Solve the given initial value problem using the method of Laplace transforms. 26, 0≤t≤6, y" + 2y' +26y=g(t), y(0) = -2, y'(0) = 0, where g(t) = 52, 6

Q: Evaluate ds, C: z = t, y =t, 0sts8

A: Given: x=t2                and      y=t⇒x'(t)=2t      and     y'(t)=1 Now: ds=x'(t)2+y'(t)2…

Q: Given: (6, 0, –2) and (0, 8, 0). (6,0, –2) × (0, 8, 0) = æi + yj+ zk. Find x +y+ z.

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Q: f ​P(E)=0.60​, ​P(E or ​F)=0.65​, and​ P(E and ​F)=0.10​, find​ P(F).

A: Let E and F are two events. The known probabilities are, ​P(E)=0.60​, ​P(E or ​F)=0.65​, P(E and…

Q: If P(A) = 0.3, P(B) = 0.3, and P(A and B) = = P(A or B) = X 0.2, find P(A or B).

A: we have probability of P(A)= 0.3 and P(B)=0.3 and P(A and B)=0.2

Q: Fird the inversc trons frm of ; F (5) = sz+ 25

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Q: P(A U B) = 0.9, P(B) = 0.8, P(A n B) = 0.5. Find P(A). %D

A: We have given that,  P(A∪B) = 0.9, P(B) = 0.8 and P(A∩ B) = 0.5 Then,  We will find P(A) = ?

Q: Let P(A) = 0.6 P(B)= 0.2 and P(AUB)= 0.7 Find P(AB) 4

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Q: B CA writen as .A (V x)(x EB → EA) .B (3x)(x EB → x EA) .C (Vx) (xEB+xE A)

A: A set 'C' is said to be subset of set 'D' if every element of  set 'C' is contained inside set 'D',…

Q: a b If p q |x y C r ZI ja+x b+y c+z 5z -r = -4, evaluate 5x 5y -P -q

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Q: If w 5x2 + 2y2, x = -3s+t, and y = s – 4t, find in terms of s and t. Provide your answer below:

A: Given:   w = 5x2 + 2y2     x = -3s + t      y = 3 - 4t

Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: Q5 1 Find proj; (w) where w= and v = 2 -2 3

A: Solution:Given     w=10-2     and     v=123To find:projvwFormula:projvw=P wwhere P=v vTvT v

Q: o(E)=3:2, find p(E)

A: Odds of E (3/2) And we have to find p(E) =?

Q: Given v = (3, –7) and w = (-2, 5), find a. v• w b. w• v c. v• v d. |||

A: Given, v=3,-7 & w=-2,5 To find, a. v.w b. w.v c. v.v d. v

Q: A car costs x wholesale. The price the dealer pays is given by the function s(x) = = x-1 – 200 where…

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Q: Given a rate of 175 pesos per hour, how many hours should you work to earn 35,962.50 pesos

A: If ∆x is the amount earned in time ∆t, then the equation for the rate of the amount earned per unit…

Q: Find (i)27 = а. i b. -i с. 1 d. –1

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Q: If p(5, r)= 2. P(6, r -1), find r.

A: Given : p(5, r) = 2. P(6, r -1)

Q: determine f ∗g. Q. f(t)=6t2, g(t)=5t3

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Q: K M N х+3 7, 4x – 9 R 12

A: Topic-Geometry

Q: Let wr₁ (t) = and r₂(t) =. Find (r₁(t)- r₂(t)). O 04t² +6t³ 0312 +8+4 0

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Q: If ​P(E)=0.55​, ​P(E or ​F)=0.70​, and​ P(E and ​F)=0.20​, find​ P(F).

A: Given that P(E)=0.55​, ​P(E or ​F)=0.70​, P(E and ​F)=0.20​ The formula of addition of two events…

Q: 2 -1 2 2.

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Q: If B = exp(r - 2), what is VxB?

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Q: Find N2 A 21 N 2 p(v) B, ) = N`, p (ν) Β..) A 31 Haitha.

A: We have to separate N2 from the equation

Q: If P (A) = 0.6, P(B)=0.1, and A and B are mutually exclusive, find P (A or B). P(4 or B) = |

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Q: Let r(t) = (a) Find 7 (t). (b) Find Ñ (t). (c) Find K (t)

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Q: 7k +5)dx t

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Q: Complete the table. h(t) |t + 4| t -5 -4 -3 -2 -1 h(t)

A: The given function is: h(t)=12t+4 which is a modulus funtion.

Q: Y (t)

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Q: Given u x = (-3, -4,-2), find (u-37) x (u + 4v).

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Q: as Find w = 1° + 2y? I = r - s; y=r+2s2

A: Given:w=x3+2y2x=r-sy=r+2s

Q: for b find y...

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

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