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Answered: 19. - Use the properties of logs to…

Math

Calculus

19. - Use the properties of logs to write in terms of simpler logs ,16, 5 (expand): loga 232 ing groph

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 8E

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In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?
A closed right circular cylinder will be built with two types of metal. The base and the top of the cylinder will be constructed of metal that has a value of $ 2 per cm2, while The side surface of the cylinder will be constructed of a metal that costs $ 2.5 per cm2. The function that allows to minimize the cost of manufacturing said cylinder is given by: the answers are in the first attached image
The median size of a new single-family house built in the United States between 1987 and 2001 can be modeled by the equation H(x) = 0.359x3 − 15.198x2 + 221.738x + 862.514 square feet where x is the number of years after 1980. 1. Determine the value of x in the domain 7 ≤ x ≤ 21 for which the median house size was increasing least rapidly. (Round your answer to three decimal places.) 2. Thus, in which year was the median house size was increasing least rapidly? 3. Find the corresponding house size. (Round your answer to one decimal place.) 4. Find the corresponding rate of change in house size. (Round your answer to three decimal places.)
Among the specifications of a company, which requires packing its product in boxes, it is found that for a box the sum of its dimensions (length (x) -width (y) -height (z)) must be 450 cm. The function that allows determining the maximum volume of the box that meets these characteristics is given by:
Suppose that the output Q (in units) of a certain company is Q = 75K^1/3L^2/3, where K is the capital expenditures in thousands of dollars and L is the number of labor hours. Find ∂Q/∂K when capital expenditures are $2,744,000 and the labor hours total 2744. Interpret ∂Q/∂K. If labor hours remain at 2744 and K increases by $1000, Q will increase about how much?? Find ∂Q/∂L when capital expenditures are $2,744,000 and the labor hours total 2744. (Round your answer to the nearest whole number.) Interpret ∂Q/∂L. If…
3 determine the value of x of the following piecewise functions please complete solution ty
A piece of wire of length 63 is cut, and the resulting tow pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square? (a) Let x be the amount of wire used for the circle. What is the function A, the combined ara of the circle and square in terms of x? A= ______ (type an expression, type the exact number using pi as needed) To minimize the combined area, the wire should be cut so that a length of ____ is used for the circle and a length of ____ is used for the square. (round to nearest thousandth) (b) To maximize the combined area, the wire should be cut so that a length of ____ is used for the circle and a length of ____ is used for the square. (round to nearest thousandth)
Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which consists of line segments and semicircles of radius 3 connecting the points (−8, 0), (−6, 6), (0, 6), (6, 6), (8, 0). What is the multipart formula for y = g(x) when -6 <= x <= 0 and when 0 <= x <= 6?
Suppose the function of earnings (in dollars) is given by G(x)=10x^3-320x^2+3410x-12090 where x is the quantity of product that is produced and sold. Suppose that this function is defined in the intervals [9, 12] G has a relative minimum if x equals______ G has a relative maximum if x equals______ The absolute maximum of the function of earnings G(x) occurs if x is equal to_____ Tha maximum earning in this case is equal to $______dollars
The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups.25-year-old drivers areinvolved in 4.1 fatal crashes per 100 million miles driven. Thus, when a group of 25-year-old Americans have driven a total of 100 million miles, approximately 4 have been in accidents in which someone died.The number of fatal vehicle crashes per 100 million miles, y, for drivers of age x can be modeled by the formulay = 0.013x2 - 1.19x + 28.24.Use the formula above and the bar graph.What age groups are expected to be involved in 10 fatal crashes per 100 million miles driven? How well does the formula model the trend in the actual data shown by the bar graph?
(i) Discuss the continuity of the function f(x)= x^2-3x if x<2 2x+4 if x ≥ 2 on the open interval 0 < x < 2 and on the closed interval 0 ≤ x ≤ 2. (ii) An efficiency study of the morning shift at a factory indicates that an average worker arriving on the job at 7:00am will have assembled f(x)= x^3+6x^2+15x units x hours later. approximately how many units will the worker assemble between 8:00 and 8:15am?
The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion (Cl−) in a solution made of equal parts of the solutions of MgCl2 and FeCl3 is given by M = X + 1.5Y. Assume that X has mean 0.125 and standard deviation 0.05, and that Y has mean 0.350 and standard deviation 0.10 .Assuming X and Y to be independent, find σM.