66. Let f(x) = ax? + bx + c (a + 0). By completing the square in x, show that 4aс - f(x) = a x + 2a 4а ban blne

Q: Discuss the nature of the quadratic form x2+4xy+6xz-y2+2yz+4z2

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Q: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: 3. Find expressions for the quadratic functions whose graphs are shown. (-2, 2), (0, 1) (4, 2)

A: Given that:

Q: 9. Determine the equation of the quadratic function that has x-intercepts 1+ V3 and 1- V3 and passes…

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Q: art of z- 2z, if z = a+ib ?

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Q: 35. By completing the square in the quadratic x² + x + 1 and making a substitution, evaluate dx x² +…

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Q: 4. Find the quadratic function f(x) Arches if it passes through the points (0, 0), (1, 7.6), (9, 6).…

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Q: Maximize B=6xy^2​, where x and y are positive numbers such that x+y^2=4.

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Q: (c) Express the quadratic form Q(x1,42. 43) = 6xj + 3x+3x-4xx2 - 21213 + 4xar1 to the sum of square,…

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Q: Show that V12 is irrational

A: A Rational Number is a number that can be written in terms of P/Q.  An irrational number can not be…

Q: - Classify the quadratic forms below. 9(x1)? - 8x1x2 + 3(x2)? b. -5(x,)² + 4x,x,- 2(x,)2 a.

A: Here is the solution of the given problem. Quadratic Forms:

Q: Compate the Cantiderivative of fox) = x²+4 xナ4 %3D x³+ax

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Q: 2 If f(x) = x+ 8x + 12 and g(x) = x + 6x + 8 then (2) (Make sure your answer is fully simplified %3D…

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Q: Q 4. (a). Show that fog = 4x² – 1, if ƒ(x) = 4x – 5 and g(x) = x² +1.

A: a. Given: The functions fx=4x-5 and gx=x2+1, To find: f∘g=4x2-1, Formula used: (f∘g)(x)=f(gx).

Q: Consider the following quadratics: Q1:x2+y2-5z2-9=0 Q2:x2+y2-8z2=0 Calculate the distance of the set…

A: Given Q1:x2+y2-5z2-9=0Q2:x2+y2-8z2=0

Q: In a study to determine the effect of vehicle weight in tons (x1) and engine displacement in in³…

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Q: If a quadratic function has zeros at and . What binomials must be used? (3x+1) and (3x– 5) or (x+ -)…

A: on using factoring binomials we get

Q: 4. Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not…

A: A cubic function is one in the form f(x)=ax3+bx2+cx+d. The "basic" cubic function, f(x)=x3 , is…

Q: If web₁x-b₂y-b3z, w= where b₁,b2, b3 are constants and b² + b² + b = 1. Show that 8² w 8² w 8² w əx²…

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Q: What happens to y=fx) when you replace y with -4y? O vertical stretch by a factor of 4 and a…

A: Vertical stretch: The graph of y=dfx is the vertical stretch of the graph of y=fx by a factor d,…

Q: What is the largest number k for which 2x + 3y = 20 and 3x + 4y = k have the same number of positive…

A: Given: 2x+3y=20...............eq(1) 3x+4y=k..................eq(2)   To find:What is the largest…

Q: Show that Live - de = In(V5- 2). -1 Vx2 + 2x +2

A: We need to show that, ∫-11-dxx2+2x+2=ln5-2

Q: prove using the IVT. 2x + 3x = 4x has a solution.

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Q: 1) ciated with the quadratic form )² – 5x,x, + 6(x,)2.

A: We have to solve the problem

Q: 1 zp- A) B) is larger than 17

A: The given integral is ∫1∞1x5+4 dx We have to determine weather the given integral is larger than…

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: et) of a ball thrown by a child is 1 -x² + 6x + 3 14 -

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Q: 19. What is the largest possible value of the quadratic form 5x + 8x3 if x = (x1, x2) and x"x = 1,…

A: We use the fact mentioned in solution.

Q: a. Prove that 8s + 13 L-1 s2 + 4s – 5) + 45 – 5 -7(7e" + 9e-st) by using completing the square…

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Q: 4x+4

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Q: Find the value of x in square EFGH. ZEZF = 3x -3 %3D

A: given that EFGH is a square and ∠EZF=3x-3 find x

Q: Use the quadratic formula to show that tthe finction flu=ax2=3A+7 does not produce on cutput of…

A: f(x) = 2x2 -3x +7

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: Use Cramer's rule and solve 6x-4z=26 7x+8y+5z=122 9x-9y=54

A: Use Cramer’srule and solve.

Q: 2. Julio knows that he makes his best serve when he holds his racket at least 3 m high. Is he…

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Q: 4. a. Prove that 8s + 13 L-1 (s² + 4s – 5) 5(7et +9e-5t) by using completing the square method.

A: Since there are two questions posted, we will answer the first question 4.a). If you want the…

Q: 3. Is (3,8) a point on y = 3x - 1?

A: if (3,8) is a point on the line y =3x-1 then it should satisfy the equation y =3x-18=33-18 =9-18 =8…

Q: Evaluate the integral 1 xp- 9x² + 6x – 8 by first completing the square and using the substitution u…

A: The given integral is: ∫19x2+6x-8dx To evaluate this integral, first, make the square by adding and…

Q: 24 Use the diagram to solve for x, FG and FH. 4x 7x +6 FG = FH = 6 8 9 DELL -> 23 $ & 3 4 7 8.

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Q: 5lim V3+x-J3 8→0

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Q: 32. If WY = 15x - 2 and XZ = 9x + 10, find WY. DELL

A: Here I am solving question 1 if you want the answer of second question repost the another question…

Q: Show that: If Iz| = 1, then: %3D z3 + 4z? – 4| Im < 3 z + 4

A: Since |z|=1 Let z=r(cos∅+isin∅) ⇒|r(cos∅+isin∅)|=1 ⇒r=1 Now

Q: 3) Let B = Find Least 10 - I- square salution of Bx = 6

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Q: Assume that y = 69 when x = -3, y=-72 when x = 15 and y = 99 when x = 27. If we…

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Q: 2,5 is equal to . V162x O True O False

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Q: 2 Find the maximum value of 7x1 + X2 + X3 + 7x4 subject to the condition that x +x, +x +x = 100.

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Q: What is the zero-product principle?

A: Zero product principle states that if ab=0  then a=0 or b=0 We apply zero product principle while…

Q: Use cubic interpolation method with two points to find µ2 , where a = 0.6, h = 0. 1, ɛ = 0. 001 and…

A: Given: Let's determine μ2 using cubic interpolation method,  here a=0.6, h=0.1, ε=0.001,ϕι=-2.7

Q: 6. Find all real solutions to V3x +1+ V9x + 4 = 11. Show your work!

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Q: 5. ) If 3x + 4yi = Z2, what is x + y equal to?

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