time of 0.330 seconds, the green car begins decelerating at a rate of -8.57 m/s/s. What is the final separation distance (in m) between the cars once stopped? (Given: 1 m/s = 2.24 mi/hr; 3.28 ft = 1 m) Enter the answer as a positive value (no - values). and A train normally travels with a uniform speed of 93.0 km/hr along a stretch of straight, level track from point A to point B, past a depot that lies in between. One particular day, the train makes a 3.53-minute stop at the depot. If the train decelerates at a rate of -1.34 m/s/s from point A to stop at the depot and then accelerates at a rate of 0.81 m/s/s back to point B, then how much total time (in minutes) is lost by the train in making the stop. Consider the decelerating time, the rest time, and the accelerating time compared to the straight-through A to B time.

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According to the psychodynamic approach, which of the following is NOT a condition to promote productivity and relationship building in order to build self-esteem? O Belonging O Empowerment O Perfectionism O Uniqueness

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What do people experience when having a panic attacks? feelings of terror, chest pains, or choking Minutes-long episodes of intense dread all of the above other frightening sensations

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2. Test if the following matrices are diagonalizable or not, then find a matrix $P$ that diagonalizes $A$, and determine $D = P^{-1}AP$ (a) $A = \begin{bmatrix} 1 & 0 \\ 6 & -1 \end{bmatrix}$ (b) $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & 1 & 1 \end{bmatrix}$ (c) $A = \begin{bmatrix} 2 & 0 & -2 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{bmatrix}$

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Question 1: a) Find the roots of the cubic equation: $z^3 - 3z^2 + 7z + 75 = 0$. Show the roots in the Argand diagram. Rubric: 3 mark for correct root found by the trial method; 6 marks for the correct factorisation of the cubic equation; 4 marks for the correct finding of two other roots; 2 marks for the correct presentation of the roots in the Argand diagram. b) Determine moduli and arguments of the roots (present the arguments in radians up to three decimal places). Present all roots in the polar and exponential forms. Rubric: 1 mark for correct module of the first root; 1 mark for correct argument of the first root; 1 mark for correct presentation of the first root in the polar and exponential forms; 1 mark for correct module of the second root; 1 mark for correct argument of the second root; 1 mark for correct presentation of the second root in the polar and exponential forms: 1 mark for correct module of the third root; 1 mark for correct argument of the third root; 1 mark for correct presentation of the third root in the polar and exponential forms. c) Connect roots in the Argand diagram by straight lines and form a triangle. Find the perimeter $p$ of the triangle (in the dimensionless form) in the exact form and in decimal up to four significant figures. Rubric: 1 mark for correct distance between the points $z_2$ and $z_3$; 3 marks for correct distance between the points $z_1$ and $z_2$; 3 marks for correct distance between the points $z_1$ and $z_3$; 2 marks for correctly calculated perimeter in the exact form; 2 marks for correctly calculated perimeter in the decimal form up to four significant figures. d) Find the area $S$ of the triangle in item c) (in the dimensionless form). Rubric: 1 mark for the correctly determined base of the triangle; 6 mark for the correctly determined height of the triangle; 1 mark for the correctly determined area of the triangle.

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Derive an expression for the effective value of the voltage waveforms shown below:

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