Convert the following equation for a hyperbola into standard form, and graph it below using the transverse axis, point, vertices, and co-vertices: 4x²16x-25y²-150y-309 = 0 Use the green key point to change the orientation of the transverse axis, and the red key points to adjust the lo the center point, vertices, and co-vertices. Provide your answer below: (1,2)

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A: The function is  f(x)=x for x &lt; 0 and f(x)=sin(x) for x≥0

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A: To find the interval. By the given graph.

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A: Given, Cost function C(x)=52900+800x+x2

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A: Given data, f8=2 and y=x-11+4

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A: use implicit differentiation for finding the derivatives.

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A: A logarithmic graph is given and we have to find its equation.

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A: We need to solve D.E.

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A: find equation of tangent line at ( 2 , 16 ) first find slope  for x = 2  slope m = 8*2 = 16

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A: The given equation is; y=x-exsinx.

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A: For relative maxima f'( x ) = 0 f''( x ) &lt; 0 g'(x) = - 3x(x + 2) (x - 3)

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A: Given query is to find the value of a.

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A: The given limit function is lim(x,y)→(9,9)x2-xyx-y  We have to find the limit value .

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A: Let st=6t3-9t2-216t, be the equation of motion for a particle.Assume -∞&lt;t&lt;∞.A To find a…

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A: 16) The given equation is; Sinx - Cosy - 2= 0

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Q: What is d dx 7x 3x O 102 sin z √2 - sint dt? O-3√2-Sin 3z - 7√2 – sin 77 O 3√2-sin 3x - 7V2 — sin 72…

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A: Given query is to find the equation of the circle.

Q: Which of the following is the linear approximation of f(x) = sin x at x = ? OL(x) 1 OL(x) = x OL(x)…

A: Given f( x )= sinx at x = π2linear approximation L( x ) = f( a ) + ( x - a )f'( a )

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A: See this solution in below.

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A: Given function is f(x)=Inx/x To find critical points we use f'(x)=0 To find inflection point we use…

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A: We can find the area of the region .

Q: Using Laplace transform to solve the IVP: y" - 7y=e5t, y(0) = 0, y'(0) = 0, then, we have Select…

A: We know, L{y"}=s²L{y}-sy(0)-y'(0) L{y'}=sL{y}-y(0) L{eat}=1/(s-a)

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A: To find the differentiation of given function.

Q: 27) Suppose y = f(x) and y = g(x) are continuous functions which intersect at x = 1, x = 4 and x = 7…

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Q: 4) Write the taylor { Cn(x-2) n não series for f(x) = ex about x = 2 as

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