Application of derivatives Questions and Answers

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Given that the graph of f x passes through the point 9 4 and that the slope of its tangent line at x f x is 3x 3 what is f 5 f 5

A car is merging onto a freeway beginning at rest accelerating at a constant rate of 17ft sec How long does it take to reach merging speed at 76mph help numbers Time in seconds

Find the most general antiderivative of the function f x Va F x 4 3 Use an upper case C for any arbitrary constants

Find the most general antiderivative of the function f t 10 cos t 3 sin t Use an upper case C for any arbitrary constants F t

A balance sheet shows Total Current Assets of 332 500 Cash of 57 000 Notes Receivable of 9500 Accounts Receivable of 161 500 and Inventory of 104 500 Total Plant Assets of 38 000 Land of 19 000 Buildings of 9500 and Fixtures of 9500 and Current Liabilities of 190 000 Determine the Current Ratio the Acid Test Ratio and evaluate the health of the company The Current Ratio for the company is to 1 Round to the nearest hundredth The Acid Test Ratio isto 1 Round to the nearest hundredth By common rules of thumb A the Acid Test Ratio suggests good financial condition but the Current Ratio is too low B both ratios suggest the company may have difficulties OC both ratios indicate a healthy company

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1 point Attempt 3 of Unlimited 11 km 6 km 2 g of the ship Round to the nearest tenth of a de 3 4

1 Fill in the blank A regular polyhedron whos

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exact value of the expression 1 sin 7T

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exact value of the expression 2 6 11 sin

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Convert to Celsius Use C 11 F 59

8 1 Points Lines Pla Angles In the figure m is parallel t m 44 121 Find the mea n 1 2 87 m 3 4 6

nd the exact value of the expression tan sin 58

the exact value of the expression COS sin 53

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exact value of the expression 1 tan1 3

Find the exact value of the expression 3 2 sec cos

the exact value of the expression 3 os sin 1

e exact value if any of the composite function sin 1

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Solve the triangle For the sides give an expression f decimal place Part 1 of 3 b 74 A 17 4 B 68 B Content 94 6 a B

Remember that showing your work in arriving at solutions is required for all problems Find x so that B 3xi 5j is perpendicular to 21 6j 1

A water trough is 5 m long and has a cross section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom 80 cm wide at the top and has height 40 cm If the trough is being filled with water at the rate of 0 2 m3 min how fast is the water level rising when the water is 30 cm deep

Find the volume of the solid whose base is the region bounded by y x y 1 and the y axis and whose cross sections perpendicular to the x axis are squares Volume

Determine the maxima and minima of the function ax by e x y 0 a b

The following function is one to one Find the inverse of the fu

3 0 71 Points DETAILS PREV stone is dropped from the upper observation a Find the distance s t of the stone

Wo sides and an angle are given below Determine whether the given information results in one triangle two triangles or no triangle at all Solve any resulting triangle s a 4 c 3 C 120 COCOS Select the correct choice below and if necessary fill in the answer boxes to complete your choice Type an integer or decimal rounded to two decimal places as needed OA A single triangle is produced where AB and b OB Two triangles are produced where the triangle with the smaller angle B has A B and b and the triangle with the larger angle B has A B and b OC No triangle is produced

Using the properties of combinations of continuous functions determine the interval s over which the function f x x x 12 is continuous O O O O a b 12 c 12 d 12

Consider the two functions 3 and b on the interval a al if a 4 2 What value does b have to be in order for the area between y and y2 and a a to equal 28 8 Round your answer to five decimal place

et a and b be real numbers The following system of equations can have exactly two solutions x 5y a x 4y b

Which of the following polar coordinate pairs does not represent the point with rectangular coordinates 2 2 Select one O a 2 2 135 ob 2 2 315 Oc 2 2 45 Od 2 2 45 Oe 2 2 225

How many permutations are there of 42 objects when taken 9 objects at a time if a particular one of these objects must always b included O a 9 42 42 9 O b 9 42 1 42 9 1 O c 9 421 42 9 d 42 421 42 9 2 e 421 42 9 2

A jar contains 23 differently coloured balls If you remove all the balls one at a time how many colour sequences are possib O a 23 23 b 23 1 O c 23 O d 1 e 23

A jar contains 22 differently coloured balls If you remove two balls one at a time how many different colour sequences are possible O a 22 O b 22 O c 221 2 O d 22 22 2 2 e 221 22 2

For what values of p is the integral convergent a All values of p less than 1 O b Oc O d O All values of p greater than 1 All values of p greater than or equal to 1 This integral is divergent for all values of p All values of n lore than or equal to 1 Coo 1 1 XP

A random variable has CDF given by JA A i 0 1 2 1 i 3 if A 0 97 then what is po F Answer

A random variable has CDF given by F A i 0 1 2 1 i 3 if A 0 37 then what is p3 Round your answer to two decimal places Answer

Minimize f x y x xy y2 subject to y 20 without using the method of Lagrange multipliers instead solve the constraint for x or y and substitute into f x y Use the constraint to rewrite f x y x xy y2 as a function of one variable g x g x

The function S Tr 40 T 50 3 r gives an ice cream shop s daily sales as a function of Temperature T in F and ain r in inches Find ST 90 2 include the appropriate units and explain what it means ST 90 2 inches per F per dollar F per inch dollars per F dollars per inch dollars per F per inch F per inch per dollar

Speedometer readings for a motorcycle at 12 second intervals are given in the table 0 12 24 36 48 60 v ft s 30 28 25 22 24 28 a Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time interva ft b Give another estimate using the velocities at the end of the time periods c Are your estimates in parts a and b upper and lower estimates Explain b is a lower estimate and a is an upper estimate since v is a decreasing function of t O a and b are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t O a is a lower estimate and b is an upper estimate since v is an increasing function of t

Evaluate TC IC sin6 x cos5 x dx