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- Show that if ax2+bx+c=0 for all x, then a=b=c=0.B. Tables of Values Use the table of values to confirm whether the relations are linear, quadratic, or exponential. i) fix) = 2x + 3 i) g(x) = x- 2 iii) h(x) = 2* 1*t 2nd 2nd y y diff. diff. diff. diff. diff. Ratio -3 -3 -3 -2 -2 -2 -1 -1 -1 1 1 2 3. 3Let A=(−1,7),B=(2,−4),C=(5,5)A=(−1,7),B=(2,−4),C=(5,5), and D=(8,−5)D=(8,−5).Let f(x)f(x) be the function whose graph consists of the three line segments: AB,BC, and CD Evaluate the definite integral by interpreting it in terms of the signed area (the area between f(x) and the x-axis). ∫18 F(x)dx=
- Find the relationConsider the set S = {4x + 1, 2x 8, 4x + a}. The set S spans P2. %3D If t(x) = 8x - 9a +43 e P2, then t can be written as a linear combination of elements of S. That is, t(x) : (4a + 1) + b. (2a – 8) + c (-4x2 + a). = a. Determine a, b, and c a = b. C = %3D2. Let m(x) = 2x² - ax - 2 and n(x) = bx² + 2x + 5. The functions are combined to form the new function p(x) = m(x)n(x). Points (1,-40) and (-1, 24) satisfy the new function. Determine m(x) and n(x). Leave the final answer in exact form.
- Use the graph attached. The linear function is f(x). The quadratic function is g(x). Use the superposition principal to draw a graph of each. Complete the table of values for each case. Please graph a), b) and c) separately. I will mark labeled and scaled x-axis, labeled and scaled y-axis, table of valuesand curve for each case.a) y= f(x)+g(x)b)y= f(x)-g(x)c) y = f(x)g(x)Use the graph attached. The linear function is f(x). The quadratic function is g(x).Use the superposition principal to draw a graph of each. Complete the table of values for each case. Please graph a), b) and c) separately. I will mark labeled and scaled x-axis, labeled and scaled y-axis, table of valuesand curve for each case. a) y=f(x)+g(x) b) y=g(x)-f(x) c)y=f(x)g(x)Show directly that the given functions are linearly dependent on the real line. That is, find a nontrivial linear combination of the following functions that vanishes identically. f(x) = 6x, g(x) = 4x², h(x) = 8x10x² Enter the non-trivial linear combination. (32)6x +4x²+) (8x-10x²) = 0
- Use the graph attached. The linear function is f(x). The quadratic function is g(x).Use the superposition principal to draw a graph of each. Complete the table of values for each case. Pleasegraph a), b) and c) separately. I will mark labeled and scaled x-axis, labeled and scaled y-axis, table of valuesand curve for each case.a)y = f (x) + g (x)b) y= g(x) - f(x)c) y = f(x)g(x)1) write the linear function f for which f(1)=3 and f(4)=0 2) write the linear function f for which f(-2)=6 and f(4)=-93) write the linear function f for which f (1)=4 and f(x)=6write the linear function f for which f(1)=3 and f(6)=0 5) write the linear function f for which f(-3)=-8 and f(1)=-2A1. Milk or meat production Y per day is best explained by the inputs: feed needed per day in kg, X₁, and (number of) milk cows or calves, X2. Based on fitting the data for milk or meat production the revenue is modelled by a Cobb-Douglas function R(X₁, X₂) = pX₁X₂ constrained by relation h(X₁, X2) = C₁ X₁ + C2X₂ = c3. For milk production, the constraint expresses a relation between the average sale price c3 of milk (per day), the average price c₁ of a kg of feed and the price c2 of a milk cow (cost per day and based on the annual cost of a milk cow). For meat production, the constraint expresses a relation between the average sale price c3 of meat (per day), the average price c₁ of a kg of feed and the price c₂ of a calf (cost per day and based on the annual cost of a calf). The parameters for the two cases have been established by linear regression of data to be the following: C1 £4.00, C₂ = C2 £1.36/d, c3 = £5.38; regarding the milk case: p = 445.69, a = 0.346, b = 0.542, c₁ = and,…