Two ships leave port at the same time t = 0. Ship A travels East at 2km/hr while ship B heads North-West (135 degrees relative to ship A) at 10 km/hr. Find the rate at which the distance between the two ships is increasing when t = 6?

Q: Differential Equation

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Q: Add or subtract as indicated and write the result in standard form. 15i - (12 - 11i)

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Q: Use Stoke’s Theorem to evaluate the line integral ∮C(y+2z)dx +(x+2z)dy +(x+2y)dz, where C is the cur...

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Q: a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the sequence is given by an=(n^2+3n+2...

A: We need to solve separately a. the sequence is given by an=1/(n^7/6)      lim n→∞ an=  b.  the seque...

Q: Evaluate ſ(r -)dr.

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Q: Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asympto...

A: We have given the rational function;

Q: How do you find the average value of a function over a region thatis expressed in polar coordinates?

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Q: Graph the polar equation: r = 1 + 2 sin θ.

A: We have given the polar equation; r = 1 + 2 sin θ

Q: Find the midpoint of the line segment with the given endpoints, (2, 6) and (-12, 4).

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Q: Verify that the power series in 5b does not converge at the endpoints x = ±1.

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Q: Find r′(t), r(t0), and r′(t0) for the given value of t0 =0 . Then sketch the curve represented by th...

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Q: finda. v . u, | v | , |u |b. the cosine of the angle between v and uc. the scalar component of u in ...

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Q: 5- Please I want answer of this question. Thanks

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Q: The volume, V, of a rectangular solid with length l, width w, and height h is given by the formula V...

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Q: Please remember this question has part a) b) c) and d)

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Q: The radius of a wheel rolling on the ground is 80 centimeters. If the wheel rotates through an angle...

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Q: Consider the region bounded above by the function z = 1/(x+3)2(y+7)2 and below by the xy plane for x...

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Q: Simplify exponential expression. 24x3y5/32x7y-9

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Q: For the function  q(x)=√x+8  find each of the following function values. q(x+h)

A: Given,  The function is q(x)=√x+8

Q: If a2+b2=117 and ab=54 Then find the value of ((a+b)/(a-b))

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Q: Let f be continuous on [a, b] and differentiable on (a, b). If there exists c in (a, b) such that f′...

A: The converse of the given statement is true but not the given statement. Counter Example: Consider f...

Q: 5-please see attached

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Q: solve for k. e2k = 4

A: Given: e2k = 4 To Find: Value of k Calculations: e2k = 4 Take natural logarithm both sides =>ln(e...

Q: Evaluate each of the following (a) lim (x -2x) x- 3x -4 (b) lim x+1 x'+6x +3 (c) lim x - 2x+1

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Q: Estimate the slope of the tangent line of the function ?(?)=squareroot(4t+1) at the point t=3. slope...

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Q: Write a definite integral that represents the area of the region. y1 = 3(x3 − x) y2 = 0

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Q: Evaluate

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Q: Towers of exponents The functions f(x) = (x*)* and g(x) = x(«*) are different functions. For example...

A: Given: To Find:  

Q: What is the Sandwich Theorem?

A: The squeeze theorem is also known as Sandwich theorem.  If a value of a limit is sandwiched or squee...

Q: True or false. If a=b then f(a)=f(b).

A: Given: If a = b then f(a) = f(b)   

Q: (r-2)(z²–3z+4) Use the graph of f(x) = (x-2)(z²–3z+4) (포-2) to evaluate lim- (포-2) O 2 3 does not ex...

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Q: A damped oscillator The displacement of a mass on a springsuspended from the ceiling is given by y =...

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Q: On February 6, 1971, Apollo 14 astronaut Alan Shepard hit the first ever golf shot on the moon. Supp...

A: Given equation is Where s(t) represents height of Shepard’s golf ball and ‘t’ represents the time i...

Q: To factor the trinomial x2 + 8x + 12, we look for two integers whose product is 12 and whose sum is ...

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Q: Differentiate between the output value and the input value?

A: Input value and output Value are the terms related to functions. Input and output values are variabl...

Q: Find the linearizations of the functionsat the given points. ƒ(x, y, z) = √2 cos x sin ( y + z) at (...

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Q: Determine the domain for the function of two variables ​

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

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Q: Factor the expression by grouping terms. x3 + 7x2 – 3x – 21

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Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the c...

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Q: Sketch the graph of a function f such that f′ > 0 for all x and the rate of change of the functio...

A: Given A function f with f’>0 and rate of change is decreasing.

Q: Write the standard form of the equation of the circle number 67&70

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Q: Calculus Question

A: Given: Graph of a function (a) To find: c = -8 Looking at the graph, we have:    

Q: Suppose the integral . Evaluate the following integralsor state that there is not enough information...

A: Given

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: We have given the curve; Formula to find the volume by cylindrical shells method is;

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

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Q: Find the exact value of the expression sin-1 (cos 2π/3). Do not use a calculator.

A: From unit circle we get cos 2π/3= -1/2

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.