Please show every step! Question: A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 5 ft/s, how fast will the top of the ladder be moving down the wall when it is 8 ft above the ground?

Q: Find the point at which the line meets the plane x=−3+5t, y=−2+2t, z=−1+6t​; x+y+z=−6 The point is…

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Q: 15. Find the area of the figure below which has three 75.0 mm diameter holes drilled out. 784mm оо…

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Q: Factor the following expression completely given that one of the roots is -5: 2³ + 182² +107z+ 210 =

A: Let's find factors of given polynomial function.

Q: * In (2¹) I -dx

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Q: Find a degree 3 polynomial having zeros -8, 4 and 7 and the coefficient of ³ equal 1. The polynomial…

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Q: An arithmetic series is defined by the formula ax= 8n - 1. Write an expression for the sum of the…

A: To find an expression of first n terms of arithmetic series.

Q: Find lim f(x) and lim f(x) for the given function and value of c. X→C+ X-C f(x) = (x + 9) x + 61 X+6…

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Q: 510 Find dy for the function y=- √x dy = (Simplify your answer.)

A: y=510xwe know  d dx(xn)=nxn-1

Q: Consider the equation below. 5y2 + z² - x - 20y - 4z + 24 = 0 (a) Reduce the equation to one of the…

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Q: Practice Problem 1. A particle moves along the x-axis with velocity v(t) = At² + 2. The particle…

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Q: ( Use lagnange multipliens to find the extreme values of f(x,y) = y²x² subjed to the constraint x² +…

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Q: f(x) = sinx, a = π/2

A: We have to find Taylor's series of the given function.

Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

A: Given: The velocity graph of the object is given in ft/sec. To find: The distance covered by the…

Q: S 1 (x + 2)² + 39 2 2 dx

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Q: A company's marginal revenue function is MR = 150 12x1/3, where x is the number of units. Find the…

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Q: Given y = (5x + 3e*)6, find dy dx

A: Given: y=5x+3ex6 To find: dydx Required formulas:  Power rule: ddxxn=nxn-1 Chain rule: fgx'=f'gx·g'x

Q: PART THREE: ab* + k ➤ In this part, you are going to explore the effect of parameter k to the…

A: Given function is f(x)=2x+k

Q: tan-¹ (sin) 0 - 4 O Оп 0-1/2

A: we know  that  sin(π2)=1let  y=tan-1(sinπ2)

Q: • Solve the equation using homogenous equation (5v-u)du + (3v - 7u)dv = 0 a.)(3v +u)² = c(v - u)…

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Q: (x+5)(7x + 6). If you have more than one solution, separate them with commas, as reduced fractions…

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Q: Use the method for solving homogeneous equations to solve the following differential equation. 7(x²…

A: The given differential equation is;  7(x2+y2)dx+4xy dy=0.

Q: Create a system of linear equations Ax = such that the matrix A is a 2x2 matrix with a determinant…

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Q: 14. Find the absolute maximum and the minimum value on the given interval: b) y = x²(2lnx-3) on…

A: Since the student has posted multiple questions and does not mention any specific question and they…

Q: 1) If f(x) = x²(2), find f'(2)

A: f(x)=x2∫2xdtt2+5we know  d dx(∫axf(t)dt)=f(x)×d dx(x)-f(a)×d dx(a)

Q: A tank is full of water. Find the work (in ft-lb) required to pump the water out of the spout. Use…

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Q: 6. What is the slope of the line y = -7? 7. What is the slope and y-intercept of the line of the…

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Q: Find an equation of the tangent line to the curve at the given point. y=4x/(x+1)^2 y = ,    (0, 0)

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Q: For the demand function D(p), complete the following. 100 D(p): р

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Q: tan (sin-)

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Q: Find the distance between the skew lines r(t) = (2,0, 4)t + (6, -5,0) and p(s) = (4, -2,0) + (7,-5,…

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Q: The following table records some values of the functions f and g. X 0 1 2 3 4 5 f(x) 1 0310 21 36…

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Q: 4. Determine lim f(x), lim_ f(x), and lim f(x) for the given piecewise function and given ₂+ x→a x→a…

A: multiple questions have been asked . as per bartleby guide line , the first question has been…

Q: 7. Find the volume of the solid obtained by rotating the region bounded by y = x³, y = 8 and x = 0…

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Q: y = C₁ e²^ + C₂ e²^ + Cze=²

A: To make a differential equation after eliminating the arbitrary constants. y=c1e-x+c2e2x+c3e-3x

Q: Find the two values of k for which y(x) = ekr is a solution of the differential equation…

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Q: Find an equation of the circle passing through the points  (−2, 3), (−5, 6), and (1, 2).

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Q: Find the derivative of ƒ(x) = x²e².5x ƒ'(x) =

A: Given: fx=x2e2.5x To find: f'x Required formulas:  Product rule: uv'=u'v+uv' Power rule: ddxxn=nxn-1…

Q: A company producing stereos can produce a stereo for $112 on top of the company's annual fixed cost…

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Q: a.) find x intercepts and y intercepts b.) odd or even multiplicities? c.) find power function d.)…

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Q: ASK YOUR The population of the world x years after the year 2010 is predicted to be 6.9e0.00743x…

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Q: in solving the problem. Directions: Find the dy/dx by implicit differentiation. X^2 + y^2 = 100 X^3…

A: We can solve the given problem by using the implicit differentiation

Q: nd all zeros of f(x) eparated by commas. = x³ - 4x² + x - 4. Enter the zeros

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Q: 2. Evaluate the given limit, or explain why the limit does not exist. a. lim √4-2² x⇒-2 4-2² b. lim…

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Q: Find the area bounded by the curve y = x2- 4 and x axis

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Q: Suppose that f(1) = 1, f(4) = 9, f '(1) = 6, f '(4) = 4, and f" is continuous. Find the value of…

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Q: Consider the function f(x) = 2x^3 - 12x^2 - 30x + 8 on the interval [ -4, 9]. a) since the…

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Q: c. Observe that the examples in (b) work nicely because of the derivati you were asked to calculate…

A: In section C we evaluate∫ x cosx   dx

Q: a. lim (2x + 3) x-5 b. lim (-²+3x − 2) - x-2 c. lim 5(t-2)(t-3) t→-1 x+3 x 3 x 2 d. lim e. lim 2(2x…

A: limit

Q: A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying…

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Q: O O O k|m9 3πT 05/2 Na -TT O T FTT/2 5 4 3 2 1- b Given the graph of the function ƒ (x) = \tan(2x)…

A: We are required to find the graph of the function f(x)=13tan(2x)