4). Use rules of replacement to prove the following:b). (pq) → r= (p⇒r) ^ (q ⇒r)d= (bvd)^(bvd) (e

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Answered: 4). Use rules of replacement to prove…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y'- 3y = 10 sinh 2t, y(0) = 0, y'(0) = 4 (b) y" + 25y = 10 cos 5t – 2 sin 5t, y(0) = 1, y(0) = 2 %3D %3D
Find r'(t), r"(t), r'(t) ·r"(t), and r'(t) × r"(t). r(t) = 올레 - 3+ 를FK 2 3 (a) r'(t) (b) r"(t) x x (c) r'(t).r"(t) x (d) r'(t) × r"(t)
Evaluate: / (In z + xe" + VTy) dy
Q3/ Find そ 52 7 =f (xxy) y =y(s,t) y (s, X = x ( sit)
X ~ Bin(30, 0.25). Find approximations for:1. Prob(X < 10)2. Prob(X > 10) 3. Prob(X=10)
Ofx)=5x"_3x²-Z+t] 4 2 find f6 and fW) (x) f =x* Inx find f') and fe
V16._ lis distance from the ground at t seconds is given by s(t) = -16t2 + 64t + 144. How fast is the ball moving 2 seconds after being thrown? A ball is thrown vertically upward from the ground at a velocity of 64 ft per second. V(t) = sTt) =16(2+)+ L04 + 144 =-32t + 64+144 S'lt) %3D (a) 0 ft per second (b) 2 ft per second -32(2) +64+144 144 () 208 ft per = secund -164 +64 + 144 {d) 44 T per ·second (e) None of tbe Above
Let_f(x,y)=x²y+√y 2. Find each value d. ƒ(a‚aª) e. ƒ. ƒ(2,-4)
Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =
Then the value of f_y (a, b) is equal toa) 26/5b) 13/2c) 13/24d) 13/12

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4). Use rules of replacement to prove the following: a). (p^~q) (p^q) = p b). (pvq) →→ r = (p → r) ^ (qr)