How much money should David invest today into a fund that earns interest at 3.50% compounded quarterly, if he wants to receive $7,500 at the end of every 6 months for the next 6 years? $73,020.00 (X) Round to the nearest cent

Q: ( (tano-1)² do

A: Given ∫[tanθ-1]2 dθTo evaluate the integral:

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A:

Q: Use the chain rule to find dz/t. z = x² + y² + xy, x = sint, y = et

A: Here we will find dz/dt,

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A: According to question,Given Integral,Let I =∫2x+1 lnx2 + 2x + 3x2 + 2x + 3 dx

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A: We have to write an equation of given graph.

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Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: Given

Q: this is incorrect please resvole

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A: Calculate the rate in the following way:-

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Q: What are all the values of k for which f* x² dx = 0? 3 -3 and 3 0

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Q: B)Is w = Zez analytical function or not?

A: In this question, we want to know whether the given function is analytic or not.

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A:

Q: B)Prove (cose + i sine)" = cosne + i sin no

A: Solution is given below:

Q: 10. Find r(t) if = (4t3+ 4t)i + 6tj + 3t²k, r(0) =i+j.

A: We have to find out r

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Q: B)Solve the differential equation **

A: Here, the given DE is: dydx=x6+4yx⇒dydx=x5+4xy⇒dydx-4xy=x5 which is a linear DE with P(x)=-4x&…

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Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

A: The solution is given below

Q: Q1A)The vectors A = 3i+j+ 4k, B= 2i-3j-k, find vector normal to A and In plane of A and, B.…

A: Let's call the vector to be found is C. C vector will be normal to both vector and A and B. we can…

Q: At point (1,-1,2). 4

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Q: Sketch the graph off and use your sketch to find the absolute and local maximum and minimum values…

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Q: Suppose that f is a function that is continuous at a number c. Which of the following statements I,…

A: use the definition of a continuous function

Q: 11. Find the angle between the planes: 4y + 3z = -12 and 3x +2y + 6z = 6.

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Q: Q6A)If y sin find Zxy.

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Q: lim x²+3x sin x x-0 0 3 01 O does not exist 0 0

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Q: S(x + ex+1) dx 0 2. Sx5¹2 (x³ + x² - 7) dx 0 2x + 1 3. dx 2 0 e

A: Topic = Integration

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Q: Use algebra to evaluate the following limits. 3x4 - 5x² x² 2x² - 2x-12 a) lim x-0 b) lim x+3 x²-9

A: Here we will use basic limit laws and algebra to find the limits.

Q: Use partial fractions to find the inverse Laplace transforms of the following functions 11-3s 1.…

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Q: 8. Find the vector equation of the line that passes through P(-3,5) and is parallel to the line 3x -…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: (b) Use L'Hopital's Rule to find the following limits: e-1 x (i) limx→0 (ii). lim-0 x-y fl (x > 0, y…

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Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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Q: ..suspended a mass of 10 kg from a ceiling by two cords that make angles of 30° and 45° to the…

A: This question can be solved using the concept of component form of vectors.

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

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Q: What is the area of a quadrilateral with vertices at (-2,-6), (1,-6), (-2,0), and (1,0)? Enter the…

A:

Q: Q6A)If y=sin-¹ find Zxy.

A: partial derivative

Q: Find the general solution of the following differential equation. 4y" +36y' +81y = 0 NOTE: Use c₁…

A:

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i-3j-k, find vector normal to A and In plane of A and, B.

A: See the details solution in below

Q: On which of the following interval is f(x) S O (0, +∞0) ○ (2, +∞) O [2, +∞0) 0 (-∞, +∞0) 1 x-2…

A: We will the fact that root value should be positive.

Q: 3. y" + y = sin x

A:

Q: (a) Assume that f(x, y, z) and F(x, y, z) are arbitrary differentiable functions such that f(x, y,…

A: Given

Q: the complex number 6√3+6i in polar form O 12(cos(n/6)+isin(n/6) O 12(cos(n/4)+isin(n/4) O…

A: As we know that; The complex number z=a+ib can be written as polar form; z=rcosθ+isinθ Where;…

Q: A price p (in dollars) and demand x for a product are related by2x2−8xp+50p2=11400. If the price is…

A:

Q: d²y dx² 2 (2x-3)² Find y = O O d²y dx² d²y dx² d²y dx² O d'y dx² = = = = 12 (2x-3)¹ -12 (2x-3)4 48…

A: Given

Q: Determine the longest interval in which the given initial value problem is certain to have a unique…

A:

Q: Solve using Inverse Operaators. y"" - y' = 4e-x + 3e2x; Particular Solution: Y=C₁+ C₂ eax + C3 ebx…

A: See the details solution in below