Calculus question and answers for August 17, 2023
- Q Let f(x) = 2x-9Determine the equation of a tangent line to f that is parallel to -24x + y = -3 . Report the solution using slope - intercept form.
- Q Of all the numbers whose difference is 48, find the two that have the minimum product.
- Q Let f(x) = 6x + 6xUse the alternative limit definition of the derivative to determine the derivative (slope) of f at (6, 252).Slope=_________
- Q The number N of bacteria present in a culture at time t, in hours, obeys the law of exponential growth N(t) = 1000e?.??a) What is the number of bacteria at...
- Q Given x = e? and y = te?; a) find dy/dxb) find dy/dx
- Q The term containing a^8 in the expansion of (b + a)^ 7 is______
- Q let h(x) = 3/?xDetermine the equation of the tangent line to h at (9, 1). Report the solution using slope-intercept form.
- Q Find the lateral area of this pyramid whose base is an equilateral triangle. Its slant height is 14 ft and the length of each side of the triangular base is...
- Q Let g(x)=x-(1/x).Determine the equation of the tangent line to g at (-6, - 35/6)Report the solution using slope-intercept form.
- Q let g(t)=2-9/x^9Determine the value(s) of t, if any, for which g has a horizontal tangent line.a)g has a horizontal tangent line at t =b)g has no horizontal tangent lines.
- Q Let h(x) = 4x - 7x +4Determine the value(s) of x, if any, for which h has a horizontal tangent line.a)h has a horizontal tangent line at x =b)h has...
- Q Find the extremum of f(x ,y) subject to the given constraint, and state whether it is a maximum or a minimum.f(x, y)=x y; 5x+y=16
- Q A disease spreads through a population. The number of cases t days after the start of the epidemic is shown below.Days after start (t) ...
- Q Let g(w) = 2w - 13w + 24w - 8Determine the value(s) of w, if any, for which g has a horizontal tangent line. If multiple solutions exist, enter the...
- Q The total sales, S, of a one-product firm are given by S(L,M) = ML - L, where M is the cost of materials and L is the cost of labor....
- Q Indicate local maxima and minima, inflections points and asymptotic behavior, and all of the calculus work necessary to find the information, of the following function, :sketch the graph of f(x)=...
- Q Use the price-demand function below, to answer parts (A), (B), and (C).p(x)=95-3x 1 ?x?25(A) What is the revenue function?R(x) =__________
- Q Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y) = 17-x - y; x +...
- Q Let g(t) = -5-t^1/2Determine the value(s) of t, if any, for which g has a horizontal tangent line..a)g has a horizontal tangent line at t =b)g has no horizontal tangent...
- Q On a May 22, 2022, Tauri visits Boston and sees a flock of birds. The angle of elevation to the flock of birds is 14. If the flock of birds...
- Q The speed of sound through air is linearly related to the temperature of the air. If sound travels at 339 m/sec at 0C and at 366 m/sec at 30C, construct...
- Q Use the revenue and cost functions below, to answer parts (A), (B), and (C).R(x) = 80x - 3x 1 ?x?20C(x) = 125 + 16x ...
- Q Let f(t) = ?t (2-2t?)Determine the derivative of f.f'(t) = ______Determine the slope of f at t = 7.f'(7) = ______
- Q Part 1: The graph of f(x) is shown; it goes through the point (1, -2).Provide two different graph transformations that produce the curve y=f(x) from the curve y = log?...
- Q Suppose the field has a length of 6,000 feet. Sally buys fencing to enclose it, but has bought 4 feet too much. Rather than throwing away the extral fencing, Sally...
- Q Three airport runways intersect to form a triangle, ABC. The length of AB is 3.1 km, AC is 2.6 km, and BC is 2.4 km. A company is hired to...
- Q A drone operator is on a road running north and south, and using a drone to observe a herd of elk 3000 yards east and 1100 yards north of the...
- Q 1).Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum.f(x,y)=20-x - y; x+4y=17There is a ____ value of ____ located...
- Q Test the series for convergence or divergence:?(7n+1)/(e^(n/5)-7) [n=1,?]
- Q Explain why the function is differentiable at the given point. Then find the linearization L(x, y) of the function at that point f(x, y) = y + sin(x/y), (0, 3)
- Q David invested $220 in an account paying an interest rate of 1.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would...
- Q Which expression does sin(?/2+?)+cos(?-?)simplify to?(a)0(b)1(c)sin?+cos?(d)2cos?
- Q Sketch a direction field for the differential equation y' = - x/y from -4 to 4. Then use it to sketch the initial conditions y(0) = 2 and y(0)...
- Q A hyperboloid is a 3D shape whose cross sections are hyperbolas. A nuclear cooling tower is in the shape of a portion of a hyperboloid. If the equation x/10000 -...
- Q Two shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation a = 30, = 60, respectively as in Fig. The shots strike an...
- Q the following limit could be helpful: lim(1+1)^n=eDoes ?n!^n converge or diverge?Does ?(2n)!^n converge or diverge?
- Q In Exercises 36-41, use the Root Test to determine convergence or divergence (or state that the test is inconclusive).?1/10^n?1^n?{k/(k+10)}^k
- Q Given the polynomial function f(x)=-4x-x+x+2, find:a). Determine the maximum number of real zeros that the polynomial may have.b). Use Decartes' Rule of Signs to determine how many positive and how...
- Q Convert the parametric or polar equations to rectangular equations. Describe the shape of the graph (parabola, circle, line, etc). It may help to draw a little sketch. a. r =...
- Q During the Apollo 14 mission, Alan Shepard hit a golf ball on the Moon. The function h(t) = 18t - 0.8t models the height of the golf ball's trajectory on...
- Q Compute the average rate of change of the function f(x) = x + 5 on the interval [0, 5].
- Q Jerry invests $6000 at 7.5%/a, compounded annually.a) Determine the equation of the amount, A, after t years.b) Estimate the instantaneous rate of change in the value at 10 years.c) Suppose...
- Q The function f(x) = ||x||, proveof(x) = {x/||x|| for x?0 s|| |s||?1 for x=0
- Q Given h(x) = g(x) * f(x) j(x) = f(x)/g(x) At x = -6, the equation of the tangent line of f is y = x + 13. At x =...
- Q 5. Suppose that the revenue realized on the sale of company's product can be modeled by the function R(x) = 600x -0.3x is the number of units sold and R(x)...
- Q Determine the distance of the centroid from the y- axis of the solid formed by revolving the bounded region by the curve x=4y and the line x = - 4,...
- Q The height attained by a weight attached to a spring set in motion after t seconds is s(t)= -6cos12?t + 5 inches. Find the maximum height that the weight rises...
- Q Topic for your initial post: It's your turn to be the teacher. In this discussion board post, your task is to create a tutorial to teach your line to a...
- Q Which of the following input values for x would generate integer outputs for the function f(x)=-1/2x-3?Select the 3 that apply.HINTSince the denominator of the slope is 2, any multiple of...
- Q Let f(y) = (2y^2 + 2y + 2)(y-2)Determine the value(s) of y, if any, for which f has a horizontal tangent line.A) f has a horizontal tangent line at y...
- Q Let f(x) = 4/(x + 1)Determine the equation of the tangent line to f at (1, 2). Report the solution using slope-intercept form.
- Q Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO). Beginning at time t= 0, cigarette smoke containing 4% CO is introduced into...
- Q 7. Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement. What...
- Q A factory manufactures three products, A, B, and C. Each product requires the use of two machines, Machine I and Machine II. The total hours available, respectively, on Machine I...
- Q Find the points on the cardioid r = sin(2?) where the tangent line is horizontal. Draw.
- Q Which integral correctly computes the length of the curve y=In(cos(x)) between x=0 and x=?/3 ?a) ?/3 ??tan(x) dxb) ?/3 ??2?ln(cos(x))?(1+tan(x)) dxc)...
- Q Jina is driving on a highway. She uses one gallon of gas every 20 miles she drives. The distance, D (in miles), she travels on g gallons of gas is...
- Q Suppose that the revenue realized on the sale of company's product can be modeled by the function R(x) = 500x -0.4x is the number of units sold and R(x) is...
- Q Kings Dominon's opening day had 1350 people visit the park. Children under 12 paid $40, Adults under 65 paid $65 and seniors over 65 paid $50. The park had combined...
- Q Find the area of the sector of a circle with radius 15 feet formed by a central angle of 35._______ square feetRound your answer to two decimal places.
- Q Below is the function f(x) = 11 - 1/2x, together with a rectangle with one side on the x-axis, and two corners on the curve. The bottom left corner is...
- Q Solve the equation for ?, where 0 ? ? ? 2. (Enter your answers as a comma-separated list.)4 cos (?) = 3? = ____
- Q Determine the minimum off(x)= (10x + 3x + x + 5)starting at x = 3 and using a step size ? = 5.0.Using region elimination: expanding pattern bounding plus six...
- Q In your own words, define the following.(a) Secant line(b). Average rate of change(c). Tangent line(d). Instantaneous rate of change
- Q Given that sin(a) = 1/3 and cos(b) = -2/6 with a and b both in the interval [ ?/2, ?], find the exact values of sin(a + b) and cos(a...
- Q The volume of a cube is increasing at a rate of 10cm3/min. How fast is the surface area increasing when the length of an edge (side) is 30 cm...
- Q Given the functions f(x) = x + 1 and g(x) = x + 1. Compute the net and the total (or absolute) area between the curves over the interval [0,2].
- Q 6. For the function y = 30 cos[2(x + 15)] - 60, the phase shift isA 30 to the rightB 15 to the leftC 15 to the rightD 60 to...
- Q Suppose is an angle such that cos(?)= -1/7If 2? < 0 < 3?,then cos(?/2)=___and sin(?/2)=___
- Q Find the ? value within [0, 2?) for function f(?) = 7 cos(7?) to reach its minimum value.? =
- Q Match each side as hypotenuse, opposite, or adjacent of angle A.Adjacent a. BCOpposite b. ABHypotenuse C. AC
- Q Determine the center and radius of a circle given that its equation is(x - 1) + (y- 8) = 49Center: Radius:
- Q Find the ? value within [0, 2?) for function f(?) = 9 sin(10 ?) to reach its maximum value.? =?
- Q The cost, in dollars, to produce a vats of ice cream is C(x) = 9x + 14. When selling them to ice cream shops, the price-demand function, in dollars per...
- Q Find the ? value within [0, 2?) for function f(?) = 9 sin(10?) to reach its maximum value.? =
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