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Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight tow...

A: Let AB represents the distance from the spot light to the bottom of the wall which is 12 m. Let heig...

Q: Here we will study the function f(x) = xe^-x , where x ∈ [0, 10] Determine where the function is...

A: Given fx=xe-x ; x∈0 ,10

Q: A circular plate with radius 8 m is submerged vertically in water as shown. Express the hydrostatic ...

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Q: Find the tangent to the curve a"-ly = x"

A: we have to calculate tangent ( dy/dx) where a is any constant an-1ddxy=ddxxn

Q: Graphf(x) = 2x and g(x) = 2x-1 in the same rectangular coordinate system. Use transformations of the...

A: To determine: Graph of f(x) =2x, g(x)=2x-1 in the same rectangular coordinate system. Use the trans...

Q: Set up the triple integrals for finding the mass and the center of mass of the solid of density boun...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: 5. Evaluate the following derivatives. (a) y" where y = x7 + 3 ln(x). %3D

A: a) find y''' where y=x7+3ln(x) First we need to find first derivative with respect to x use power ...

Q: Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Mo...

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Q: Find an equation of the tangent line to the curve at the point (1, 1). y=ln(xe^x^9) (e is raised to...

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Q: A 5-m ladder leans against a wall. Assume the bottom slides away from the wall at a rate of 0.6 m/s....

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Q: x/42 Evaluate x tan (14x)dx. /42 x tan (14x)dx = Type an exact answer, using t and radicals as neede...

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Q: Use your calculator to complete the table for f(x) = e2x. (Round your answers to six decimal places....

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Q: Write an equation for the function illustrated in the graph below.

A: The given function is a piecewise function. It has different functions in different domains. The do...

Q: A kite 100ft above the ground moves horizontally at a speed of 8ft/s. At what rate is the angle betw...

A: Given Kite flies at the height of 100ft horizontal speed of kite is 8ft/s To find the rate of angle...

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: 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: Find an equation of the tangent to the curve at the point corresponding to the given value of the pa...

A: Given: x = cos(θ) + sin(4θ) y = sin(θ) + cos(4θ)

Q: Let sin t = a, cos t = b, and tan t = c. Write the expression sin(-t - 2π) + cos(-t - 4π) - tan(-t -...

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Q: Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = (1...

A: Given, r(t)=(1+t2)i+t2j To find the unit tangent vector at the point t=1.

Q: The area on the first quadrant bounded by the parabola x2 = 8y, x = 4, and the x – axis is revolved ...

A: the area on the first quadrant bounded by the parabola x2=8y, x=4, and the x axis is revolved about ...

Q: Assume that f is a one-to-one function. (a) If f(4) = 14, find f −1(14). f −1(14) = (b) If f −1(46)...

A: Suppose a function y=fx is defined on its domain. Then we always can find y such that x=f-1y. If f i...

Q: angle between A and B.

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Q: Consider the function given by ?(?) = 18x^2 ...

A: Consider the given function fx=18x22x-92

Q: $20,000 invested for 14 years compounded at 8% semiannually results in how many compounding periods ...

A: Given principle amount(p) = $20000 Interest rate(r) = 8% = 0.08 Compounded semiannully(n) = 2 Time i...

Q: A storage box with a square base must have a volume of 90 cubic centimeters. The top and bottom cost...

A: Given that Length of the sides of the square base = x Height = y Volume of the box = 90 cubic cm.

Q: Model the data using an exponential function f(x) = Ab*. f(x) -46 -52.9 f(x) =

A: For x=1, y=-46 f(x)=Abx-46=Ab1Ab=-46 ......(1)For x=2, y=-52.9 f(x)=Abx-52.9=Ab2Ab2=-52.9 ....(2)

Q: In Exercises 17-20, show that T is a linear transformation by finding a matrix that implements the m...

A: Given that Tx1,x2,x3,x4=0,x1+x2,x2+x3,x3+x4

Q: The percentage of adult height attained by a girl who is x years old can be modeled by f(x) = 62 + 3...

A: Given: The percentage of adult height attained by a girl who is x years old can be modeled by fx=62+...

Q: Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places log1...

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Q: cos-1(cos x) = x for every x in the interval________.

A: To find the interval.

Q: Determine the points at which the graph of the function has a horizontal tangent line f(x)= x2/x-5 ...

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Q: True or False. If the statement is true, explain how you know. If the statement if false, give a cou...

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Q: Let f(x) = cx + ln(cos(x)). For what value of c is f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as follo...

Q: Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all ...

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Q: Use f(x) = 2x − 4 and g(x) = 5 − x2 to evaluate the expression. a) (f ∘ f)(x) b) (g ∘ g)...

A: Given fx=2x-4 and gx=5-x2 Now, af∘fx=ffx =f2x-4 =22x-4-4 =4x-16-4 ...

Q: A rectangular coordinate system with coordinates in miles is placed with the origin at the center of...

A: Consider x,y is the set of points which represents the epicenter.

Q: Find the surface area of a sphere of radius a.

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Q: Based on the graph of a function that I attached how do I Find the graph of its derivative

A: See from the given graph of the function fx, the graph becomes parallel to x axis at the points x=-2...

Q: On a certain route, an airline carries 7000 passengers per month, each paying $90. A market survey i...

A: Given 7000 passengers per month paying $90. Each $1 decrease in the ticket price. The airline will g...

Q: For each of the given functions f(x), find the derivative (f-1)'(c) at the given point c, first find...

A: (A)Given: fx=3x+7x23; c=-10Thus, f'x=3+161x22We can say that f(x) is a polynomial and thus it is con...

Q: Use reference angles to find the exact value of the expression cot(7π/4). Do not use a calculator.

A: Given expression is cot7π4.

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

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Q: a) What is the particle's position at time 2? b) What is the particle’s displacement from t= 1 to t=...

A: (a) The function representing the position is X(t)=t3-15t2+48t. To find the position of the particl...

Q: Prove that the second equality is true and find the values of C and δ depending on A, B, ω*.

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Q: In problems 13-16 determine whether theorm 1.1 guarantees that the differential equation y,=√y2-9 po...

A: To determine whether the theorem guarantees that the differential equation y'=y2-9 possesses a uniqu...