Basic Math question and answers for November 09, 2024
- Q The graph of the velocity of a car accelerating from rest to a speed of 90 km/h over a period of 30 seconds is shown. Use this graph and a...
- Q To determine the size of the motor required to operate a press, a company must know the amount of work done when the press moves an object linearly 5 feet....
- Q A damping force affects the vibration of a spring so that the displacement of the spring is given byy = e 3t(cos 6t + 5 sin 6t).Find the average value...
- Q The price-demand equation for a particular flashlight is given by p= 113 0.004x, where x is the number of flashlights demanded when the price is p dollars each. The flashlight...
- Q Find the producers' surplus if the supply function for pork bellies is given by the following.S(q) =q7/2+3q5/2 + 55Assume supply and demand are in equilibrium at q = 9.The producers'...
- Q The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s= 3 sin(?t) + 4 cos(?t), where t...
- Q Which formula would be used to calculate the trapezoid approximation of ?4x dx using five subintervals?T5 = 0.2/2 [4(0.0) + 2(4)(0.2) + 2(4)(0.4) + 2(4)(0.6) + 2(4)(0.8) + 4(1.0)]T5 =...
- Q Let R be the region in the first quadrant bounded by the graphs of y=?x, x = 4, and the x-axis. What is an integral expression for the volume of...
- Q Use polar coordinates to find the volume of the given solid.Inside both the cylinder x2 + y2 = 13 and the ellipsoid 4x ++4y2 + z = 64.
- Q Find the area bounded by yx - 12/22-32-54, x=4, x=8, and y = 0.(Round the answer to four decimal places.)
- Q Let ? be the solid located above the plane z = 1 and below the hemisphere z = ?5-x - y. Using cylindrical coordinates, that is (z, r, ? coordinates),...
- Q Let f(x) = 1 / (x^2 - 2), and compute the Riemann sum of f over the interval [2, 5], using three subintervals of equal length (n = 3) and...
- Q Consider the following.f(x) = {-5x, x ? 4f(x) = {x2 - 4x + 7, x > 4Find the x-value at which f is not continuous. Is the discontinuity removable? (Enter...
- Q Use a definite integral to find the area under the curve between the given x-values.f(x) = ex/3 from x = 0 to x = 3square units
- Q For the function, do the following.f(x)=?x from a = 3 to b = 6.(a) Approximate the area under the curve from a to b by calculating a Riemann sum using...
- Q Find the area of the following region.The region common to the circle r = 5 and the cardioid r= 5(1- cos 0)The area shared by the circle and the cardioid...
- Q Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis...
- Q A particle that moves along a straight line has velocity v(t) = te-3t meters per second after t seconds. How many meters will it travel during the first t seconds...
- Q The rate of growth of profit (in millions) from an invention is approximated by P'(x)=xe OA. P(x) = -5e 1 OB. P(x) = -- ze OC. P(x) = -5e OD....
- Q Evaluate the following integral using trigonometric substitution.??64-x dxBe sure your written work includes your trigonometric substitution (for x, dx) and the conversion back to the original variable.
- Q Evaluate the following integral.?x2 +40x-16/x3-16x dx
- Q Find the indefinite integral using the substitution x = 10 sin(?). (Use C for the constant of integration.)?1/(100 - x)3/2dx
- Q Find the indefinite integral.18/1 + 81x dx
- Q Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by parts. Use C for the constant of integration.)? xe4x dx
- Q Find the general indefinite integral. (Use C for the constant Integration.)?(x^5)^1/4 dx
- Q Find the indefinite integral. (Use C for the constant of integration.)?e??(1-e?) dx
- Q Evaluate the indefinite integral?41cos(17x)dx
- Q A factory is discharging pollution into a lake at the rate of r(t) tons per year given below, where t is the number of years that the factory has been...
- Q Evaluate the integral using the fundamental theorem of calculus when appropriate (your answer should be exact. Make sure you use C if needed.):f(x) = ?(4x^2 3x+4+3x--x-^2) da
- Q Find the general solution of the differential equation. (Use C for the constant of integration.)dy/dx = 9x / ?(7 + x)y =
- Q Find the indefinite integral and check the result by differentiation.?(7x +1/(3x) ) dx
- Q Find the particular solution that satisfies the differential equation and the initial condition.f'(s) = 18s-8s,f(3) = 6
- Q Identify a function f that has the given characteristics. Then sketch the function.f(0) = 3f'(x) = 3,00 < x < 00Step 1We are given f '(x) = 3, -?0 <...
- Q Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)7x - 9x + 3xF(x) =f(x):=X>0-3-9 ln(x)= +7x+C
- Q Find the most general antiderivative of f(x)= 7-8x7/ x5
- Q 5A curve y = f(x) defined for values of x > 0 goes through the point (1, 0) and is such that the slope of its tangent line at (x,...
- Q An object moves along a coordinate line with acceleration a(t) = (t + 2) units per second per second.The initial velocity is 5 units per second.The velocity function is v(t)...
- Q Find the derivative of the function.h(x) = x arctan(4x)
- Q Use integration to find f(4), if df/dx = 3x^1/3, and f(1)=4.8.04412.87213.76316.037
- Q Find the indefinite integral.?18(x-7)^8dx
- Q You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide...
- Q Evaluate the integral:? -25 / (x?(x+36) dx(A) Which trig substitution is correct for this integral?x= 36 tan(?)x= 36 sin(?)x= -25 sec (?)x = 6 tan(?)x = 36 sec (?)x =...
- Q For any time t>0, the acceleration of a particle is given by a(t) = 1 +3/?tA) The velocity at a general time t> 0 is v(t)=B) Now suppose the particle...
- Q The temperature at time t hours is T(t) = -0.3t + 4t + 50 (for 0 ? t ? 12). Find the average temperature between time 0 and time 10.
- Q A certain vehicle can accelerate from a standing start to a speed of v(t) = -0.27t + 12t feet per second after t seconds (for0 ? t < 30).(a)Find a...
- Q Let f be the function with derivative defined by f '(x) = cos(x2) on the interval -2<x<2. How many points of inflection does the graph of f have on this...
- Q A baseball is travelling on a path given by the equation y 0 011x 1 15x 1 22 The profile of the bleachers in the outfield can be modelled with...
- Q A rectangular solid with a square base has a volume of 1 728 cubic inches Let w represent the length of the sides of the square base and let h...
- Q O cm cm cm cm cm s The function V r models the volume of a basketball that is deflating due to a puncture If V r is measured in...
- Q Given this function f x 35 arcsin 11 an equation for the line tangent to the graph of y f x at the point where x Y is
- Q Apie is removed from your oven with an internal temperature of 165 F It is placed on your counter to cool The temperature of the room is 65 F If...
- Q Which of the following would not be a representation of the differentiable function f where f 5 3 6 points O The slope of y f x at x 5...
- Q 9 A farmer has 5000 meters of fencing to enclose a rectangular field and subdivide it into three equal plots The enclosed area is to be a maximum Determine the...
- Q Farmer Ed has 650 meters of fencing and wants to enclose a rectangular plot that borders on a river If Farmer Ed does not fence the side along the river...
- Q Correct The total revenue for Fred s Estates LLC is given as the function R x 100x 0 4x where x is the number of rooms rented What number of...
- Q 1 2 A drone flies in a straight line with a positive velocity v t in miles per hour at time t hours where v is a differentiable function of...
- Q f 3 12 5 4 3 2 1 2 3 1 2 3 4 5 At the point shown on the function above which of the following is true Of...
- Q Problem 4 10 Points Words Words Words part 1 5 points each You boss decides to launch a new product cerebrum vastatorem and you are tasked with finding the optimal...
- Q 1000 The population of deer in a park can be modeled by P t where P t is the 1 60e t number of deer and t 0 is time...
- Q Bryan has 180 feet of fencing to fence off his rectangular garden He will use the wall of his house as one side of the garden garden 1 Write an...
- Q 8 A radioactive isotope is decaying at a rate of 18 every hour Currently there are 100 grams of the substance Part B How much will be left one day...
- Q A twice differentiable function f is defined for all real numbers x The derivative of the function f and its second derivative have the properties and various values of x...
- Q The function h represents the height of an object t seconds after it is launched into the air. The function is defined by h(t) = -5t + 20t+18. Height is...
- Q The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 4x-x. What rainfall produces the maximum number of mosquitoes?A....
- Q Use the first derivative test to determine the location of each local extremum and the value of the function at that extremum.f(x) = (7-5x)4/3 +7A. Local minimum at (7/5,7)B. Local...
- Q Find the producer's surplus if the supply function of some item is given by S(x)=x+2x+8. Assume that supply and demand are in equilibrium at x = 30.A. 12,700B. 17,200C. 18,900D....
- Q Given that the variable cost is given by 2x + 4x and fixed cost is 5000. Determine the:A. total cost functionB. marginal cost functionC. average cost functionD. average cost when...
- Q Taylor is on one side of a river that is 50 meters wide and wants to reach a point 200 meters downstream on the opposite side as quickly as possible...
- Q Given the function g(x) = 6x + 45x + 72x, find the first derivative, g'(x) = 0 when a = 4, that is, g'(-4) = 0.Now, we want to know...
- Q Find the minimum value of the objective function f(x, y) = x + ysubject to the constraint y = r +1(a) Use the constraint to rewrite the objective function with...
- Q Consider the differential equationdy/dx = x (y + 1).Sketch a slope field for the given differential equation on your paper for the domain [-3, 3] and the range [-3, 3].Part...
- Q Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of liters) is given by the function C(x)= x - 3x +9x +50,...
- Q Let'f be a twice-differentiable function with derivative given by f '(x) = 4x - 24x.Part A: Find the x-coordinate of any possible critical points of f. Show your work.Part B:...
- Q Complete the table with positive, negative, or 0 to describe g' and g". Justify your answers.positive positive positive positivePart B: Find the x-coordinate of each critical point off and classify...
- Q The continuous function g, consisting of two line segments and a parabola, is defined on the closed interval [-3, 6], is shown. Let f be a function such that f(-1)=-...
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