Basic Math question and answers for November 08, 2024
- Q A rocket is fired from a building 240 ft tall. The height of the rocket with respect to time (inseconds) is modeled by f (t) = -161 +32t + 240....
- Q Given the function f(x) =1/x^2a. Find the average rate of change between x=__and x= (choose two consecutive negativeIntegers)b. Find the instantaneous rate of change at x=_______ (choose a negative integer...
- Q You need to use 12 straight pieces of wire to make a frame for a rectangular box with square top and bottom:The wire for the vertical edges costs $8 per...
- Q Consider the differential equation dy/dx=x^2(y + 1).Sketch a slope field for the given differential equation on your paper for the domain (-3, 3) and the range (-3, 3).A): List five...
- Q Diana has available 3200 yards of fencing and wishes to enclose a rectangular area.(a) Express the area A of the rectangle as a function of the width W of the...
- Q The function V(t) =33.8 7.4t gives the value (in thousands of dollars) of an investment after t years. Interpret the Slope in this situation. The value of this investment is_______...
- Q Consider the differential equation dy/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].(A)...
- Q A 10 foot ladder is leaning against a wall with the base of the ladder 6 feet from the wall. If the bottom of the ladder is pushed towards the...
- Q What is the maximum vertical distance between the line y = x + 12 and the parabola y = x for -3 ? x ? 4?
- Q A company found that new employees prefer training sessions of moderate length, shorter training sessions provided too little instruction to complete a task, while longer training sessions contain too much...
- Q Find all relative extrema and saddle points of the function. Use the Second Partials Test where applicable. (If an answer does not exist, enter DNE.)f(x, y) = -8x - 5y^2...
- Q Consider the function f(x) = 7x - 7x.a.Determine, without graphing, whether the function has a minimum value or a maximum value.b.Find the minimum or maximum value and determine where it...
- Q The radius r of a sphere is increasing at a rate of 2 inches per minute.(a) Find the rate of change of the volume when r = 11 inches.in.3/min(b) Find...
- Q Approximate the area under the graph of F(x) = 0.9x +9x -0.9x-9 over the interval [-6, -1] using 5 subintervals. Use the left endpoints to find the heights of the...
- Q A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The...
- Q NASA launches a rocket at t= 0 seconds. Its height, in meters above sea-level, as an equation of time is given by h=- 4.9? + 139t + 269.How many seconds...
- Q Find the absolute maximum value on (0, co) for f(x) = 9x - 5x In x.Select the correct choice below and, if necessary, fill in the answer boxes to complete...
- Q Find the equation of the tangent line to the curve (a lemniscate) 2 (z + y) = 25 (x - y) at the point(3, 1). The equation of this tangent...
- Q You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 73 km south and 200 km east. Mt. Rainier is located approximately 56 km east and 40 km south...
- Q The expression f(x+h)-f(x)/h for h#0 is called the difference quotient. Find and simplify the difference quotient for the following function.f(x)=3x +5x+6
- Q A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by...
- Q Use a graphing calculator to approximate the critical numbers of f(x) to two decimal places. Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing,...
- Q The polynomial function F(x) = 2x +8x-7 has a critical point at which of the following x-values?A. x = -7B. x = 0C. x = -2D. x = 2
- Q A rice producer fills boxes with the same weights of different rice varieties to produce rice blends. The machinery filling each box is designed to put 42 ounces of rice...
- Q A ball is thrown from the top of the school. The height of the ball (in feet) written in terms of the time (in seconds) is modeled by f(t) =...
- Q Consider the function f(x) = xe^5xf(x) has two inflection points at x = C and x = D with C < Dwhere C isand D isFinally for each of the...
- Q At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 24 knots....
- Q A basketball is thrown and the path can be modeled by (x) = ?16x + 15x + 6 where xrepresents time in seconds and f (x) represents height of the...
- Q Answer the following questions for the functionf(x)=x?x + 25defined on the interval -5 ? x ? 6.f(x) is concave down on the interval x =f(x) is concave up on the...
- Q Consider the function f(x) = 2 - 5x on the interval [ - 3, 7].The average rate of change of f(x) on this interval is:f(7) - f(-3) / 7-(-3) =The...
- Q Consider the function f(x) = 8(x - 2)^2/3. For this function there are two important intervals: (-?, A)and (A, ?) where A is a critical number.A isFor each of the...
- Q The function f(x) = 6x + (4/x) has: a local minimum at x = with value f(x) = a local maximum at x = with value f(x) =
- Q You know that the following information about f(x):f(3) = 14f(14) = 2f'(14) = 2f'(3) = 13If F(x) = f(f(x)) and G(x) = (F(x)) then:F'(3) =G'(3) =
- Q The critical numbers of the function f(x) = (8x - 8) e^4x are:
- Q The circumference of a sphere was measured to be 75 cm with a possible error of 0.5 cm. Use linearapproximation to estimate the maximum error in the calculated surface area.Estimate...
- Q Use implicit differentiation to find y' and then evaluate y' at the point (3,5).y - 3x +2=0
- Q For the polynomial function f(x) = -0.02x4+.36x2 - 1.62, find all local and global extrema.No local extrema exist.The only extrema point is (-1.62, 0).The only extrema point is (9, 0).The...
- Q A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 16...
- Q Find the equation of the line through P = (9,8) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area.(Use symbolic...
- Q A poster of area 6000 cm has blank margins of 10 cm wide on the top and bottom and cm wide on the sides. Find the dimensions that maximize the...
- Q The volume (r) (in cubic meters) of a spherical balloon with radius r meters is given by V(r) = 4/3?r.The radius W (t) (in meters) after t seconds is given...
- Q Given this function: f(x)=35+arcsin(x/11) an equation for the line tangent to the graph of y = f(x) at the point where x=11/2 is:
- Q A cardboard box without a lid is to have a volume of 5,324 cm. Find the dimensions that minimize the amount of cardboard used.(Let x, y, and z be the...
- Q Find the average rate of change of g (x)=2x +8 from x=2 to x = 4.
- Q In Problems 3-6, find the slope msec of the secantline through the two given points and then calculatemtan = lim h?0 msec.3. f(x) = x(a) (-2,4), (-2+h, (-2+h)2)(b) (0.5, 0.25),...
- Q Given f(x) = 10x - 5x + 11 and m(x) = 20x - 5:a) Write the equation of the tangent line to f(x) when x = 2.b) At what ordered...
- Q Gravel is being dumped from a conveyor belt at a rate of 20 ft/min. It forms a pile in the shape of a right circular cone whose base diameter and...
- Q Let f(x)=x-7/2x+6Find an equation for the tangent line to the graph of f at x = 3.Tangent line: y =
- Q Consider the following vector function.r(t) = (7t2, sin(t)- t cos(t), cos(t) + t sin(t)), t> 0(a) Find the unit tangent and unit normal vectors T(t) and N(t).T(t) =N(t) =(b) Use...
- Q A cylinder shaped can needs to be constructed to hold 450 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The...
- Q A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 22 ft/s.At what rate...
- Q A road perpendicular to a highway leads to a farmhouse located 2 mile away. An automobile traveling on the highway passes through this intersection at a speed of 55mph. How...
- Q If an arrow is shot straight upward on the moon with a velocity of 72 m/s, its height (in meters) after t seconds is given by s(t) = 72t -...
- Q A 16 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t = 0 and slides away from the wall...
- Q The minute hand on a watch is 8 mm long and the hour hand is 4 mm long How fast is the distance between the tips of the hands changing...
- Q Use an appropriate local linear approximation to estimate the value of the given quantity.(2.04)3
- Q A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the...
- Q A silver bar with a specific heat of 0.235 J/gC has a mass of 250. g and is heated from 22.0C to 68.5C. How much heat will the silver bar...
- Q A cylinder shaped can needs to be constructed to hold 300 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The...
- Q (A) Find the average rate of change of the area of a circle with respect to its radius r as r changes from(i) 5 to 6 ?? Average rate of...
- Q A box with a square base and open top must have a volume of 48668 cm. We wish to find the dimensions of the box that minimize the amount of...
- Q For what values of a does the graph of f(x) = 2x + 3x - 12z - 4 have a horizontal tangent line?Answer(separate by commas): x =
- Q Find the rate of increase (with respect to r) in the surface area (S = 47) of a spherical balloon when:(A) r = 1 inches ? Rate of increase =(B)...
- Q Suppose that 108 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle as...
- Q Use differentials to estimate the amount of paint needed to apply a coat of paint .05 cm thick to a hemispherical dome with diameter 50 m.
- Q A spotlight on the ground is shining on a wall 12m away. If a woman 2 tall walks from the spotlight toward the building at a speed of 0.8m/s, how...
- Q A 15 Rt ladder leans against a wall. The bottom of the ladder is 5 ft from the wall at time t= 0 and slides away from the wall at...
- Q A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that...
- Q If f(x) = 4x - 2x + 4 then:'(2)=An equation for the line tangent to y = f(x) at the point where x =y =
- Q An equation for the line tangent to the graph of f(x) = 5x - 3+ 9ex at the point where x = - 5:y =
- Q Given the function g(x) = 6x +54x + 90x, find the first derivative, g'(x).g'(x) =Notice that g'(x) 0 when a = 5, that is, g'(-5) = 0.Now, we want to...
- Q Suppose that a certain radioactive element has an annual decay rate of 8%. Starting with a 4,329 gram sample of the element, how many grams will be left in 10...
- Q This function:f(x)=- 40x4e-xhas critical numbers:On the graph of y = f(x) the smallest critical numbercorresponds to:a local maximuma local minimumneither a local maximum or a local minimumOn the graph of...
- Q A company sells tires and rents out a portion of its warehouse toanother company for a fixed rent of $8,000. The accountingdepartment claims the company's monthly profit is determined by...
- Q The number of mosquitoes in Brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled bym(x) = -2(x-4)What is the maximum possible number of mosquitoes?
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