Use the Laplace transform to solve the initial value problem: 2y" + 3y' - 2y = te-²t, y(0) = 0, y'(0) = -2

Q: y² = 2x = x² 1- y² = (x - 1)² x = 1+√1-y²

A: (a-b)2 = a2 - 2 a b +b2

Q: Var(5 + 2vx) = 4(E(x) – (E(Jx))² true False O

A: From the provided information, Var (5 + 2√x) = 4(E (x) – (E(√x)))2

Q: Can you answer it and explain your steps

A: Step 1:   Step 2: Step 3: Step 4:

Q: h (x) = -4x² +5 g (x) = 6x -3 a. find (h/g) (-2) b. find all values that are not in the domain of…

A: a. h (x) = -4x² +5 g (x) = 6x -3 hg(-2)=-4x2+56x-3=-4(-2)2+56(-2)-3=1115

Q: 3(4)0* =21

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Q: 24. The square of equals the square root of (A)- (B) (C) 16 (D) 256 112-14

A: 24    Let the square of14 equal square root of x               ⇒142=x               ⇒116=x

Q: K 111(x)=4x² - 6x +5, solve f(x) = 21. X= (If necessary, round to two decimal places.)

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Q: If x* +y* = 1, find an expression for By dx 3x2 (a) 2 x4 (b) – (c) (d) 2 x2 (e)

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Q: (1/2)t -(1/5)v = 7/2 (2/3)t + (1/4)v = 7/12 Could you please solve the above sysytem? Thanks

A: Consider the provided equations, 12t-15v=72...... (1)23t+14v=712 ...... (2) Solve the above…

Q: Let f(r) = 4x + 2 and g(z) = 5a² + 5x. After simplifying, (fo g)(x) =

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Q: Consider 6x + 1/(2x). When increasing/decreasing? It's decreasing on both sides of 0. Explain why…

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Q: b. During a nationwide program to immunize the population against a new strain of the flu, public…

A: Given, the cost of inoculation x% of the susceptible population would be C(x)=(1.85x)/(100−x)…

Q: (b) Write z = (3- 3i)+ in the form of x +iy.

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Q: V(X) = i

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Q: This into an equation?

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Q: 6(t+2)=5(3t-4)

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Q: r)- x- 5 9(x) = 2x - 1 h(x) = 2x - 11x + 5 3.- )(x) 4. 4

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Q: The number of people in a school that have caught a cold can be modeled by C(d) = 3(4) where C(d) is…

A: c(d) = 3(4)d after 5 day so d =5 c(5) = 3(4)5 c(5) =3(1024) c(5) = 3072   time to catch 192 people…

Q: (3x² - 10)dx x² - 4x + 4

A: The given integral is ∫3x2-10dxx2-4x+4

Q: Please solve the following:   1.  5/6 (3/8-x)=16 2.     6(5m-3)=1/3 (24m+12) 3.

A: Step 1: Step 2: Step 3: Step 4:

Q: 8. Differentiate the following: A. h(x) = (2x+1)' (4x-3)² 2x+1 B. g(x)=. 2x-1

A: The solution of the questions A and B is given below

Q: A person on an assembly line produces P items per day after / days of training, where P(t)= 400 1 +…

A: We can make it easier for you.

Q: Mutiply : 3(9/20) x 2(1/12) = ? 17 x 1(3/34)=? 1(11/24) x 16 =  10/39 x 2(3/5)=?

A: We can do these multiplications as below

Q: (3x + 1)(x – 3) = 4x(3x – 2) – 7

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Q: When a ball is tossed into the air, the height h is feet of the ball t seconds from the time that…

A: ht=-16t2+80t+4 Comparing with ht=at2+bt+c, we get a=-16, b=80 & c=4 Now maximum value occurs at,…

Q: d(n) = 28, find one value of n smaller than 1000

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Q: 7t +9 , Suppose f(t) = 5 (a) Evaluate f(8). f(8) = help (fractions) %3D (b) Solve f(t) = 4. t = help…

A: Given function is ft=7t+95, a We have to evaluate f8. b And we have to solve for ft=4. Solving a: In…

Q: A company involved in the export of trucks has estimated that the profit (U) in millions of dollars…

A: Given: The profit U in million of dollars depends on "n" number of containers expoterd by the…

Q: xS(ux), then pro (16) = () (16) = %3D

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Q: The height of a rocket is modeled by h(x) = -(4x-8)(4x-24). About how long after reaching maximum…

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