Basic Math question and answers for November 12, 2024
- Q Find the general solution of the given second-order differential equation. 25y" 15y' - 4y = 0
- Q Use implicit differentiation to find y'. Then evaluate y' at (-1,1).x^5 + y^5 = lny
- Q Given the differential equation dy/dx = 2x^2+5/3y^2, find the particular solution, y = f(x), with the initial condition f(-3) = -2.
- Q First find f' and then find f.f"(x) = 6x + 10x + 3x +3,f'(1) = -1,f(1) = -9.f'(x) = f(x) =
- Q Suppose that the concentration y(t) of glucose in the bloodstream satisfies the followingdifferential equation,dy/dt =r-ky,where r and k are positive constants. Determine the concentration at any time t by solvingthe...
- Q Suppose a park has a total area of N km, and that A(t) km of this area iscovered in weeds (with time t in days since the start of spring)....
- Q Some medicines can wear off in the body exponentially. In this case, assume the rate decays hourly for a starting amount of 250 mg of medication according to the equation:M...
- Q Monthly sales of a Jeep Wrangler are expected to increase at a rate ofS' (t) = -24t3 Jeep Wrangler per month, where t is time in months and S(t)is the...
- Q A circle has the equation x2 + y + 6x-4y-23=0.(a) Find the center (h,k) and radius r of the circle.(b) Graph the circle.(c) Find the intercepts, if any, of the...
- Q A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 10 in /min, how...
- Q A thermometer reading 24 Celsius is placed in an oven preheated to a constant temperature. Through a glass window in the oven door, an observer records that the thermometer read...
- Q Find dy/dx by implicit differentiation.x? + y? = 6
- Q A closed box is constructed of 4200 cm of cardboard. The box is a cuboid, with height h cm and square base of side x cm. What is the value...
- Q First find the general solution (involving a constant C) for the given differential equation. Then find the particular solution that satisfies the indicated condition.ds /dt = 11t+5t-5;s-76 at t=0The general...
- Q Park rangers released 4 fish into a pond in year 0. Each year, there were threetimes as many fish as the year before. How many fish were there after xyears?...
- Q Using our quadratic equationknowledge match the following scenarios.1. Hitting a golf ball on the moon2. Hitting a golf ball on Earth from thetop of a tall building3. Hitting a baseball...
- Q Solve the following initial value problem. By this we mean that you should find y = y(x) which satisfies both equations below. (See the linkedexample.)2=13/03 +5x, _y(1) = ?19x?ANSWER: y(x)...
- Q 15. Plutonium-239 is the isotope that is most often used in nuclear reactors, and has a half-life of 24,100 years. At the time of the 1986 accident at Chernobyl, there...
- Q When a cake is removed from an oven, its temperature is measured at 300F. Three minutes later its temperature is 200F. i. Find the temperature T(t) of the cake after...
- Q The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 51.3% of their carbon-14. How old were the bones...
- Q Use Euler's Method to make a table of values for the approximate solution of the differential equation with the specified initial value. Use n steps of size h. (Round your...
- Q Determine A, B, and C so that y = A cosh (Ca) + B sinh (Cx) satisfies the conditions yn - 9y = 0, y(0) = 1, y' (0) =...
- Q Verify that the general solution satisfies the differential equation. Then find the particular solution that satisfies the initial condition(s).y = Ce-12xy' +12y = 0y = 24 when x = 0
- Q Find the equilibrium solution of the following equation, make a sketch of the direction field, for t20, and determine whether the equilibrium solution is stable.y' (t) = -(y/2)-4The equilibrium solution...
- Q Write and find the general solution of the differential equation that models the verbal statement. (Use k for the constant ofproportionality. Use C for the constant of integration.)The rate of...
- Q A test to measure aggressive tendencies was given to a group of teenage boys who were members of a street gang. The test is scored from 10 to 60, with...
- Q The half-life of the radioactive element plutonium-239 is 25,000 years. If 16 grams of plutonium-239 are initially present, how many grams are present after: (round your answer to the nearest...
- Q Determine whether the following equation is separable. If so, solve the given initial value problem.sect (y' (t)) = 1, y(0) = 6Select the correct choice below and, if necessary, fill...
- Q If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in cm/min) at which thediameter decreases when the diameter is 9...
- Q For the following expression, find the correct partial fraction decomposition.11y - 68y +48/ y(y - 4) (4y - 4)Enter your answer as the sum of fractions with a constant in...
- Q Verify that the given function y is a solution of the differential equation that follows it. Assume that C is an arbitrary constant.y(t) = C? sin 12t+C? cos 12t; y''(t)...
- Q The mess in a house can be measured by M(t). Assume that at M(0) = 0, the house starts out clean. Over time the rate of change in the mess...
- Q The rate of change of N is inversely proportional to N.IfN (0) = 4, and N(2) = 6, what is N(5)?8.031733.33325.3337.629
- Q The percentage of compression on the lumbar vertebral disks causes strain in an adult human. The strain can be measured by S(x) = 7.2956 In(0.0645012 x^0.95 + 1), where x...
- Q Suppose that a point moves along a curve y = f(x) y=f(x) in the xy-plane in such a way that at each point (x,y) on the curve the tangent line...
- Q A company produces and sells electric cars. The company's profit, P, in thousands of dollars, changes based on the number of cars, x, they produce per month.The rate of change...
- Q The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value...
- Q In this problem, y = 1/(x + c) is a one-parameter family of solutions of the first-order DE y' + 2xy = 0. Find a solution of the first-order IVP...
- Q Find the general solution of the given higher-order differential equation.y''' + 2y" - 9y' - 18y = 0
- Q Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.(x - y) dx + x dy = 0
- Q Solve the given initial-value problem. The DE is a Bernoulli equation.x^2dy/dx - 2xy = 6y^4, y(1) =1/4
- Q The given two-parameter family is a solution of the indicated differential equation on the interval (-?, ?). Determine whether a member of the family can be found that satisfies the...
- Q Solve the given initial-value problem. The DE is homogeneous. (x + 2y) dx/dy = xy, y(-1) = 3
- Q Find the general solution of the given differential equation. dy/ dx = 8y y(x) = Give the largest interval over which the general solution is defined. (Think about the implications...
- Q XA company manufactures mountain bikes. The research department produced the marginal cost function C'(x) = 600-10-? , 0?x? 900, where C'(x) is in dollars and x is the number of...
- Q A candy box is made from a piece of cardboard that measures 37 by 20 inches. Squares of equal size will be cut out of each corner. The sides will...
- Q Factor the trinomial. Check the factorization using FOIL multiplication.?-20y+75Select the correct choice below and, if necessary, fill in the answer box to complete your choice.OA. Y - 20y+75=B. The trinomial...
- Q A 39-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wallis increasing at 10 meters per minute.At a certain instant,...
- Q Solve the following differential equations by finding the general solution first then the particular one that satisfies the given constraint in each case.1. xyy' = ln x, y(1) = 2.2....
- Q Find the derivative of the function.y = In ( 5 +e^x )/(5-e^x)y' =
- Q (1 pt) In cold weather, we feel colder when the wind blows. This is quantified by the wind chill index W which is supposed to predict how coldwe will feel...
- Q The total number of acres of genetically modified crops grown worldwide from 1997 to 2003 was changing at the rate given belowin million acres/year.R' (t) = 2.463 18.56t+ 47.38(0 st?...
- Q Find f.f(x)f"(x) = 6 + 6x + 24x, f(0) = 2, f(1) = 10
- Q A chemical plant is adding pollution to a lake at the rate of 35?3 tons per year, where t is the number of years that the plant has been in...
- Q The function y = 100e^(-0.045t) models the amount, y, of radioactive material remaining, in grams, as a function of time t, in days. Calculate the half-life of this radioactive material....
- Q A flu epidemic hits a college community, beginning with five cases on day t = 0. The rate of growth of the epidemic (new cases per day) is given by...
- Q II.Obtain the general / particular solution for the following differentialequation. Show your solution in bond paper.(15 Points each)1. (xy + x) dx = (xy + x + y +1)dy2. (1+Inx)...
- Q A cone is expanding at the rate of 6 cm/sec. The formula for the volume of a cone is: What is when r = 2?
- Q The radius of a sphere is measured as 9 centimeters with a possible error of 0 025 centimeter a Use differentials to approximate the possible propagated error in cm in...
- Q Find the surface area of the composite figure 3 cm 5 cm 4 cm 8 cm 8 cm 5 cm 7 cm 10 cm SA cm Enter
- Q 10 ft 8 ft 6 ft Find the area of this figure Round your answer to the nearest hundredth Use 3 14 to approximate A ft Notice that only half...
- Q The length of a picture frame is 7 inches more than the width For what values of x is the perimeter of the picture frame greater than 154 inches loca...
- Q You are building a patio of the back of your house The diagram shows the plan for the patio Each unit in the coordinate plane represents 1 5 feet Find...
- Q ose a table to fit in a very small space He has 5 choices and wants to choose the table with the smallest area Which of the table tops below...
- Q A garden is shaped like a regular hexagon Each side of the hexagon measures 10 meters and the heigh of one of the isosceles triangles in the hexagon is about...
- Q Kevin s grandmother gave him an old lamp that needs a new lampshade He wants to buy some fabric to make a new lampshade The lampshade is 10 inches tall...
- Q Find the surface area of the composite figure 4 cm 3 cm 4 cm 13 cm SA 12 cm 2 cm 5 cm 3 cm Enter
- Q Which of the following integrals represents the area enclosed by the smaller loop of the graph of r 1 2 sin B E 11 6 7 6 11 6 7...
- Q Question 2 W B Q 0 1 25b D B 0 b C 0 0 A a 0 A plan for a triangular garden was plotted on coordinate axes with...
- Q Raymond has a circular garden with a radius of 9 feet He wants to build a walkway that is feet wide around the garden A What will the area of...
- Q In Exercises 21 and 22 the area of the shaded sector is shown Find the indicated measure See Example 4 21 area of OM K 50 M 22 radius of...
- Q The diameter of a standard basketball is 9.5 inches. If the basketballs are covered in rubber, what is the minimum amount of rubber needed to manufacture a set of four...
- Q Four congruent isosceles right triangles are added to the edges of a regular octagon to form a square, as shown. If the legs of each of the four triangles are...
- Q The Walmart parking lot is a rectangle that measures 420 feet long and 218 feet wide. Each parking space is a rectangle that measures 18 feet long and 9 feet...
- Q If two opposite sides of a square are increased by 7 meters and the other sides are decreased by 2 meters, the area of the rectangle that is formed is...
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