Application of derivatives Questions and Answers

X Given the two points A 2 3 and B 3 9 Find the mid point

If C x 14000 400x1 6x 0 0042 is the cost function and p x 1600 7x is the demand function find the production level that will maximize profit Hint If the profit is maximized then the marginal revenue equals the marginal cost units

The frame for a kite is to be made from six pieces of wood The four exterior pieces have been cut with the lengths indicated in the figure To maximize the area of the kite how long should the diagonal pieces be horizontal vertical Queeri a b A

Find the area of the largest rectangle that can be inscribed in the ellipse 2 y 1 a 62

Find the dimensions of a rectangle with area 1331 m whose perimeter is as small as possible If both values are the same number enter it into both blanks

A right circular cylinder is inscribed in a cone with height h and base radius r Find the largest possible volume of such a cylinder Question Help Message instructor

15 Given a 3 B 5 and a b 7 determine a b

11 The vertices of quadrilateral ABCD are given as A 0 3 5 B 3 1 17 C 7 3 15 and D 4 1 3 Prove that ABCD is a parallelogram

Suppose that triangle ABC is a right triangle with a right angle at C and hypotenuse c Also note that a is the length of the side opposite angle A and b is the length of the side opposite angle B Given that b7 and A 43 determine the values indicated below Round to four decimal places when needed a C B 47 degrees

Question 6 Solve the rational inequality Write your answer in interval notation 4 3 C 2 0

Solve the polynomial inequality 12 3x 2x 0 You may need to factor the polynomial to solve State your answer using interval notation Use U for union and oo for o

Solve the inequality 4 x 2 0 Select all the intervals below that are included in the solution x 4 2 x 4 X 2 x 2 x 4

In the figure a line segment of length L is to be drawn from the given point to the positive x axis in order to form a triangle For what value s of L can the following be drawn a two triangles b exactly one triangle c no triangle a For what value s of L can two triangles be drawn Select all that apply A L 4 B L 4 C L 5 CIXD D 4 L 5 E L 5

Watch the video that describes using the Law of Cosines to solve a triangle SSS Click here to watch the video Solve the triangle if possible I A 12 19 C 10 B Find the measure of angle A Select the correct choice below and if necessary fill in the answer box to complete choice A A Do not round until the final answer Then round to two decimal places as needed

Watch the video that describes using the Law of Sines to solve a triangle SAA Click here to watch the video Find the exact length of side a Do not use a calculator C 15 1 a 120 B A Length of a Simplify your answer Type an exact answer using radicals as needed Rationalize all denominators

For u 2 1 v 5 1 and w 1 2 evaluate the expression 4u v 4u v Simplify your answer

The angle between 1 3 and 2 6 is Round to the nearest tenth as needed

Write the vector 4 17 in the form ai bj C

Find the dot product of u and v u 4i and v 3i 5j V Simplify your answer

For u 2 5 and v 4 3 find u v u v

he vector in the form a b 2 30 Q Q The vector is Simplify your answer including any rac integers or fractions for any numbers in the expression

Given vectors u and u 9 7 v 2 0 a 4u

A 142 94 b 5 385 feet a 7 947 feet Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or decimal Do not round until the final answer Then round to the nearest hundredth as needed OA The triangle has one solution B C c feet OB The triangle has two solutions The measurements for the solution with the longer side c are as follows B C C feet The measurements for the solution with the shorter side c are as follows B C C feet C The triangle has no solution

B 67 30 c 36 m a 73 m What is the length of side b b m Round to the nearest whole number as needed What is the measure of angle A A 0 0 Round to the nearest whole number as needed What is the measure of angle C c Round to the nearest whole number as needed

a b

a Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression 60 24

Find the value of 0 in the triangle Do not use a calculator 0

K Determine the number of triangles ABC possible with the given parts A 44 7 a 8 7 b 10 3 How many possible solutions does this triangle have

K hgle ABC has standard labeling and complete the statement below a Determine whether SAA ASA SSA SAS or SSS is given b Decide whether the law of sines or the law of cosines should be used to begin solving the triangle a b and C a If the values of a b and C are known which arrangement of information is given Choose the correct answer below ASA SAS SAA S55 SSA b Should the law of cosines or the law of sines be used law of sines Olaw of cosines

ermine the remaining sides and angles of the triangle ABC where A 100 83 8 30 14 and b 150 feet

Determine the remaining sides and angles of the triangle ABC where A 118 45 B 37 95 and b 120 feet C c

Determine the remaining sides and angles of the triangle ABC A Round to the nearest degree as needed COL 4 6gd a 15 m 44 B

a Simplify your answer including any radicals Use integers or fractions for any numbers in the expression A 450

Find the particular solution of the differential equation dy 3 dx 1 x y 0 1

Find the particular antiderivative of the following derivative that satisfies the given condition dy dx 3x2 7x 1 y 1 3

Graph the particular solution to Choose the correct graph OA y X dy x 2 that goes through 0 1 dx OB ST y OC y AT X

According to molecular orbital theory what is the bond order in the O ion O 5 5 05 04 O2 5 O 1 5

Use a calculator to evaluate the function at the indicated value of x Round your result to the nearest thousandth f x 7 2e x x 300

The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below where R x is revenue in dollars 400 x 1 R 0 0 Find the revenue function Find the revenue from the sale of 1 000 pairs of shoes R x 30 0 02x Find the revenue function R x R x 30x 0 01x 400 In x 1 Use integers or decimals for any numbers in the expression Find the revenue from the sale of 1 000 pairs of Ishoes The revenue the sale of 1 000 pairs of shoes is Round to the nearest cent as needed ACCEM

OH 1 6 am a do Hisoblang To Determinantni hisoblang 2 2 3 1 2 2 3 TOTO 20

9 Find the limit using l Hospital s Rule if appropriate lim 1 9x x ANSWER 1 AT SuleV 085M or to assas Daly

A company producing computer components has established that on the average a new employee can assemble N t components per day after t days of on the job training as indicated in the following table a new employee s productivity usually increases with time on the job up to a leveling off point UNA 96 t N t 3 15 12 0 12 132 20 53 5 40 70 B 96 60 78 TER The number of units is approximately Round to the nearest integer as needed 132 80 83 Q Q G SEEX 100 86 OC 96 3 5 12 120 87 132 Q OD 96 3 12 132 B Use the regression equation and a numerical integration routine on a graphing calculator to approximate the number of units assembled by a new employee during the first 100 days on the job CO

what the shaded area represents Choose the correct answer below OA The total number of miles traveled in t hours OB The total number of hours it takes to travel t miles OC The aver miles per hour in t hours OD The average number of miles traveled in t hours Velocity in miles per hour Time ir

A company finds that the marginal profit in dollars per foot from drilling a well that is x feet deep is given by P x 3 x Find the profit when a well 250 ft deep is drilled Set up the integral for the total profit for a well that is 250 feet deep P 250 JOdx 0 The total profit is Round to two decimal places as needed

The total accumulated costs C t and revenues R t in thousands of dollars respectively for a photocopying machine satisfy 1 C t 1 and 76 R t 5t e t where t is the time in years Find the useful life of the machine to the nearest year What is the total profit accumulated during the useful life of the machine The useful life of the machine is year s Round to the nearest year as needed

Show that fand g are inverse functions algebraically graphically and numerically f x 5x 6 g x x 6 X x20 a algebraically f g x W g f x 9 b graphically y 15 X 10 f 3 15 10 g 3 J x c numerically 10 12 14 10 12 14 x 15 10 15 10 g 16 20 10 12 10 12 14

Consider the following functions f x g x 2 X Show that f and g are inverse functions algebraically f g x f g f x g 2 2 Use a graphing utility to graph fand g in the same viewing window Describe the relationship between the gi The graph of f is the translation of the graph of g relative to the line y x The graphs of fand g are the same as the graph of y x The graphs are the same The graph of f is the reflection of the graph of g in the line y x

Sketch the function 3 p x x x 2x The end behavior of the gunction is on the right and on the left

Question Answer Attempt 1 out of 2 The function y f x is graphed below What is the average rate of change of the function f z on the interval 6 2 10 8 6 4 2 100 80 60 40 20 20 40 60 80 100 6 8 10 Submit Answer Watch Video x Show Examples

Careers G google translate G Member Login US YouTube to Mp3 C CCBubble Knee Len estion answer Attempt 1 out of 2 10 8 6 e function y f x is graphed below What is the average rate of change of the function f x on the interval 1 x 0 4 2 100 So 60 0 20 20 40 y A 60 80 100 2 6 8 O Watch Video 10 All Bookmarks Show Examples