Solve the assigned situation to you and create an appropriate word problem on given values. Show the complete step-by-step solution (including the illustration) in getting the final answer. SITUATION A An 8 – meter ladder with its foot 4 meters from the wall slides away at a rate of 1.5 m/s.

Q: 3. Let ø(x) be a solution to the initial value problem: y" + 2y' + 5y = 0; y(0) = 0, y'(0) = 4. Let ...

A: We need to find ratio of solution of D.E.

Q: 1. It is the process of finding the set of all functions whose derivative is known. B. antiderivatio...

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Q: (a) P(blue, then red) (b) P(clear, then clear)

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Q: Below is a graph of the derivative of a function f. y 3| (x from -1.3 to 2) A.0 -0.5 -1 0.5 1.0 1.5 ...

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Q: A sphere has a volume of 36 cubic meters. The rate of change in volume is 9 cubic meters per minut...

A: Let's find. 

Q: A - Evaluate the following integral. e2x cos3x dx

A: Given I=∫e2x.cos3x dx

Q: 12 DO NOT include spaces in between characters. * Find the equation of the tangent line to the graph...

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Q: = cx + In(cos x). For what value of c is f'(T/4) = 7? C =

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Q: 1. lim x2 – 2x + 4 x→1 f(x) f(x)

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Q: 10 [(3-4w)(4w - 6w+7)" dw.

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Q: Find the area of the triangle with vertices P(1, 4, –2), Q(0,0,0) and R(4,5, 1). NOTE: Enter the exa...

A: We can find the area as below.

Q: Given the function (x³ – 2x 2 if x < 2 f(x) = v2 - x if x 2 2 Determine if f is continuous at x1=2. ...

A: Continuity 

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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Q: Write the expression as the sine, cosine, or tangent of an angle. 3 COS sin)sin() COS - 7

A: Note that: cos x cos y-sin x sin y=cos (x+y)

Q: Find the volume enclosed by the torusp = 4 sin().-

A: The volume is given by: V=∫∫∫dv In spherical co-ordinate dV=ρ2sin φ dρ dφ dθ

Q: Solve the following initial value problem. ye) -2y"+ y' 4 +8x e*; y(0)= y'(0) = 0, y"(0)= 1 The solu...

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Q: Write the expression as the sine, cosine, or tangent of an angle. sin 50° cos 5° + cos 50° sin 5°

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Q: The population of a herd of deer is represented by the function A(t)=180(1.21)t, where t is given in...

A: Solved below

Q: Consider the following limit. 6x2 + x - 1 lim x - (-1/2)+ 10x² - 5x - 5 Simplify the rational expres...

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Q: In Exercises 19-24, find the absolute maximum and minimum of the function subject to the given const...

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Q: 10. Consider the bit strings in B (bit strings of length 6 and weight 2). (a) How many of those bit ...

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Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: What is the equation of the line tangent to the curve 9x^2 + 25y^2 – 225 = 0 at (0, 3)?  a. x + 3 = ...

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Q: 10. Given the functions /(x) = 3x² + 2x + x+1 and g(x) = 2x² – 1, find (f - 9)x. a 3x +x b. 3x +x+2 ...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: B. lim, 0+(1 + 2r)In(2=)

A: Given: limx→0+1+2xln2x   As we know from the limit rule; If the limit is limx→afxgx and it result of...

Q: 7T then 6. If 0 = sin(0) = cos(0) = COS %3D

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Q: DO NOT include spaces in between characters. 31² Determine f'(2) if f(t)=log10 2t – 1 Your answer

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Q: Q3 : Evaluate the following integral. x+V9-x2 xps

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Q: B. Directions: Using special functions, evaluate the following:

A: Question 1,Given,           limx→0sinlnx5lnx

Q: Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 5,000 + ...

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Q: Note: Values of x should be typed in INCREASING order from LEFT to RIGHT. DO NOT include spaces in b...

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Q: Type your answer in the following order and format: a=0,b=4. DO NOT include spaces in between charac...

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Q: (6w+12w") /w +w° dw

A: Given: I=∫6w-4+12w-7w-3+w-64dw So, we can also write as: I=∫6w-4+12w-7w-3+w-64dw=∫6w4+12w71w3+1w64dw...

Q: Evaluate the integral L(9te") i + (9e 2") j+ (4) kļat. J[(otea") i+ (9e 2) j+(4) k]at = ([ i+ +. (Ty...

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Q: Find f'(x) and f"(x) of f(x) = 11x³.

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Q: 2. Given: LKEI S LTEI Prove: AKET ATEI Proof: Statements Reasons 1. 1. 2. 2. 3. 3. El EI 4. 4.

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given ...

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

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Q: xy = 4, y = x,y = 1; about the x-axis.

A: Find your answer below 

Q: Q3 : Evaluate the following integral. X4V9-x2

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Q: A Given yesin (ITX2)= InGe) XyZ of Find Zx and Zy.

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Q: (a) Find the critical points, if any, of the following function on the given interval. (b) Determine...

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Q: The sum of a geometric series is as follows: S = 1.0 + 1.1 + 1.21 + 1.331 +... up to 50th term. Dete...

A: SUM OF GEOMETRIC SERIES

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v ort...

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Q: 12. Find the value of the limit: lim a. +00 b. -00 d. Indeterminate

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Q: Biologists stocked a lake with 250 fish and estimated the carrying capacity (maximum pop- ulation fo...

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Q: Select ALL possible answers if there is more than one. * 1 16 Let f(x) =- ifx<- 2 . If f(x) is conti...

A: Let's find. 

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(r) = 4x + 7...

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Q: Find the derivative of g(x)= using the limit definition

A: Solution:we have use formula g'x=limh→0gx+h-gxhgx=1x-1g'x=limh→0gx+h-gxhg'x=limh→01x+h-1-1x-1h=limh→...

Q: e area between the two loops of the limacon r = 1+2 sin 0.

A: We are asked to find the area between the loops.