A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/sec. How long it will take for the stone to reach the ground?

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i + 7 sin(t)j +…

A: Here we will find the curvature and radius of curvature,

Q: Use substitution to find the Taylor series at x=0 of the function e -9x. Choose the correct Taylor…

A: Explanation of the answer is as follows

Q: Find V · (F × G), if F(x, y, z) = 3ri+j+6yk and G(x, y, z) = xi+ yj – zk. V· (F × G) ||

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Q: For the function f (x) = xe¬*: a) Determine the coordinates of the critical point. Use exact values.…

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Q: 1 Find the equation of the line tangent to y = e 4X at x = - In 3. 4 The equation of the line…

A: We have to find the equation of tangent.

Q: 5n

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Q: Please do it right

A: We have to solve

Q: Find the standard form of the equation of the ellipse with the given characteristics.

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A: Green's theorem states that for  counterclockwise direction∮CPdx+Qdy=∬R∂P∂y-∂Q∂xdxdy

Q: Evaluate the integral. yz dx dz dy O8 68 3.

A: We have to evaluate the given integral

Q: Evaluate the line integral |-ydx + xdy along the curve C: y = 30x from (30, 30) to (0,0). %3D NOTE:…

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Q: The point P(p, 1), where p > 0, lies on the curve x² + 2xy³ – 3y* = 0. a) Calculate the value of p.…

A: Since point , P(p,1) lies on the given curve, therefore this point will satisfy the curve .Using…

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. | (4x2 + 9) dx…

A: To find the value of definite integral using  fundamental theorem of calculus.

Q: Question 6 of 17 Find an equation of the parabola with vertex (1, 4) and directrix x=-3.

A: Given that vertex of parabola (1,4) and directrix x=-3  To find the question of parabola  Again…

Q: Find the inverse Laplace transform: 1 (s(s² + 1).

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Q: 00 2+n Does the series converge absolutely, converge conditionally, or diverge? 6+n n=1 Choose the…

A: The given series is: ∑n=1∞(-1)n+12+n6+n Let, an=(-1)n+12+n6+n; n≥1

Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

A: topic- differential equations

Q: 1. The point P(p, 1), where p>0, lies on the curve x? + 2xy -:y* = 0. a) Calculate the value of p.…

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Q: 5. Two people are 50 feet apart. One of them starts walking north at a rate so that the angle shown…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Given: f(t)=-16t2+444t+8

Q: We need to enclose a rectangular field with a fence. We have 500 ft. of fencing material and a…

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Q: olve the following differential equations of

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n5 +…

A: Use alternating series test for checking the convergence of series .

Q: Ql use the gauss elemen tution find? X-3Y+42=D0 2W-2x+3 -b+4X+34-82=0

A: Firstly , write the given system of equation in augmented matrix form and after that apply row…

Q: 7. For what values of m does the function y = e™* satisfying the following equation y" – 3y' – 10y =…

A: We have to find the values of m.

Q: h) (3X 9'+4y)dx + (3 X'9 +2x) dj = 0 I) sin X dy dx Sin 2X -y cos X

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Q: Find V. (F x G), if F(x, y, z) = 3.xi +j+ 6yk and G(x, y, z) = xi + yj – zk. V· (F x G)

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Q: Find the equation of the tangent line to the curve at the point (5,3) given that x2+xy+2y2=58

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Q: 2003 yo0, Find he Let, hC), 9 gph of h la) where the fangenf bnd is or2ontal where the foogen…

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Q: A particle is moving in a straight line according to the position function s(t) = t³ – 6r² +9t + 5,…

A: Given: s(t)=t3-6t2+9t+5,t≥0 d)After breaking once the velocity of the particle becomes zero.i.e. v=0…

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n6 n-…

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Q: 7 Does the series 2 converge or diverge? n= 1 Choose the correct answer below. O A. The series…

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Q: 3. Use trigonometric substitution to evaluate Sx V9 – x² dx

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Q: 2-V8

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Q: Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformations.…

A: Given :

Q: Suppose that f(x) is a differentiable function satisfying the data in the table below on the…

A: Left -hand approximationa=4 , b=12  ,n=4∆x=b-an∆x=12-44=84=2Subintervals are 4,6,6,8 , 8,10 ,…

Q: Describe the graph of the equation. r = 3 cos t i – 18 sin tj+ k O An ellipse in the plane z = 1,…

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Q: Use the function f and the given real number a to find (f ¯-)'(a). (Hint: See Example 5. If an…

A: Given:      f(x) = ( x+7) / (x+2)

Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

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Q: Use the figure to give approximate values for the following (if they exist). Enter your answer as a…

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Q: S- (1+x²) = x*dx Using trigonometric substitution, tan ode A sece sin Ode B cose S tan od0 sec20 sec…

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Q: Calculate z=e^-a sin(x)+10 √y  for a=5 , x=2 and y=8 in decimal value

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Q: Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the…

A: Write an iterated triple integral in the order dz dy dx for the volume of the region in the first…

Q: QUESTION 13 nd all possible corner points of the feasible region described by the following system…

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Q: x³dx is equivalent to Using trigonometric substitution, Vx² –4 A 6/ tan*0 seco do B) None © 8 sec0…

A: I am attaching image so that you understand each and every step.

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx

A: see below the answer and calculation with steps

Q: Find the standard form of the equation of the parabola with the given characteristics and vertex at…

A: The directrix is the line y =-3, this is a horizontal line. The vertex is at the origin (0,0), so…

Q: Use a change of variables or the table to evaluate the following definite integral. 10 e 2X dx 2x…

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Q: cosxdx 3T +Sinx

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Q: 5. Find the area of the region bounded by the xr-axis and the graph of f(x)= -over the interval (-o.…

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