Math 216 Homework webHW1, Problem 8 Find the solution to the initial-value problem Then put the solution in the form of: dy dx = (4y +10) cos(x); y(0) = C.

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: An RC circuit with a 100 Q resister and a 10^(-2) F capacitor is driven by a voltage…

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Q: What is h′(b) when b=4 and h(x)=(6x)^4x?

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Q: What is teh solution to the equation; 4^-2x+3k=16^4x+k

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Q: 52 Simplify: [-p ^ (p v q)] → q-

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Q: What is the inverse of f(x) =6x^3+8 ?

A: Given:

Q: Suppose the function f is updated from f(x)=x^3 to f(x)=−3.5x^3. How does changing the coefficient…

A: There are two big changes you introduced to the function when you change the coefficient from 1 to…

Q: In step 2, I don't understand why gf=f^-1g^-1.

A: Here We will show how in the step 2,  has come.

Q: (D^3-2D^2-5D+6)y=e^(3x)

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Q: What is the simplified form of i^(13) ?

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Q: If y= 4sqrt(9x^3+10), then y'=

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: (x^3 + x^4)dx + 8y^(3)xdy = 0

A: x3 + x4dx + 8y3xdy = 0

Q: (10x-19) (3r + 2) (5x-3)

A: We will use the exterior angle property of a triangle that states that an exterior angle is equal to…

Q: Is the equation( e^2x) + (xcosx) +(-2) =0 has real roots ?

A: Using mean value theorem for continuous functions

Q: Solve 12sin^2(w)−11sin(w)+2=0

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Q: x^2-1

A: Equate the equation to 0 first ie x^2-1=0 now move 1 to the RHS and apply square root on boths sides…

Q: 5x^2−3x−8 has roots at x=

A: Consider the quadratic equation To find - roots

Q: find the general solution (D^2+9)y=5e^x-162x^2

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Q: differentitate f(x)= (ax^3+b) (cx^2+d)?  I know to use the product rule but am having trouble…

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Q: In a given community, the number of thousands of people infected with a strain of flu t weeks after…

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Q: In step 3, how did you know to use yp = ( 1 / (D^2 + 9) ) 4sin(2x)?

A: The given initial value problem y''+9y=4sin(2x), y0=1, y'0=1. We have to find the solution of the…

Q: 5x/(x^1/3)(y^2/3)

A: Given expression is

Q: Rewrite y = 3 * (8) ^ (t / 15) in the form y^ prime =a(1+r)^ t or y = a(1 - r)

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Q: Find the inverse: f(x)=-x- 3 A. f-^(x) = x = 12 X-12 B. f-'(x) = 3x – 4 C. f-'(x) = 4x+ 12 x+3 D. f…

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Q: why X"/X=-lamba and T"/(a^2)*T=-lamba.

A: Consider the given information: X"/X=T"/(a^2)T =-λ

Q: ∫dv/(B-v^2), B is a constant

A: This question is about to evaluate indefinite integral.