Interest Formula. Suppose you work at a bank and the manager provides a new type of formula to calculate interest when merging two loans together. Suppose there are two loans with one interest rate at 4% and a second loan at 5%. The manager writes the first part of the formula for the new interest rate as e(4In(5) + 5ln(4)) Which of the following is equivalent to the manager's expression?

Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: Y1=25-82 = 25 – x², Y2 = 0 Y1 = Rotate @ y axis SHELL METHOD B V = 2 · T • (C·a - aº) · dE = G A…

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Q: A ball is being inflated such that the volume is increasing at a constant rate of 100cm3/s How fast…

A: Given  and

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Q: 3x2+10ху + 3y3 = = 11

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Q: Choose the point which shows the correct location for the polar coordinate (-3, 315°). 90° WIN 150°…

A: Since the given polar coordinates are ( -3, 315⁰ ) Hence to plot the given point we have to follow…

Q: Let u = (-3, 2), v (0,-1) and A = %D %3D %3D NOTE: Give ezact answers. (a) Find ||u|| relative to…

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Q: Sketch the region R of integration and switch the order of integration. /49-х2 f(x, y) dy dx y Show…

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Q: If f(x) = -2x^3 + 5x^2 - 3x - 3,  Find an expression for the second derivative f"(x).  f"(x) =

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Q: Verify Green's Theorem by evaluating both integrals aN aM y2 dx + x2 dA ду ax for the given path. C:…

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Q: Second Derivative Test. Consider the function f(x,y) = 2xy + 3ln(x) + 10y (a) The critical point of…

A: The given function,   f(x,y)=2xy+3ln(x)+10y

Q: 4 dx X-X-2Ą

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Q: Water is fallins on a surface vettins A Greuer arca that is expanäns at a rate of 9/S. hov fost is…

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Q: Fundamental Theorem of Calculus. The Fundamental Theorem of Calculus says: All of the statements are…

A: The given data is: The fundamental theorem of calculus says:

Q: */2 2 cosx dx 1+ (sin x)2 -n/2

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Q: Find the indefinite integral of f(x) = x^1/3

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Q: Given the power series Σ 2 3 A x" n =0 Use the technique that we covered in this lesson to force the…

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Q: Given the power series 2 5 A, x" n =0 Use the technique that we covered in this lesson to force the…

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Q: Given the power series expression Σ 4 n x" + 2 n (n - 2) x" n = 0 n = 3

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Q: Use the definition of the Laplace transform to compute L[f(t)]. For each, state the domain of…

A: Solve the following

Q: A firm's profit is determined by subtracting the cost of production from its revenues. Suppose we…

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Q: x- 1. a. Find the derivative of y =

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Q: cos x dx 1+2 sin x

A: SOLUTION-

Q: Use the situation below to answer the following problem: The population of Guinea pigs in a certain…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

A: Given: z=0z=x2x=0x=3y=0y=3

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: area =s(s-a)(s-b)(s-c) where s = (a+b+c)/2 s= (12+17+9)/2 s= 19 area = 19(19-12)(19-17)(19-9) area =…

Q: d'y If 4x2 + y = 40 then evaluate when = 3 and y = 2. (Answer accurate to two decimal places.)

A: Topic = Derivative

Q: Use the given acceleration function and initial conditions to find the velocity vector v(t), and…

A: Given:  a(t) = -cost i- sint jv(0) =j+k, r(o) = i

Q: Water is falling on a surface, wetting a circular area that is expanding at a rate of ? s How fast…

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Q: Sketch the curve with the given polar equation.

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Q: Determine wnea ther the sequence con verges diverges. Lf It converges Find or its limits. an : cos…

A: Given query is to find sequence converges or diverges.

Q: Object Height. Suppose an object is thrown straight up from the ground. The height after t seconds…

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Q: tch the vector field with its graph. F(x, y) = yi y 事 5 -5- -6+ y 1信 I 5 5 -5+

A: Given  F(x,y)=yi Option (1) is correct by given graph

Q: (a) Find the numbers at which the following function y =f (x) is discontinuous. And at which of…

A: We have to find the continuity and discontinuity points. According to our guidelines we can solve…

Q: 6 Tangent Line. If p(x) = 5x² + 5x4 + 4 %3D Then the equation of the tangent line to the function…

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Q: Solve the following differential equations of (2x* +y)dx+(x'y-x)dy = 0

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Q: find the indefinite integral of (3lnx)/x dx

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Q: Vx +7 lim x-2 x2 – 4x +4

A: Given,            limx→2x+7x2-4x+4

Q: Use an improper double integral to find the volume of the indicated solid. z = e-(x + y)/7 0s x < 00…

A: Volume , V = ∫∫R f(x,y) dy dx

Q: Textbook Videos [+] Given the function below f(x) = V 196x + 539 Find the equation of the tangent…

A: The given function is  f(x)=(-196x3+539)1/3, At x=1.

Q: If f(x) = (1 − x)2 and g(x) = 8 − x, find f(g(x)) and g(f(x)) f(g(x)) = g(f(x)) =

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Q: Choose the point which shows the correct location for the polar coordinate (3, 625°). 工 90° 2 WIN…

A: 625°=540°+85° 540° is on negative x axis. This means we need to move 85° anticlockwise of negative x…

Q: find a power series representation for this function?

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Q: 10 The following series is divergent. (-7)-/2 + 17 Select one: O True O False

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Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

A: This question is based on integration by parts.

Q: the sides with length x, there is a gap of 0.5x that has no fence. The goal is to find the…

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Q: The r.m.s. value of f(t) V2x – 1 across [-2,1] is Answer:

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

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Q: 4. Find the critical numbercs) for gx) =IRCX+1) t, en cuaracterize ealh, one as 1ocal min, or…

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Q: Let y=A cos x + B sinx is the solution of the differential equation

A: Follow the procedure given below.