Give an equation of the form f(x)= a to define the exponential function whose graph contains the point (2,81). f(x) =D

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A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts fo...

Q: Problem 5. A consumer purchases quantities of two commodities, fruit and chocolate, each month. The ...

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Q: O which of the following valve of S vill not show that lim Xーダ a) min (1,1E-i -1) 6) min (1, JE -1) ...

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Q: In the linear differential equation of the form, Po (x)y") +Pp1 (x)y(n-) +...+Pr1 (x)y' +P, (x)y = R...

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Q: Consider the binomial distribution with n trials and AS) - p. (a) Show that Ply) Dly- 1) (n-v+ 1P fo...

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Q: Solve the system Y' = AY, Y'(0) = Y, by computing

A: Given,         Y'=AY, Y'(0)=Y0 Where,            A=23-1-2, and  Y0=-42

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Q: j) Draw the graph of y -3(x+5)² - 4. Label the x and y intercepts (with actual values) on the graph.

A: To draw the graph of the below equation and to label x and y-intercepts. y=−3x+52−4

Q: Solve the following differential equations: dy y%3D =Vx² +y² . dx

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Q: Calculate the perimeter and area of the shaded region in the drawing of two circles below. Show all ...

A: Area of the shared region

Q: If A and B are 3 × 3 matrices, det(A) = 1, det(B) = -2, then det(AB) = -2 det(-3A) = det(A") = det(B...

A: Given, Two square matrices A and B of order 3, such that det(A)=1, det(B)=-2 1: Since det(AB)=det(A)...

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Q: Solve the following  complex numbers in their rectangular form. Use the given formula and use 4 deci...

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Q: (3) (a) Let p be a polynomial of degree n with n distinct root c1,€2, ...,Ca. Show that 1 1 p(r) F (...

A: The complete solutions are given below

Q: Jared invested $1,900 at the beginning of every 6 months in an RRSP for 11 years. For the first 4 ye...

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Q: 1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k F...

A: Here the given matrices are                                      A=abcd and B=dcba We have to show t...

Q: ogy of the land on nodule tilt and azim

A: The topology effect is given as,

Q: Q3: Write the equation in slope-intercept form of the line that is parallel to the graph of each equ...

A: 1. Given equation: y=3x+6 Concept: Now we know that the slope intercept form of the equation is in t...

Q: Spanning Sets In Exercises 19–24, determine whether the set S spans R³. If the set does not span R³,...

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Q: Given the equation 9x^2 + 199 + 100y = 108x-25y^2, it is verified that its center (h, k) and semi-ma...

A: Given the equation 9x2+199+100y=108x-25y2

Q: x dx + (y - 2x) dy = 0 %3D

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Q: 7. Given the space curve r(t) = (4 sin t,4 cos t, 10t), Find T, N, B, and T(torsion)

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Q: Prove the ratio test in the following steps. Assume that ) `ak satisfies ap + 0. Assume furthermore ...

A: We will use the basic knowledge of limits, sequences, and series of real numbers to answer this ques...

Q: used to find the Roots a he initial guess is x 1

A: Given as,

Q: If Y and Y are the first and last column vectors in the inverse of a [1 -1 2] matrix A = 0 3 2 then ...

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Q: Twenty students in a group of 40 at UB High enrolled in Science. Eleven students enrolled in Latin. ...

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Q: Directions: Find the equations given the derivatives. Encircle the letter of your answer. 1. Which o...

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Q: Prove using Rules of Inference that: ~[(P→~Q)^ (Q → ~ P] = PAQ State each law that you use for the p...

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Q: Drawa direction field for the given differential equation. Based on the direction field, deternine t...

A: We will use basic knowledge of calculus to answer this question.  

Q: A pair of dice is rolled. let X be the sum of the number of dots onthe top faces. The table below sh...

A: We have to find probability that the sum is at least 8.

Q: Evaluate: 2

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2) abo...

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Q: Xp X,2s>

A: We have to evaluate the definite integral ∫csc6xdx or antiderivative of  csc6x. As per the definitio...

Q: Testing for Linear Independence In Exercises 27-40, determine whether the set S is linearly independ...

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Q: Find the characteristic polynomial of the matrix A. 9 5 5 9. a. 56+ 18A-X2 b. 2 - 18A+25 c. 2 + 18A ...

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Q: The production function for a firm is p(x, y) = 72x"y"", where x and y are the number of units of la...

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Q: A pair of dice is rol d. let X be the sum of the number of dots onthe top faces. The table below sho...

A: Given A pair of dice rolled. we have to find the probability that sum is atmost 10.

Q: Find the supremum and infimum of the set {r € R[10/T – 1 > 0}, if they exist. If they exist, provide...

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Q: Let f: X → Y and g : Y → Z be functions. (a) Show that if g of is one-to-one (or "injective"), then ...

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Q: 3. 6y" – 7y' – 5y = 2x + e-5 [5 marks]

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Q: In the figure below, Y W and XZ are diameters of circle A. What is the arc measure of major arc Y W ...

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Q: Solve the pollowing: () (^) 2+j =j(xtjy) X = ? y=? (1) (2+j)(3-j2) = a+jb () (x-j2y) -(y-j«)-2tj a:?...

A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy compa...

Q: Determine if the following argument is valid or invalid. State if valid or invalid and the the law o...

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Q: Solve the following  inverse trigonometric and hyperbolic complex numbers in their rectangular form....

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Q: Determine whether the polygons to the right are similar. If so, write a similarity statement and giv...

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Q: Explaining Why a Set Is Not a Basis In Exercises 15-22, explain why S is not a basis for R. 22. S = ...

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Q: Give an example of a real life situation that illustrates combination. a. Formulate a problem b. S...

A: We have to solve given combination problem.

Q: 3. Evaluate: e-x²+2x dx (Hint: let t = (x – 1)²) |

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Q: The special integrating factor of y'dx+(3xy + y² -1dy = 0 is: a. e3y b. Зу С. У d. y-3

A: Solution

Q: H If drciso , then find the heal part and the imuginary part, i r=l; n=3

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