Calculus question and answers for November 17, 2023
- Q In 17 years, Maggie Oaks is to receive $100,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.4%, compounded continuously, what is the...
- Q In 2004 (t = 0), the world consumption of a natural resource was approximately 18 trillion cubic feet and was growing exponentially at about 10% per year. If the demand...
- Q Find the accumulated present value of a continuous stream of income at rate R(t) = $132,000, for time T = 17 years and interest rate k= 3%, compounded continuously.
- Q Find the present value Po of the amount P = $200,000 due t = 6 years in the future and invested at interest rate k = 7%, compounded continuously.
- Q Find the future value P of the amount Po invested for time period t at interest rate k, compounded continuously.Po = $200,000, t = 7 years, k = 4.8%
- Q Solve for r to two decimal places.3= e ^3r
- Q Solving A = Pe^rt for P, we obtain P = Ae^rt which is the present value of the amount A due in t years if money earns interest at an...
- Q The price-earnings ratio of a stock is given byR(PE)=P/Ewhere P is the price of the stock and E is the earnings per share. Recently, the price per share of a...
- Q Determine the domain of the function of two variables.g(x,y)= 8 / 2y-7x^2
- Q Of all the numbers whose sum is 32, find the two that have the maximum product.
- Q Determine two positive values such that the sum of the two numbers is 216 and the product of the first number and the square of the second number is a...
- Q Find a positive number such that the sum of its reciprocal and 6,912 times its square is as small as possible.
- Q Determine two positive values such that the product of the two values is 10658 and the sum of the first number and two times the second number is a minimum.Enter...
- Q Graph all three functions, sin(x), 2 sin(x), sin(2x), on one axis. Make sure to label your functions.
- Q A firm has the marginal-demand function D'(x) = - 1800x/?(25-x2), where D(x) is the number of units sold at x dollars per unit. Find the demand function given that D...
- Q Let f(x) = 8 - 13x - 2x5 + 3x6. Find the following:Degree of the f(x) =Leading coefficientEnd behavior: (Note: type "infty" for ? and "-infty" for -? )As x...
- Q Find the missing factor, A.x (A) = -14x
- Q Use long division to find the quotient and remainder.(2x + 9x - 12) (x + 5)What is the quotient?What is the remainder?
- Q Find the extreme values of f on the region described by the inequality. (If an answer does not exist, enter DNE.)f(x, y) = e^-xy, x + 4y ? 1maximumminimum
- Q Find the x-values (if any) at which f(x)=x/x^2 -2x is not continuous.f(x) is not continuous at x=0 and f(x) has a removable discontinuity at x=0.f(x) is not continuous at x=0,...
- Q If the length of the diagonal of a rectangular box must be L, what is the largest possible volume? cubic units
- Q Heather has $45.71 in her savings account. She bought six packs of markers to donate to her school. Write an expression for how much money she has in her bank...
- Q Determine the leading coefficient and degree of the polynomial.(2x+5)(x-1)(3x + 2)a. The leading coefficient is b. The degree is
- Q Evaluate the polynomial function for x = -4 and x = -1.f(x)=x-5x - 14f(-4)=f(-1) =Based on the results and the Intermediate Value Theorem, which statement is correct?Because both f(-4) and...
- Q Solve the following equation.3x - 6x - 4x + 8 = 0
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