In a cubic spline approximation assume that we know that S;(x) = 3 + 2x - x2 + 4x3 S+1(x) = a + bx + ca2 + x if 1

Q: Need only handwritten solution only (not typed one).

A: The given function is .We have to find the inverse function.

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: H.w Exl Let f(x)= 4x+2X+243and go)=3x+3x+3xx +4, where 2. t. f(x),900€75LX] Compute POX) +g (x).and…

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Q: 3 4 Find /(-12²¹ - ³ - -/-/- 2 √²) dax S 1x³ X x6 + C

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Q: Find the counterexample to show that the following conjecture is false. (x + Y)^2 = x^2 + y^2  is…

A: We need to show that the conjecture: x+y2=x2+y2 is false using a counter example. It is known that…

Q: Show that Q(4 - i) = Q(1 + i), where i = √-1.

A: To show that ℚ4-i=ℚ1+i. That is we need to show that ℚ4-i⊆ℚ1+i and ℚ1+i⊆ℚ4-i. Here i=-1 that is…

Q: Which polynomial function would have the end behaviour of as x→ too, Y→ co? a) f(x) = 7x³ - 8x* -…

A: Topic = Functions

Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

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Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: b) f(x) = x* + 29x² + 100.

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Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c>0. No sign change, by Descartes rule of…

Q: Algebraically, find all zeros of f(x) = 8x3-6x2-36x + 27 in simplest form, %3D 4. Format Font - Size…

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Q: Given the function h (x) = 9x¹ - x² A) Factor: h(x)= [Select] B) Determine the real zeros: [Select]…

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Q: 3. (12 points) Given f(x) = −0.25x3(x − 2)² (x + 1)4 - Find all of the zeros and state their…

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Q: Prove that 3x3+ 5x - 11 has a root between x=1 and x=2. Thanks!

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Q: In(7x – 1)= In(3x + 7)

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Show that Q[x]/⟨x 2 − 2⟩ ≅ Q[x]/⟨x 2 + 4x + 2⟩.

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Q: Consider the following problem: max(x + 1)(y + 1) {x,y} x + y< 10

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Q: 5. Let P(x) be the statement "x spends more than five hours every weekday in class," where the…

A: Introduction: Quantification is the application of numerical indicators to the subject or predicate…

Q: Find x, y, z, and w. X = y = Z= W = x 7 (2x y 6 - 5) (2x = ¹) ] - [ (²x - ² 9y Z 9 By + 8) ] 8 (w +…

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Q: 20. What is the largest possible value of the quadratic form 9(x1)2 + 7(x2)? +11(x3)² – 8x1x2 +…

A: What is the largest value of the quadratic form9x12+7x22+11x32-8x1x2+8x1x3if xTx=1.

Q: 3 x+2 x-3 2x+1 3x-1 2x+1

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Q: Show that x19 + x8 + 1 has multiple zeros in some extension of Z3.

A: To Show :x19+x8+1 has multiple zeroes in some extension of Z3.

Q: Which function is not quadratic? (O Ax) = (6x+ 9) -9 ()-x(x-9)(6x + 8) U Ax) = 7x + 8 Ax) = 6(x- 9)2

A: We have to check

Q: Which of the following is a factor of the cubic expression x'-2r -5x+6? (1) x+1 (3) x-3 (2) x-2 (4)…

A: (x-3) is the factor of given equation.

Q: 2.x2 + 2x + 9 dr J (x – 2)(x² + 4x + 9)

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Q: Express the polynomial in the form an(x - ₁)(x-₂)(x-rn). x² + 11

A: The polynomial is given by x2+11 To determine: The expression of the polynomial in factored form.

Q: 4. Find the roots of the following over C (a) x2 + 18x + 97 (b) x3 +3x2 - 6x -8 yes that is a cubic…

A: a)  x2+18x+97 Using the formula, x=-b±b2-4ac2a x=-18±324-3882x=-18±-642x=-18±i82x=-9±4i   c)…