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Q: Let a, b, and c be real numbers such that a + 2b + c = 4. Find the maximum value of (ab + bc + ca).

A: Given that a,b,c∈ℝ such that a+2b+c=4            (1) we have to find the maximum value of  ab+bc+ca…

Q: 16) A quadratic function is given as f(x) - x+8x + 6. Rewrite the given function in an equivalent…

A: since you have asked multiple questions in single request so we will be answering only first…

Q: Let a, b, and c be real numbers such that a + 2b + c = 4. Find the maximum value of (ab + bc + ca).

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Q: Solve the faliewing Optimization preblm by usihg The Lagarange Mulkiplier Me thof Mimimize fexioMr)…

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Q: Solve the linear programming problem. Maximize z=10x+10y subject to 6x+6y2102 15x-13y 287 x + y ≤ 45…

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Q: g(x) = 8 : ²^_ (4,-4)

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Q: bx3 - 24x + 1 Зах4 f(x) : - 4 If the function has an extremum at x = 2 and a turning point at x =1,…

A: Given, f(x)=3ax4/4 -bx3/3 -24x +1

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A: Given functtion, gx=3x-3x2-122x+6

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Q: Find the minimum value of f(x,y.z) = x? +y² +z? subject to 6x + 2y – 4z = - 56. The value of f at…

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Q: Give an example that: the absolute maximum is not a local minimum.

A: Consider an example of the function:  in a interval [-2,3]

Q: A quartic function has zeros -5, ½, 3 and 9.   a) Determine an equation for the family of quartic…

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Q: 19. Suppose that A0)=2 and f"(x)<-3 for all values of x. How large can A3) possibly be? A) -7 B) -1…

A: "Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Every letter below corresponds to a different digit. Note that MPOW is a 4-digit number where M ±0.…

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Q: Optimize Z= In(4x2 - 24x + 2y2 - 20y) optimize the function. Find Zx, Zy, Zxx, Zyy, Zxy. Comment…

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Q: so² + 15t+ 2, where t is the time in seconds, and h is the height i How long is a puck in the air if…

A: It is given that,  The given model is,  h(t)=-5t2+15t+2

Q: Let a, b, and c be real numbers such that a + 2b + c = 4. Find the maximum value of (ab + bc + ca).

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Q: Fast please..

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Q: Let a, b, and c be real numbers such that a + 2b + c = 4. Find the maximum value of (ab + bc + ca).

A: Hint:  Using Lagrange Multiplier

Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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Q: A farmer is fencing a rectangular area for cattle and uses a straight portion of a river as one side…

A: A farmer is fencing a rectangular area for cattle and uses a straight portion  of the river as one…