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Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point. ...

A: Given that a hot air balloon is rising vertically is tracked by an observer located 7km from the lif...

Q: Find the arc length

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Q: In(t) Let y = %3D (a) ( Find y' using the quotient rule. (b) Rewrite y as a product, then find y' us...

A: Given that y=lntt3. (a) Compute the derivative using quotient rule. y'=lntt3'=t3lnt'-lntt3't32=t3t-3...

Q: Explain how the graph of g is obtained from the graph of f. (a) f(x) = x , g(x) = − ...

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Q: Question attached

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Q: Find the area of the surface generated by revolving the curve x = 2 cos θ, y = 2 sin θ, 0 ≤ ...

A: If x=f(t), y=f(t) then surface area is, About x axis: S=2π∫abydxdt2+dydt2dt About y axis: S=2π∫abxdx...

Q: 1. Divide: 1296 + 4

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Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how ...

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Q: If x^2/36 + y^2/25 = 1 and y(1) = 4.93, find y’(1) by implicit differentiation.

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Q: I have two functions. Function f models total world population x years after 2000 and function g mod...

A: I have two functions. Function f models total world population x years after 2000 and function g mod...

Q: A potato is launched vertically upward with an initial velocity of 116 feet per second from a potato...

A: Given:s(t)=-16t2+116t+96

Q: If x2 + y? = 36 and dx/dt = 3, find dyldt when y is positive and (a) x = 0: dyldt = (b) x = 1: dyldt...

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Q: A breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to th...

A: Given : Initial amount present is 190 pounds Remaining after 10 years is 0.9997 * 190 pounds we need...

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your a...

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Q: Explain how to use the graph of f(x) = 2x to obtain the graph of g(x) = log2 x.

A: given: the function f(x)=2x the other function is g(x)=log2x. let the given function f(x)=2x as y. t...

Q: The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day,...

A: Consider x and y as the number of children and adults who entered the park. On a certain day 2200 pe...

Q: ***The answer is NOT (5√2, 10) Identify the open intervals on which the function is decreasing. (En...

A: Let f(x)=y. Differentiate the function with respect to x, to find f'(x). fx=y=x100-x2f'x=x12100-x212...

Q: Find the implicit differentiation

A: Using differentiation formula:ddxxn=n.xn-1

Q: A rectangle is bounded by the x-axis and a parabola defined by y= 4-x. Refer to the figure below. No...

A: Given, a rectangle is bounded by the x-axis and a parabola defined by y=4-x2and area of the rectangl...

Q: Use logarithmic differentiation to find the derivative of the function. y = (cos(9x))x

A: Given y=cos9xx First take natural logarithm on both sides y=cos9xxlny=lncos9xxlny=xlncos9x ...

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: If T(æ) = + is the temperature of a runner (in Fahrenheit) at a distance x from the start line (in m...

A: Given: The function of temperature of a runner at a distance x is given as T(x)=1x+1x9. The objectiv...

Q: Problem 6: Find the equation (in symmetric form) for the line of intersection between the following ...

A: Solution :-

Q: Express number as ratio of the integers:

A: consider the equation

Q: Maximizing Profits An apartment complex has 100 two-bedroom units. The monthly profit (in dollars) ...

A: The given function is p(x)=-10x2+1660x-4700. To maximize the profit differentiate the function with ...

Q: Consider the function on the interval (0, 2π). f(x)=x/2+cosx a. Find the open intervals on which th...

A: given that f(x)=(x/2)+cosx we need to find: (a) the open interval on which the function is increasin...

Q: the gaming company t games recently released their new game among us the cost of production x games ...

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Q: Find the absolute extrema of f(r) = x/4 x on the interval [-1, 2]

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Q: Use a graphing utility to graph the equation and show that the given line is an asymptote of the gra...

A: Given, Polar equation r=2-secθ and asymptote x=-1

Q: Write the equation of the line that is tangent to the function y = xVx and is parallel to y = 2x + 1

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Q: Please draw the picture as well and solve 3A, B, and C

A: given that a box has a sides of length of x=3m ,y=7m and z=1m. and also the rate of change of this l...

Q: ) Given that f(x) = 2x + cos(x) is one-to-one, use the formula 1 f'(f-1(x)) f-1)'(1).

A:

Q: Sketch the space curve r(t) = −ti + 4tj + 3tk and find its length over the given interval [0, 1] .

A: Given space curve is rt=-ti+4tj+3tk. Sketch the above space curve as shown below.

Q: Assume that the radius r of a sphere is expanding at a rate of 30 cm/min. The volume of a sphere is ...

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Q: Find the distance between the pair of points(2√3, √6) and (-√3, 5√6). Ifnecessary, express answers i...

A: we know that distance d between given two given points x1,y1, x2,y2 is given by d=x2-x12+y2-y12

Q: dy + P(x) = Q(x) A. Write the given D.E in the standard form de P (X) = b. Q(x) = a. O = eS P dx %3D...

A: Consider the equation

Q: (2x 1) (x+5) 3) Let R(x)= %3D (3-x) (x+4)2 3a) Determine the intercepts of R. 3b) Fin the equations ...

A: Given: Rx=2x-1x+5 3-xx+42

Q: A few weeks into the deadly SARS (Severe Acute Respiratory Syndrome) epidemic in 2003, the number of...

A: Here, r=0.04ao=1804

Q: Use logarithmic differentiation to find the derivative of the function. y = (x5 + 2)2(x3 + 4)4

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Q: The equation for f is given by the simplified expression that results after performing the indicated...

A: Simplify: 2x2+3x+2-4x2+4x+3