A power plant generates electricity over a twenty-four hour period. The number of megawatts, M, of electricity generated at various times during the day is shown by th graph below. The variable t represents the number of hours since midnight on a given day. Megawatts 95- 900 85 80 75 70 65- 60 35 10 45 40 ● 35 30 25 20 15 10- s 0 • • 2 ● ● ● ● • ● Hours since midnight ● . ● · IN ● ● 20 22 24

Q: 2. A circular cylindrical hole is bored through a solid sphere, the axis of the hole is being a…

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A: Please see the attachment

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Q: Find the inverse Laplace transform of the following functions F(9)= (+2X8+3) 68 +25 F(s)= sl + 5)²…

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Q: 3. (30 points) Diagonalize the matrix A = 5 0 1 -1 05 0 0 0 0 4-3 0 -2 0-3 if possible.

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Q: Solve the given initial-value problem. y(x) = y" + 6y'7y = 11e²x, y(0) = 1, y'(0) = 1 -7.x 11e2x 7e…

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A: Please see the attachment

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

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A: From the above details we have,

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Q: (a) State the Fundamental Theorem of Calculus Part I

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Q: Given the function below, is fx (x,y) (the derivalue of f with respect to x) continuous at origin?…

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Q: max st. z = 3x1 + 2x₂ + 5x3 2x₁ + x₂ < 20 X₂ + 2 v

A: Max Z = 3x1+2x2+5x3 subject to  2x1+x2≤20x2+3x3≤30x1+x2≤25x1,x2,x3≥0 Add the slack variables…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.