1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement at 12th sec. If the acceleration of the particle is 6 cm/sec2, calculate the initial velocity.

Q: Solve (2y³ – x³) dx + 3xy² dy=0; y (1) = 1 O a. x² (5y³ x ³) = 4 b. ? (5y® — g - 23) x³) = 0 ○ c. x²…

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Q: Let f(x) = ln(x² + 16x + 68) f'(x) =

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Q: a polynomial a 17 minimal poly ent. dent.

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Q: The original quantity of a radioisotope was 100 mCi. How long will take to reduce to 75 mCi, if the…

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Q: In this question, consider the vectors 10 8 V1 ~- - ( ) - ~- - ( ) - - - () ---- () v2 = V3 = b and…

A: The objective of the question is determine the coefficient matrix" A" without simplifying.

Q: Evaluate O O In O In In a:² In |-2|³ |x + 1/² x+2/8/3 |x-1/5/3 O 3 ln x²-x-2+C x-1/5/3 x+2/8/3 x+7…

A: We have to evaluate ∫x+7x2-x-2dx.

Q: If C(x) = n=0 ∞ n=0 2n + 1 2n + 2 2n ²n and S(x) = ∞2n+2 2n + 3 n=0 -x²n+ find the power series of…

A: The given power series, Cx=∑n=0∞2n+12n+2x2n and Sx=∑n=0∞2n+22n+3x2n+1

Q: A body of mass 4 kg is projected vertically upward with an initial velocity 34 meters per second.…

A: Solution is given below:

Q: Use cylindrical coordinates to integrate f(x, y, z) = z over the intersection (i.e. all the volume…

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Q: Evaluate the indefinite integral. 2x - 3 (2x² - 6x + 1)6 dx + C

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Q: When completing the square for the quadratic equation shown below, how is c calculated?

A: Our Aim is to show how c is calculated when completing the square for thequadratic equation…

Q: Match each equation in rectangular coordinates with its equation in polar coordinates. x² + y² = =…

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Q: For a cost function, f(x, y), the minimum cost for a production of 56 is given by f(49, 84) = 1400,…

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Q: e cos(x) = 1 + sin(xy) 2 2

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Q: Find the derivative of the given function. COS ³ (1) g(x) = 2 cos3 O a) g'(x) = -3 cos² (sin() Ob)…

A: Given, g(x)=2 cos3x2

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given figure  with areas Now V=∫010f(x)dxV=∫03f(x)dx+∫35f(x)dx+∫57f(x)dx+∫710f(x)dx

Q: In addition to 1 and 21, what are the factors of 21? 3 and 6 3 and 7 10 and 11 1 and 20

A: Question: In addition to 1 and 21 , what are the factors of 21 ?

Q: The weekly marginal cost of producing x pairs of tennis shoes is given by the following function,…

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Q: Consider the function f(t) = 5 sec²(t) — 9t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: • S X √x²-4 dx

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Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

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Q: 3. Including all steps, charts, and derivations details, use the curve sketching methods to sketch…

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Q: I have a question about the problem solved…

A: The explanation of your query can be solved using the concept of function.

Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area

Q: Find two positive numbers with product 625 and whose sum is a minimum. Enter your answers in…

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Q: Consider points A(4, -1, 3), B(3, 1, 6), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

A: The given problem is solved below in detail.

Q: Find the inverse of f(x) = = 1 7x-3 at x = 1. Simplify your answer.

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Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

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Q: ● f sec³(x) dx ● ► f sec¹(x) dx • f sec³(x) dx MTH 32

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Q: Q6. Evaluate S¹, S₂ Sp dz dx dy.

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Q: Write the equation r²+r(10 sin 0-8 cos 0) = 0 in Cartesian coordinates and identify the…

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Q: Find the exact value of sin (77) 3 sin T 3

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Q: i) lim cos x-0 7 πCOS²x x²

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Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 4 8 16…

A: We know that the nth term of a geometric sequence is given by  a·rn-1 where a is the first term and…

Q: Compute the given integral. fcos¹ a a sin ædx = +C

A: Our Aim is to evaluate the integral given below:-∫cos7 (x) sin (x) dx -(i)

Q: the area of the ellipse 9x^2 + 8y^2 = 72 answer: 26.7

A: To Find: Area of the ellipse  9x2+8y2=72

Q: Consider the equations of two planes. x + y + z = 0, 8x - y + z-5=0 (a) Determine whether the planes…

A: This question can be solved using the concept of angle between two planes.

Q: Find the nth term of the arithmetic sequence with given first term a and common difference d. What…

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Q: fin(x² + 1)dx (Ans: xln(x² +1)−2x + 2 tan¯¹ x + C)

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Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 4 8 16…

A: Topic = Sequence

Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

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Q: Question 21 Consider the region in the third quadrant between the circles a² + y² = 4 and a² + y²…

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Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

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Q: 37. Problem Using polar coordinates, a point is at (7, 38). Find its rectangular coordinates. a)…

A: As per bertleby guideline I  have to solve only problem 37. For answer to others resubmit the…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find each of the following when f(x) = t³d =…

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Q: Find the first six partial sums S₁, S2, S3, S4, S5, S6 of the sequence whose nth term is given. 2,…

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Q: 8. Evaluate F. dr using Stoke's theorem when F = (2xy — x²)ī — x² − y² )ī and C is the boundary of…

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Q: 2x lim(x,y)→(0,0) x² + x + y²

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Q: Question 4 (a) Calculate the following: i. the area of the region in the first quadrant bounded by…

A: According to students we will solve second part for you.