Calculus question and answers for October 19, 2023
- Q You invested $6000 between two accounts paying 2% and 9% annual interest, respectively. If the total interest earned for the year was $470, how much was invested at each rate?
- Q Find fx, fy, fx(2,-5), and fy(4,6) for the following equation.f(x,y)=?(x +y)fx= (Type an exact answer, using radicals as needed.)fy= (Type an exact answer, using radicals as needed.)fx(2,-5) =(Type an exact...
- Q Find fx, and fy, for f(x, y) = 2(7x-5y+12)^5 fx(x,y)=fy(x,y)=
- Q Find fxx, fxy, fyx, and fry for the following function. (Remember, fx means to differentiate with respect to y and then with respect to x.)f(x, y) = e^6xyfxx=fxy = fyx=fyy=
- Q Solve the following system of equations using Gaussian elimination or Gauss-Jordan elimination.8x - y + 2z = 112x + y - z = -3- 6x + y + 2z =...
- Q Consider the following.7x - y = 6(a) Find y' by implicit differentiation.y' =(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.y' =
- Q Given a circle where the center is (-6, 8) and another point on the circle is (-3, 4),(a) Write an equation of the circle in standard form.(b) Graph the circle.Part...
- Q Simplify the expression: 102x 10dx10x101 210-2z1 2
- Q Consider the Logistic Growth Model xt+1 = 1.5rxt(1 - xt).What condition on r guarantees that the equilibrium x* = 0 is stable? Remember to use the stability test.
- Q Find the derivative.y = In(2 + ex 2 - ex)
- Q Let f'''(x) = 8Find the particular solution to the above differential equation that satisfies the following initial conditions.f has a horizontal tangent line at (3, 7).f' has a horizontal tangent...
- Q A canyon is 1966 meters deep at its deepest point. Suppose a rock is dropped from the rim of the canyon above this point. Determine the time required for the...
- Q Let f''(z) =7/x^3Find the particular solution to the above differential equation that satisfies the following initial conditions. f'(-3)=3 f(-1) = -1f(z) =
- Q Differentiate.f(?) = (?-cos?) sin?f'(?)=
- Q Find the derivative of the function.F(t) = (1 9t + 1)3F'(t) =
- Q Find the derivative of the function.f(x) = (2x - 7x + 9)6f'(x) =
- Q Find the derivative of the function.y = 7?x
- Q Rewrite the rational exponent,In 3?50=In (50
- Q Suppose a product's revenue function is given by R(q)=-7q+500g, where R(q) is in dollarsand q is units sold.Find a numeric value for the marginal revenue at 5 units, and record...
- Q A graphing calculator is recommended.Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by looking at a graph to find initial approximations. (Enter...
- Q Let f(x) = x4(x - 2).(a) Find the critical numbers of the function f. (Enter your answers from smallest to largest.)smallest valuelargest value(b) What does the Second Derivative Test tell...
- Q Find a function that gives the vertical distance v between the line y = x + 42 and the parabola y = x2 for -6 ? x ? 7.v(x) =...
- Q Minimize Q=6x + 3y, where x + y = 9.
- Q Find the derivative of the functionF(x) = x4-7x + ?x xin two ways: by using the Quotient Rule and by simplifying first. (Check that your answers are equivalent. Which method...
- Q The graph of the derivative f' of a continuous function is shown. (Assume continues to m.)(a) On what interval(s) is increasing? (Enter your answer in interval notation.)On what interval(s) is...
- Q Consider the following function. (If an answer does not exist, enter DNE.)h(x) = (x + 1)9 - 9x - 2(a) Find the interval of increase. (Enter your answer using interval...
- Q A function f(x) is given below. Express the relationship between f'(x) and f(x) in words, and write a differential equation that f(x) satisfies.f(x) = 19e-xExpress the relationship between f'(x) and...
- Q Find the derivative of f with respect to x of f(x) = In x ^15The derivative of f with respect to x of f(x) = In x^ 15is
- Q Find the indicated derivative for the function.f''(x) for f(x) = 2x^4 - 7x +5x-7f''(x) =
- Q Let f (x) = (1/3)^x-2 . Find the y-intercept and the equation of the asymptote.y-intercept: type your answer...asymptote: choose your answer....
- Q Complete the equation to illustrate the identity property of multiplication.1(k+p) =
- Q Use only the associative property to rewrite the following algebraic expression.10+(1+x)
- Q A parabola opening up or down has vertex (4, 5) and passes through (-14, -61/4). Write its equation in vertex form.Simplify any fractions.
- Q Find the indicated derivative for the function.h''(x) for h(x) = 5x-3 - 8x-8h''(x) =
- Q Find the derivative and simplify.d/dx 5x4 - x +7x+8What is d/dx 5x4 - x +7x+8? Choose the correct answer below.A. 5x4-x +7x+8 (4x - 2x + 7) In 5B. 5x4-x...
- Q Differentiate the following function.f(x)=7+5x+4 exf'(x) =
- Q Differentiate the following function.f(x) = -8 + 5x + 6 exf'(x) =
- Q Find f'(x).f(x) = 9xe - 4 exf'(x) =
- Q Find the coordinates of a point on a circle with radius 5 corresponding to an angle of 145?(x,y) = (,)Round your answers to three decimal places.If ?=1?4?=1?4, thensin(?)sin(?) =cos(?)cos(?) =Give...
- Q To measure the height of a building, a person stands away from the base and measures the angle of elevation to the top of the building to be 52. Moving...
- Q Simplify the expression as much as possible.cos (t) - 1/sin(t)
- Q A city has a population of 220,000 people. Suppose that each year the population grows by 3.75%. What will the population be after 9 years? Use the calculator provided and...
- Q Use the price-demand equation below to find the values of p for which demand is elastic and the values for which demand in inelastic. Assume that price and demand are...
- Q If f(3) = 3 and f'(x) ? 2 for 3 ? x ? 5, how small can f(5) possibly be?f(5) ?
- Q Use the price-demand equation x = f(p)=??522-6p to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and...
- Q Find the derivative of f with respect to x of f(x) = ln x^10
- Q Find the dimensions of a rectangle with an area of 225 square feet that has the minimum perimeter.The dimensions of this rectangle are ft.
- Q Two sides of a triangle have lengths 13 m and 17 m. The angle between them is increasing at a rate of 20/min. How fast (in m/min) is the length...
- Q A price ceiling is given along with demand and supply functions, where D(x) is the price, in dollars per unit, that consumers will pay for x units, and S(x) is...
- Q At age 35, Cynthia earns her MBA and accepts a position as a vice president of an asphalt company. Assume that she will retire at the age of 65, having...
- Q A point is moving on the graph of xy = 12. When the point is at (4,3), its x-coordinate is increasing by 4 units per second. How fast is the...
- Q Assume x and y are functions of t. Evaluate dy/dt for 3xy-3x+6y = -42, with the conditions dx/dt = 12, x=6, y = -1.
- Q Find the derivative.d/dt (9t-5)^6/t+3
- Q Find the indicated derivative and simplify.y' for y= 8x - 6/x + 7x
- Q Find the indicated derivative and simplify.y' for y = (1 + 4x ? 3x) e^x-
- Q Find the derivative.d/dx [2x (x-1)^4]
- Q Use one or more of the six sum and difference identities to find the exact value of the expression.sin(45 +60)
- Q Find the indicated derivative.y' for y = (2x + 3x) (5x-2)
- Q Find fx and fy for f(x,y) = y In (9x + 5y).
- Q Find the indicated derivative.f'(x) for f(x) = 8x/7x - 1
- Q 6Find f and f, for f(x, y) = 3(9x ? 4y + 8)^6fx (x,y)=fy(x,y) =
- Q Use the product rule to find the derivative.y = (2x + 3)(3x - 4)
- Q Find the four second-order partial derivatives for f(x, y) = 6x^6y^7 + 9x^5y^8.
- Q Find fxx, fxy, fyx, and fry for the following function.f(x, y) = e^9xy
- Q Find dy/dx for the indicated function y.y = 3^x + e
- Q Present value. A promissory note will pay $40,000 at maturity 10 years from now. How much should you be willing to pay for the note now if money is worth...
- Q A zoo supplier is building a glass-walled terrarium whose interior volume is to be 16 ft. Material costs per square foot are estimated as shown below.Walls: $1.00Floor: $2.00Ceiling: $2.00What dimensions...
- Q Find the four second-order partial derivatives.f(x,y) = 4x8y-5xy + 8yfxx (x,y) =fxy (x,y) =fyx (x,y) =fyy (x,y) =
- Q Find all second order derivatives for r(x,y)= xy / 8x + 5yrxx(x,y) =ryy(x,y) =rxy (x,y)=ryx (x,y) =
- Q Find fxx fxy: fyx and fy for the following function. (Remember, fx means to differentiate with respect to y and then with respect to x.)
- Q Give the domain of f, the domain of g, and the domain of m, where m(x) = f[g(x)].f(u) = In u; g(x) = 25-x
- Q Find the absolute extrema of the function f(x) = 12+x / 12-x on the interval [4,6].The absolute maximum occurs at x =The absolute minimum occurs at x =
- Q Suppose y = 5 cos (7t +27) + 6. In your answers, enter pi for ?.(a) What is the phase shift?(b) What is the horizontal shift?
- Q Find fx, fy, and f?. The symbol ? is the Greek letter lambda.f(x, y, ?) = x + y-?(2x +9y-6)
- Q The total sales, S. of a one-product firm are given by S(L,M) = ML-L2, where M is the cost of materials and L is the cost of labor. Find the...
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