Basic Math question and answers for August 24, 2024
- Q A population numbers 15,000 organisms initially and grows by 4.8% each year. Suppose P represents population, and t the number of years of growth. An exponential me the population can...
- Q The demand for a certain portable USB battery charger is given by D(p) = -4p +3p+5, where p represents the price in dollars.(a) Find the rate of change of demand...
- Q Terri Vogel, an amateur motorcycle racer, averages 129.55 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.27 seconds. The distribution of her race...
- Q 413)For each equation, find-dy. Show all necessary work. You may leave answers defined implicitly if necessary.Quiz 2dx1. y = cos(?x)) = sin(?7)= (+57)autsideinsidedartside (inside) (inside).7. y - y = lnx...
- Q Let f(x) and g(x) be functions such that f'(-5) = g'(-5) and the line tangent to the graph of f at x = -5 is y = 4x + 2.For...
- Q Find the derivative of the trigonometric function.g(t) = 4 (cos(?t))4
- Q Use logarithmic differentiation to find dy/dx.y = (1 + x)2/x
- Q Differentiate.y = 8x cos(x) cot(x)
- Q A population numbers 18,000 organisms initially and decreases by 5% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population...
- Q There is 0.998615 probability that a randomly selected 20-year-old male lives through the year. A Fidelity life insurance company charges $178 for insuring that the male will live through the...
- Q A ball is thrown upward and outward from a height of 7 feet. The height of the ball, f(x), in feet, can be modeled byf(x) = -0.2x +2.1x+7where x is...
- Q Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t)=-16t2 +16t+480,...
- Q (1 point) Use the graph of y = |x - 5| to determinewhere the function is not differentiable.The function is not differentiable at x =(If there is more than one...
- Q 3.) For each of the following functions, find of and(i) (2 pts) f(x, y) = x +y - 3xyxyx + y(iii) (2 pts) f(x, y) = xey(ii) (2 pts) f(x,...
- Q Calculus is a powerful tool used in all areas of physics. One of the initial applications areas is classical physics, particularly Newtonian mechanics, An important function is the position function...
- Q A plane flying horizontally at an altitude of 2 miles and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from...
- Q The stock price for a certain corporation can be approximated for the years 2011 through 2016 by f(x) = 7.8x-221x + 1586, where x = 11 corresponds to the year...
- Q Jesaki Water Sports incurs the following costs in producing a water ski vests in one day, for0<x< 150:fixed costs, $304;unit production cost, $23 per vest;equipment maintenance and repairs, 0.06 x...
- Q Use the First Derivative Test to find the location of all local extrema for the function given below. Enter an exact answer. If there is more than one local maximum...
- Q A friend concludes that because y = In 6x and y = In x have the same derivative, namely dy/dx = 1/x'these two functions must be the same. Explain why...
- Q The differential equation y' = 2y will produce which of the following? (6 points)A slope field with parallel tangents along the diagonalA slope field that does not have rows or...
- Q Find the derivative of the function.y =1/2 [X? 36 - x + 36 arcsin(x/6)]y'(x) =
- Q Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.u(-6, 7) = 6us(-6, 7) = -9ut(-6, 7) = 0Fu(6, 4) =...
- Q Katie and Sarah are working on taking the derivative of f(x) = -2x3x + 4Katie uses the quotient rule to get f'(x) =product rule and the chain rule (shown below)....
- Q The students in a physics class are performing an experiment to determine the acceleration due to gravity. They drop water balloons from the top of a building and estimate the...
- Q At the Williams County fair, Savannah rides a ferris wheel with a radius of 18 feet that is rotating at a rate of two revolutions every minute. How fast is...
- Q Create DQ 5 Discussion Board in response to the following questions: What does the limit definition have to do with slopes of secant lines and the slope of a tangent...
- Q The monthly profit from the sale of a product is given byP(x) = -1.5x - 12x + 20dollars.25. What level of production maximizes profit?a) x = 4.0 unitsb) x =...
- Q Let f be a continuous function on the closed interval [-2, 5]. If f(-2) = -7 and f(5) = 1, then the Intermediate Value Theorem guarantees thatf (c) = -2...
- Q A model rocket is launched from the roof of a building. Its flight path is modeled by h = -5t +30t +10 where h is the height of the rocket...
- Q Find the function f given that the slope of the tangent line to the graph of f at any point (x, f(x)) is f'(x) and that the graph of f...
- Q Suppose that f(4) = 5 and f' (4) = -1. Find h'(4). Round your answer to two decimal places.(a) h(x) = (2f(x) - 5e^x/9)3h'(4) =(b)h(x)= 50Inf(x)/x + 2h'(4) =(c)h(x) =...
- Q Find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f.f(x) = x-12x-8(A) f'(x) = 3x - 12(B) Find the partition numbers for f'. Select...
- Q The radius of the base of a cylinder is decreasing at a rate of 12 kilometers per second.The height of the cylinder is fixed at 2.5 kilometers.At a certain instant,...
- Q Find the derivative of each function.h(x) = (4x + 8x)(16 5x)OO145x7 - 240x4 - 192x + 128-160x7+240x5 - 128x - 192192x7 + 145x5+240x4 - 128-160x7 - 240x + 192x +...
- Q Let h be a differentiable function with a tangent line at x = n. The equation of the tangent line is y=-0.2x+0.5. What must be true about h and h'...
- Q In the function f(x) = 5.62 cos(0.7x) - 1.93, what is the first positive x value where the function has a minimum?1.746.738.984.49
- Q Differentiate the function.f(x) = In(In 3x)
- Q Find all critical numbers of the function y =or minimum.x-9/x-5, x?5. Then use the second-derivative test on each critical number to determine whether it leads to a local maximumSelect the...
- Q Find the derivative of the function..y = (x2 + 2) coth(x/8)y'=
- Q Differentiate the function.g(x)=ln?[xcosx/(4x+5)^3]
- Q A retailer who sells backpacks estimates that by selling them for a dollars each, he will be able to sell 112 x backpacks a month. The quadratic function R(x) =...
- Q A rectangular playground is to be fenced off and divided in two by another fence parallel to oneside of the playground. Six hundred feet of fencing is used. Find the...
- Q For the function below, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.f(x) = (x+8) /...
- Q On a particular day, the power used in a particular state (in thousands of megawatts) could be approximated by the function P(t)= -0.0068881 +0.19181 -0.7085t+20.74, where t is the number...
- Q Use implicit differentiation to find dy/dx3 cos (xy) = 2x + 7y
- Q Find an equation of the line tangent to the curve at the point corresponding to the given value of t.x=t-1, y=t +2t; t = 3(Type an equation. Type your answer...
- Q Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.x + y = 169(a) Find dy/dt, given x = 5,...
- Q Describe the transformations we would expect to see to the toolkit function f(x) = |x| in the given function.f(x) = -|x - 3| +2Translate left 3 units, up 2 units,...
- Q A spaceship approaching touchdown on a distant planet has height h, in metres, at time t, in seconds, given by h = 25t - 100t + 100. When does the...
- Q A particle moves in a straight line with the velocity functionv(t) = sin(wt)cos^8(wt). Find its position functionX = f(t) if f(0) = 0.
- Q Given s(t)=t+2, where s(t) is in miles and t is in hours, find each of the following.a) v(t)b) a(t)c) The velocity and acceleration when t = 2 hrd) When the...
- Q 1. Consider the curve given by xy2 - xy = 6.a. Show that dy/dx = (3xy-y)/(2xy - x)b. Find all points on the curve whose x-coordinate is 1, and write...
- Q Find the difference quotient of f(x)=x+2; that is find (f(x+h)-f(x))/h Be sure to simplify.
- Q a. Use the Product Rule to find the derivative of the given function.b. Find the derivative by expanding the product first.f(x)=(x-6)(5x + 3)a. Use the product rule to find the...
- Q The median weight of a boy whose age is between 0 and 36 months can be approximated by the functionw(t) = 7.76 +1.74t-0.003612 +0.0008651where t is measured in months and...
- Q Differentiate the function.g(x) = 4x- (x4 - 4x + 12x-3)g'(x) =
- Q If f x exe 8 and g x f x lim x 0 g x 2x then Your answer needs to be in exact form Your written work should use...
- Q The graph below shows the profit P from the daily production of x thousand kilograms of an industrial disinfectant Use the graph to complete parts a through f to the...
- Q The amount of income tax t an individual owes is defined by piecewise function t and is based on the individual s income where is taxable income in dollar 0...
- Q 2 1 0 1 2 3 4 8 x values 6 b Find X 2 2 g x values Limit values of g x x 2 4 1 2 1...
- Q Find all points where the function is discontinuous.A. NoneB. x=2C. x = 4D. x = 4, x = 2
- Q Let f(x) = -8 - 5/x+16Complete the tables below. Round all table values to four decimal places, if necessary. Enter DNE if a function value is undefined.Using the data in...
- Q Let f(x)=?x6 +5x - x - 3.Complete the tables below. Round all table values to four decimal places, if necessary. Enter DNE if a function value is undefined.Using the data...
- Q (1 point) Find an integer which is the limit oftan(8x)/2xas x goes to 0. (Enter I for infinity or DNE for does not exist.)
- Q Use a graph or table of values near x =?/2 to estimate the value of this limit:limx - 72cos(7x)/x-?/2i
- Q Let f be the function defined as f(x)= 3 for x<5 x+7 for x? 5 Which of the following statements is true?f is not differentiable...
- Q Use the Direct Comparison Test to determine the convergence or divergence of the series. ? ...
- Q In a study on the speed of muscle contraction in a certain species of frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. In...
- Q You want to be able to withdraw $25,000 from your account each year for 25 years after you retire. You expect to retire in 30 years. If your account earns...
- Q Given a continuous function f(x) with f(-5) = - 1 and f(9) = - 8:There must be a number c with ? 5 < c < 9 and f(c) =...
- Q Use the graph of the function f shown to estimate the following limits and the function value. Complete parts (A) through (D).(C) Find the limit lim x?1 f(x).Select the correct...
- Q Given a function f(x) with f(? 8) = 1 and f(9) ,m= 2:There must be a number c with -8 < c < 9 and f(c) = 1.4.There might be...
- Q Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function s(t), where t is the time, in seconds, after the...
- Q Let f be the function defined as f(x)= 2 for x<4f(x)= 4x-3 for x?4Which of the following statements is true?f is not differentiable at x = 4 because fis not...
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