Basic Math question and answers for November 07, 2024
- Q A ball is thrown upward from the top of a building 340 feet tall. The height of the ball is described by the function h(t) = -16t +320t + 340,...
- Q 8) A cylindrical can without a top is to be made to contain 150 cubic centime- ters of liquid. Find the dimensions that will minimize the cost of the metal...
- Q If a stone is thrown vertically upward from the surface of the moon with a velocity of 10 m/s, its height (in meters) after t seconds is h(t) = 10t...
- Q Find the equation of the tangent line to y = 4^(x^2-6z+1) at x=2 y=
- Q Sand is poured onto a surface at 20 cm/s, forming a conical pile whosebase diameter is always equal to its altitude.How fast (in cm/s) is the altitude of the pile...
- Q The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 11 cm...
- Q A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formular(t) = 5- 605/(t + 11)with 7 in centimeters and t in...
- Q A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f on [a, b]. If so, find all values c in...
- Q Consider the function f(x)=-42+2 on the interval (0, 4) Verify that this function satisfies the three hypotheses of Rolle's Theorem on the invervalThen by Rolle's theorem, there exists at least...
- Q Find the open intervals on which the function h(x)= x + x is increasing and decreasing.Identify the function's local and absolute extreme values, if any, saying where they occur.(a) On...
- Q A management consultant estimates that the number h of hours per day that employees will work and their daily pay of p dollars are related by the equation 90h5 +...
- Q Find the absolute maximum and minimum values of f(z) = (x+x)^2/3 over the interval [-2, 3].absolute maximum isand it occurs at x =absolute minimum isand it occurs at x =Notes:...
- Q Find the smallest perimeter and the dimensions for a rectangle with an area of 49 in.The smallest perimeter for a rectangle with an area of 49 in is in. (Simplify...
- Q At 2:00pm a car's speedometer reads 50mph, and at 2 10pm it reads 70mph. Use the Mean Value Theorem to find an acceleration the car must achieve Answer( in mi/h)
- Q Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = -0.01p + 8p, where p and f(p) are in hundreds. Find the population that...
- Q For the following expression, identify all the points of discontinuity, list the coordinates of any holes, and list any vertical and horizontal asymptotes.x - 5x / x+1Enter DNE if an...
- Q Find the coordinates of any local extreme points and inflection points. Use these to graph the function y=x- sin(-x) on the interval 0?x?2R.Choose the correct answer regarding local extreme points.A....
- Q (A) Use interval notation to indicate where f(x) is increasing.Note: Use 'INF' for oo, '-INF' for -oo, and use 'U' for the union symbol.Increasing:(B) Use interval notation to indicate where...
- Q f(x)=32-15 ln(3x)on the interval [3,9].Enter DNE for any absolute extrema that does not exist.Absolute maximum =Absolute minimum=
- Q A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 4 ft/sec. After 12 seconds, how rapidly is the area inclosed...
- Q A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $60/ft and on the other three sides by a metal fence costing $50/fL....
- Q A girl flies a kite at a height of 300 ft, and the wind carries the kite horizontally away from her at a rate of 25 ft/sec. How fast must...
- Q The length, width, and height of a box are measured as 8 ft, 7 ft, and 6 ft, respectively, with an error in measurement of at most 0.1 ft in...
- Q The original 24 m edge length x of a cube decreases at the rate of 5 m/min.a. When x = 5 m, at what rate does the cube's surface area...
- Q Water is dropped at the rate of 2cm/sec into a cone of semivertical angle 45. The rate at which periphery of water surface changes when height of the water in...
- Q A rectangular piece of cardboard, 100 cm by 40 cm, is going to be used to make a rectangular box with an open top by cutting congruent squares from the...
- Q Determine the intervals on which the following function is concave up or concave down. Identify any inflection points.f(x) = 6(x + 2)5/2 (2x-7), on [-2,00)
- Q A company sells x ribbon winders per year at $p per ribbonwinder. The demand function for ribbon winders is given by p = 250- 0.04x. Determine the elasticity of demand...
- Q Ernesto is considering buying a dishwasher for $600. According to a consumer magazine, he can expect to pay $40 per year for the electricity to run the dishwasher. He created...
- Q A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in the figure(a) Find a function that models the cross-sectional area of...
- Q a. Write the equation of the line that represents the linear approximation to the following function at the given point a.b. Use the linear approximation to estimate the given quantity.c....
- Q Which of the following is true about the graph of f(x) = 2 sin(x) + 3 sin(x) + 2 on the interval [0, ?]?a) f(x) has a local minimum at...
- Q A toy manufacturer determines that the daily cost, C, for producing x units of a dump truck can be approximated by the function C(x) = 0.01x-x+104.a. How many toy dump...
- Q The profit for a product can be described by the function P(x)=202x-5000-x dollars, where x is the number of units produced and sold. To maximize profit, how many units must...
- Q For what values of x does the graph off(x) = 2x - 12x + 0x + 12have a horizontal tangent? Enter the x values in order, smallest first, to 4...
- Q A rock is thrown off of a 100 foot cliff with an upward velocity of 50 m/s. As a result its height after t seconds is given by the formula:h(t)...
- Q If a person's temperature after x hours of strenuous exercise is T(x) = x(7-x) + 98.6 degrees Fahrenheit (for 0 ? x ? 2), find the rate of change of...
- Q Find the average rate of change of the given function between the following pairs of x-values.f(x) = 4x + 5x(a) x = 1 and x = 3(b) x = 1...
- Q Use the Generalized Power Rule to find the derivative of the function.f(x) = (3x + 1)^4 (3x - 1)^5f'(x) =
- Q At time t seconds, the position of a body moving along the s-axis iss = (-12t + 45t) m.(a) Find the acceleration of the body each time the velocity is...
- Q 1. (5 pts) Graph one continuous function f(x) such that all of the following hold:a. f(x) is increasing on (-?, -4)b. f(x) is constant on (-4,2)c. f(x) is decreasing on...
- Q A Kite 50 feet above the ground moves horizontally at a speed of 9 ft/sec. At what rate is the angle between the string and the ground decreasing when 140...
- Q Bert is going to claim a depreciation tax credit for his business car. The car costs $28,000 when new, and Bert anticipates it will be worth $16,000 three years later.(d)...
- Q For what values of x does the graph of f(x) = x + 2x + x + 16 have a horizontal tangent?
- Q A sales team estimates that the number of new phones it will sell is a function of the price that it sets. It estimates that if it sets the price...
- Q We determined R = 0.0825 and T = 9/15The amount of the loan, the principal, was $70,000, giving P =Substitute these values into the formula to find the amount of...
- Q Solve the problem. Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x)=20x^2 + 60x + 600 dollars....
- Q A rectangular box has a height of 5 feet. The sum of the length and width of the box is 8 feet.(a) Express the volume V (in ft) of the...
- Q The height y (in feet) of a ball thrown by a child isy =-1/12 x + 2x + 3where x is the horizontal distance in feet from the point at...
- Q The population of a certain town is growing at a constant rate. Suppose the population is 1900 initially, and after 2 years, the population is 2020.Which of these expresses the...
- Q Given g(x) = -2x +96x and g'(x) = -6x +96, select the local maximum and minimum of g(x).A. Local Max: (-4,0); Local Min: (4,0)C. Local Max: (-4,256); Local Min: (0,0)B....
- Q Use logarithmic differentiation to find dy/dx.y = (2 + x)^3/x , x > 0dy/dx=
- Q A farmer is building a fence to endose a rectangular area against an existing wall, shown in the figure below.Three of the sides will require fencing and the fourth wall...
- Q When the annual rate of inflation averages 4% over the next 10 years, the approximate cost C of goods or services during any year in that decade is given below,...
- Q The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p) =-80p+2560p-17,600, where p...
- Q The power P required to propel a ship varies directly as the cube of the speed s of the ship. If 6500 hp will propel a ship at 13.0 mi/h,...
- Q Assume that a snowball is in the shape of a sphere. If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate...
- Q What is the average rate of change of f(x) from x? = -1.6 to x? = 4.7? Please write your answer rounded to the nearest hundredth.f(x) = -6/7x + 4
- Q For the quadratic function f(x) = 2x + 2x-6, answer parts (a) through (f).(a) Find the vertex and the axis of symmetry of the quadratic function, and determine whether the...
- Q Ying is a professional deep water free diver.His altitude (in meters relative to sea level), a seconds after diving, is modeled by:D(x) = 1/36(x-60) - 100How many seconds after diving...
- Q What is the expected profit if Jesaki Inc. produces and sells 31,006 widgets?Round to the nearest dollar.Note: The profit may be negative, if Jesaki Inc. experiences a loss.
- Q The number of strikeouts per game in Major League Baseball can be approximated by the function f(x)corresponds to one year of play.Step 2 of 2: What is the value of...
- Q Consider the following function.f(x) = (x-8)e^x(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)(b) Find the open intervals on which the function is increasing or...
- Q A local internet provider is constructing a function that will model its profits (P) in thousands of dollars (USD) as a function of the number of internet subscribers (s) in...
- Q The position of an object moving along a line is given by the function s(t)= - 10t +80t. Find the average velocity of the object over the following intervals.(a) [1,9]...
- Q A closed box has height h cm and a square base of side x cm. It has volume 100 cm. What is the value of x which minimises the surface...
- Q The Mean Value Theorem applies to the given function on the given interval. Find all possible values of c. Then sketch the graph of the given function on the given...
- Q At a certain factory, it is determined that an output of Q units is to be expected when L worker-hours of labor are employed, whereQ(L) = 3600?La. Find the average...
- Q The gross annual earnings of a certain company were A(t) = 0.3t + 12t + 21 thousand dollars t years after its formation in 2008. At what percentage rate were...
- Q Analyze and sketch a graph of the function over the given interval. Label any intercepts, relative extrema, points of inflection, and asymptotes. (Order your answers from smallest to largest x,...
- Q Malik, the business manager of a company that produces in-ground outdoor spas, determines that the cost ofproducing x spas is C thousand dollars, whereC(x) = 0.06x + 2.1x + 50a....
- Q Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x)=30x2 + 45x + 400 dollars. At what rate...
- Q If a formula for a linear function is given by f(x) = mx + b, find the best match below:b< 0b=0m < 0my-intercept is below the x-axisThe line passes through...
- Q The point of diminishing returns is the point at which the rate of growth of the profit function begins todecline. Find the point of diminishing returns.The point of diminishing returns...
- Q Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, andasymptotes.Begin by finding the intercepts. (If an answer does not exist, enter DNE.)To find...
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
- Unlimited Question Access with detailed Answers
- Zin AI - 3 Million Words
- 10 Dall-E 3 Images
- 20 Plot Generations
- Conversation with Dialogue Memory
- No Ads, Ever!
- Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!