1. A navigator wishes an aircraft to fly W22°N with a groundspeed of 300km/h. There is a 60km/h wind from the direction S15°W. a) Draw a vector diagram to illustrate the situation. b) Calculate the direction and the airspeed that the navigator should use. c) How long will it take the aircraft to travel a distance of 2000km?,

Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: 5. Write an expression equal to - log. (c) · log (b) |using exactly one log. (hint: the base of the…

A: To answer the given question of logarithms.

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A:

Q: raluate the following definite integrals.

A: Topic:- definite integration

Q: Solve the system of differential equations x' 4x – 15y ly' 2а — 7у - x(0) = 3, y(0) = 1 x(t) = y(t)…

A: We solve the given problem using method of elimination by use of operator D  .

Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

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Q: Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 74-kilometer mark…

A: Solution is done in step 2

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A: Given :

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A: Explanation of the answer is as follows

Q: 162 + 1 Compute the given integral. 1 +C 16x2 + 1

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Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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A: The critical point of a function: A critical point on the graph of a function y = f(t) is a point t,…

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Q: d f'(3).

A:

Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

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A: We need to find points of intersection.

Q: Let the functions 13:R-¬R, with 3 メー X2 Proove that. V(4xs) =3 (Vx{)-4 (Vx)

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Q: teger n is odd if and only if 3n + 1 is even.

A: Here I am providing my handwritten solution

Q: dr a 2 1 +3

A:

Q: -3 2. (2x+4)3 8x dX use integration by parts and then find the value of definite integral.

A: A detailed solution is given below.

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Q: Convergent. or divergent dx ra5-x 3 25-X

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Q: Evaluate the integral 7x sin y dy dx. 00 The value is (Type an exact answer, using x as needed.)

A:

Q: -3

A: topic- definite integral

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Q: -dx is an improper integral. A) True B) False

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Q: Determine the directional derivative of f at the specified point and direction. f(x) = x³ + y³ – 3x2…

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Q: Use the graph to complete the following.

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Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: Find the polar equution for the cartesian curve r=8 sin o Cos o r=8 sec e tan E r=8 sine tan E r=8…

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Q: Question 5 Find parametric equations for the line described below. The line through the points P(-1,…

A: Given: P-1,-1,-1   and 6i-3j+3k

Q: If f(x) = [ V19+ t² dt , find f'(3)

A:

Q: Use the summation properties and rules to evaluate the series. 5 E (312 - 21 + 6) i= 1 5 E (31? - 21…

A: Use the summation properties and rules to evaluate the series.

Q: How much work is required to pump all the water from a right circular cylindrical tank, that is 8…

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Q: ph of the parabola to fill in the table. 10- (a) Does the parabola open upward or downward? O=0 6+…

A: Given query is to find characteristics of parabola.

Q: Differentiate. 9. y e 10. y- e

A:

Q: Suppose that a, b, and c are unknown constants such that f(x) = x² + ax +b and g(x) = e3z-3) +c are…

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Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

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Q: Evaluate the integral directly by integration with respect to x and y. 4 x= (y/4)+ 1 4x - y -dxdy 4…

A: We have to find the value of the double integral ∫04∫x=y4x=y4+14x-y4dxdy Since dx present first in…

Q: Q3) Apply the logarithmic differentiation to find the derivatives of: x+1 y=(sinx-x)**

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Q: + 3x² 4)dx

A: Given query is to find the value of the integral.

Q: Solve the following differential equations of e • dx+2(xe" – y)dy = 0;

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Q: 1 Given Rn 7+i- cos 7+ i- , express the limit as n → ∞ as a definite integral, n i=1

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Q: Evaluate the integral using the following values. 8 8. x3 dx = 960, x dx = 24, dx = 4 x3 dx

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Q: Find T(t) and N(t) at the given poi: x = e cos t, y=e' sin t, z = %3D %3D T(0) = N(0) = %3D

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Q: Without graphing, find the horizontal and vertical asymptotes, if any, of the curves. Show your…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

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Q: 3. The tens digit of a two-digit number is thrice the units digit and their difference is 6. Find…

A: Solution: Let unit digit =x  and tenth digit=y  Now According to question: y=3x ---------(I) y-x=6…