Calculus question and answers for August 15, 2023
- Q Find the Fourier expansion of f(t) = sin (t).
- Q Consider the autonomous equationdx/dt = (1-x)e^x.(a) Sketch the phase line for the equation. Label each equilibrium as a sink (stable), source (unstable), or node (neither).b) Predict the asymptotic behavior as...
- Q One hour after the start of an experiment there were 105 bacteria and after five hours the count was 8505. Assuming that the population grows exponentially, that is according to...
- Q Use the definition of a logarithm to rewrite the equation as an exponential equation. log196 (14) = 1/2
- Q Find cif a = 2.34 mi, b 3.68 mi and ?C= 40.7 degrees Enter crounded to 3 decimal places.
- Q A company produces two types of solar panels per year. x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars,...
- Q Find the equation of the tangent line to the graph of the given function at the specified point.15.) y = x + 3x + 4, at (1, 2)
- Q An object at the origin at time t = 0 has velocity measured in meters per second,t 20 if 0 ? t ? 60v(t) = {3 if 60 < t...
- Q A 70 lb weight stretches a spring 10 feet. The weight hangs vertically from the spring and a damping force numerically equal to 7 2?5 times the instantaneous velocity acts...
- Q The functions f, g, and h are defined as follows.f(x)=2+?-4+x g(x) = ?10+2x x h(x) = -2 |x-8|Find f(7), g(4), and h (2).Simplify your answers as much as possible.
- Q The function fis defined below.f(x) = x +6x-16 x-4Find all values of x that are NOT in the domain of f.If there is more than one value, separate them with...
- Q Find the area of the surface.The part of the sphere x2 + y2 + z = 49 that lies above the plane z = 2.
- Q Find the area of the surface.The part of the sphere x + y + z = 4z that lies inside the paraboloid z = x + y.
- Q The exposure index EI for a 35-millimeter camera is a measurement of the amount of light that hits the film. It is determined by the equation EI = log? (+)....
- Q If f(x) is a differentiable function and f' (c) = 0 at an interior point c of f's domain, and if f" (x) > 0 for all x in the...
- Q Mr. K's math class is 1 1 4 hours long. After working problems on the board for 55 minutes (11 12 hour), he gave the students the rest of the...
- Q The function y = cotx - 2?3 3csc x has an absolute maximum value on the interval 0<x< ?. Find it.
- Q A team of engineers is testing an experimental high-voltage fuel cell with a potential application as an emergency back-up power supply in cell phone transmission towers. Unfortunately, the voltage of...
- Q Find the equation of the vertical asymptote.f(x) = ln (11-x)
- Q Solve the system of equations.3x-5y-2z=29x-15y-6z=72x-3y-5z=4Select the correct choice below and fill in any answer boxes within your choice.A. There is one solution. The solution is(Type exact answers in simplified form.)B....
- Q In a certain country people own a total of about 348 million fish, cats, and dogs as pets. The number of fish owned is 14 million more than the total...
- Q Suppose a person 5 feet tall throws a rock vertically upward. Determine the initial velocity, vo, of the rock, if the rock reaches a maximum height of 39.52 feet. Round...
- Q Suppose you are driving along 1-95 at 134 kilometers per hour, when you notice a large board in the road ahead. You immediately begin to brake. If the large board...
- Q Let h' (u)=6/uFind the particular solution to the above differential equation that satisfies the following initial condition.h(e^8) =-2h(u) =
- Q Let h''(v) = 0Find the particular solution to the above differential equation that satisfies the following initial conditions.h'(8) = - 4h(9) = -6h(v)=
- Q Let dh/dx = 3x - 3Find the particular solution to the above differential equation that satisfies the following initial condition. h(8) = -8h(x)=
- Q Consider the following function.f(x) = x - 3x2 + 3xFind the derivative of the function.f'(x) =Use the derivative to determine whether the function is strictly monotonic on its entire domain...
- Q Find the general solution of the differential equation below and check the result by differentiationdp/dz=-16z^7P(z)=-2z^8+1P(z)=-2z^8P(z)=-112z^6P(z) = -2z^8+ CP(z)=-112z^6 +C
- Q Find f.f"(x) = ?2 + 12x - 12x, f(0) = 8, f'(0) = 14
- Q Find the vertex of the graph of the function. Do not enter any spaces in the answer.f(x) = (x+80) - 21
- Q Find the point on the line y = 4x + 2 that is closest to the origin.(x, y) =
- Q A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.)If the...
- Q Find the (a) period, (b) phase shift (if any), and (c) range of the following function.y=-3-tan (x + ? 2)
- Q Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the inflection points.f(x) = -x6 +...
- Q Letg(x) = 6x-18x+8, f?(x) = |g(x)|, f?(x) = |f?(x) - P?|,f3(x) = |f?(x) - P?|and ifP? = 7then the range ofP?such thatf3(x)has exactly 10 points of non-differentiability is,(A).(1,5,7)(B).[2,5,8](C).[2,9](D).(1,8)
- Q Find two numbers whose sum is 25 and whose product is a maximum.
- Q Find two positive numbers whose product is 22 and whose sum is a minimum.The two numbers are(Type an exact answer, using radicals as needed. Use a comma to separate answers...
- Q Find two numbers whose sum is 24 and whose product is a maximum.The two numbers are(Simplify your answer. Use a comma to separate answers as needed.)
- Q Which slope field is associated with the differential equation given below?dy/dx= 1-y
- Q Gonzalez Manufacturing borrowed $33000. Part of the money was borrowed at 10%, part at 12%, and part at 14%. The annual interest was $3980, and the total amount borrowed at...
- Q Find the x and y coordinates of all inflection points.f(x) = x +27xWhat is/are the inflection point(s)? Select the correct choice below and, if necessary, fill in the answer box...
- Q Find the x and y coordinates of all inflection points.f(x)=x +21xWhat is/are the inflection point(s)? Select the correct choice below and, if necessary, fill in the answer box to complete...
- Q Of all numbers whose difference is 12, find the two that have the minimum product.What are the two numbers?(Use a comma to separate answers as needed.)
- Q Find two positive numbers whose product is 91 and whose sum is a minimum.The two numbers are(Type an exact answer, using radicals as needed. Use a comma to separate answers...
- Q Find two numbers whose sum is 22 and whose product is a maximum.The two numbers are(Simplify your answer. Use a comma to separate answers as needed.)
- Q Of all numbers whose difference is 16, find the two that have the minimum product.What are the two numbers?(Use a comma to separate answers as needed.)
- Q Inspect the graph of the function to determine whether it is concave up, concave down or neither, on the given interval.A cube function, m(x)=x^3, on (-?,0)On the interval (-?o,0), the...
- Q Find two numbers whose sum is 9 and whose product is a maximum.The two numbers are(Simplify your answer. Use a comma to separate answers as needed.)
- Q Suppose f(x) = ln (3)3x. Determine and graph four distinct antiderivatives of f.
- Q Number 2.) 8, 21, 46, 89, 156, ...General Rule = ?23rd term = ?32nd term = ?
- Q First use appropriate properties of logarithms to rewrite f(x), and then find f'(x).f(x) = 4 In(2/x)
- Q Simplify the expression as much as possible. tan(x) cos(x) =
- Q If possible, find a solution to tan(4? + 1) = -4. If no solution exists, enter NONE.radians help (angles)?
- Q How many years will it take $9,000 to grow to $14,200 if it is invested at 3.50% compounded continuously?
- Q Consider the following curve.y =X+3/X-4Find the slope m of the tangent line at the point (3, -6).m =y =Find an equation of the tangent line to the curve at the...
- Q Consider h(v) = 13v / (v+18)Determine the intervals on which h is decreasing.h is decreasing on:h is decreasing nowhere.Determine the intervals on which h is increasing.h is increasing on:h is...
- Q Let g(x) = x +24xDetermine the absolute extrema of g on [1, 5]. If multiple such values exist, enter the solutions using a comma-separated list.The absolute minimum of g is...
- Q At 2:00 p.m. a car's speedometer reads 30 mi/h. At 2:10 p.m. it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the acceleration is exactly 120...
- Q Find the demand function p, given the marginal-revenue function dr/dq below.dr/dq=299-8q-0.3qFind y subject to the given conditions.y''' = 12x, y''(0) = 16, y'(0) = 6, and y(0) = 7y(x) =...
- Q First use the appropriate properties of logarithms to rewrite f(x), and then find f'(x).f(x) = 13x + In 13xRewrite f(x) using properties of logarithms.f(x) = (Do not simplify.)Find f'(x).f'(x) =
- Q Find two numbers whose sum is 10 and whose product is a maximum.The two numbers are
- Q A couple who borrow $80,000 for 30 years at 6%, compounded monthly, must make monthly payments of $479.64.(a) Find their unpaid balance after 1 year. (Round your answers to the...
- Q Consider the following function.f(x) = 16 - x^(2/3)Find f(-64) and f(64).Find all values c in (-64, 64) such that f'(c) = 0. (Enter your answers as a comma-separated list. If...
- Q Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?f(x) = 3x - 4x + 2, [0, 2]Yes, it does not matter if f is...
- Q The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2/min. At what rate...
- Q D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that...
- Q A Company operates 12 oil wells in a designated area, Each pump, on average, extracts 156 barrels of oil daily. Company can but well reducep every added output of each...
- Q Solve for the variable P to two decimal places.63,300 Pe ^0.072(9)P = (Round to two decimal places as needed.)
- Q An investor bought stock for $20,000. Eight years later, the stock was sold for $40,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000...
- Q A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars,...
- Q Of all points (x,y,z) that satisfy x + 3y + 2z = 27, find the one that minimizes (x-1) + (y-1)+(z-1).The given function has a minimum at which satisfies x...
- Q Mari needs to design an open-top box with a square base. Due to the nature of the project, the box must have a volume of 48,668 cubic inches. Determine the...
- Q Determine two positive values such that the sum of the first number and four times the second number is 546 and whose product is a maximum.Enter the solutions using a...
- Q A cylindrical container must hold 92 cubic centimeters of fluid. Determine the radius the cylinder such that the construction materials necessary are as least as possible.
- Q Find the relative maximum and minimum values.f(x,y) = e^x +9y +15Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.A. The function has...
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