Application of derivatives Questions and Answers

A plane is flying at a constant altitude The angle of depression from the center of the plane to the base of a control tower is 32 After the plane flies 5 miles toward the control tower the angle of depression is 40 At what altitude is the plane flying 5 miles 40 Round your answer to 2 decimal places 328 E Not drawn to scale

Find the area of the triangle below Round your answer to 1 decimal place C 5 3 ft B 85 62 A

Diagram not drawn to scale 25 6 18 1 C D 136 3 71 9

Find 8 Round to the nearest tenth 39 0 7 43 1 46 9 0 35 47

How many triangles can m A 41 c No Triangles

Carbon 14 is a radioactive isotope of carbon found in all living organisms While the organism is alive carbon 14 is continually restored to maintain a roughly constant amount When the organism dies however carbon 14 begins to decay into more common isotopes of carbon The rate of decay of carbon 14 is proportional to the amount currently present with a positive constant of proportionality k a If y is the amount of carbon 14 present in a dead organism then y satisfies the differential equation dy dt 9 years hint your answer may contain the variables y t and or the positive constant k Since carbon 14 decays over time one would expect the rate of change to be negative b Given that the half life of carbon 14 has been experimentally determined to be approximately 5730 years determine the value of k Give your answer correct to at least 6 decimal places k years c In 2007 a baby wooly mammoth carcass was found buried in the permafrost in northern Russia Via a chemical analysis it was found that the carcass contained approximately 1 1 of the carbon 14 assumed to be present in an actual living woolly mammoth How old was the carcass Give your answer correct to at least the nearest year years

Consider this differential equation for y y x dy 1 y dz 1 x Find the general solution and use it to complete parts a c below a Find the solution y z for that satisfies the additional requirement y 0 0 Determine the largest open interval containing z 0 on which the identity is valid Use interval notation to enter your answer type inf to represent co y x for a E b Repeat part a but use the modified initial condition y 0 5 y x for a E c Repeat part a but use the modified initial condition y 0 5 y x for a E E

A bacteria culture starts with 940 bacteria and grows at a rate proportional to its size After 4 hours there will be 3760 bacteria a Express the population after t hours as a function of t population b What will be the population after 2 hours c How long will it take for the population to reach 1670 function of t

Find the solution to the differential equation Answer y x dy da 5xy In y whose graph passes through the point 0 e

A police car is located 70 feet to the side of a straight road A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second How fast is the red car actually traveling along the road The actual speed along the road of the red car is feet per second

The profit of manufacturing x toasters in one day is given by the following P x 0 05x 27x 450 0 x 400 a List all the critical values of P x Enter your answers as a comma separated list If an answer does not exist enter DNE X b Find the interval s where P x is increasing Enter your answer using interval notation c Find the interval s where P x is decreasing Enter your answer using interval notation d List the x value s of all local maxima of P x Enter your answers as a comma separated list If an answer does not exist enter DNE X e List the x value s of all local minima of P x Enter your answers as a comma separated list If an answer does not exist enter DNE

Let g x cos x and h x 2x Find the exact value of the expression Do not use a calculator 7 3 hog Sim hog 1 0 3

If the total cost function for a product is C x 240 0 02x 5 dollars where x represents the number of hundreds of units produced producing how many units will minimize average cost hundred units Find the minimum average cost per hundred units

Find the Taylor series of the next functions step by step pls d exp x e arc cos x

A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0 1 cm min At what rate is the volume of the snowball decreasing when the radius is 18 cm Note the answe is a positive number cm min 4 Hint The volume of a sphere of radius r is V p3

Next question Get a similar question Let f x 5x 5x 2 10 f x 50 5x 1 5x 5x 2 9 Question Help Video

Find dy dt dy dt at x 2 if y 2x 3 and dx dt 5

on 11 1 g x 2 x values g h x then Out y values 5 4 3 2 1 h x 1 2 x valu

d the following using the table below 2 3 1 3 2 2 4 X 1 f x 3 2 f x 1 4 g x 1 3 4 g x 1 3 2 4 4 x f g x then h 2

A rectangular field is bounded on three sides by a fence and on the fourth side by a stream The field is divided in two by a fence perpendicular to the river The total length of fence is 1800 m What is the maximum area that can be enclosed and what are the dimensions of the field Answ

f x x 8x 15 a Express fin standard form f x x 4 1 0 b Find the vertex and x and y intercepts of f If an answer does not exist ente x y 4 1 vertex x intercepts y intercept x y x y x y c Sketch a graph of f 5 0 3 0 0 15 10 9 8 7 6 5 smaller x value larger x value Clear All 191 A FULL

For f x x and g x 6x 5 find the following composite functions and state the domain of e a fog b gof c fof d gog a fog x 6x 5 Simplify your answer Select the correct choice below and fill in any answer boxes within your choice 5 The domain of fog is x x2 6 Type an inequality Simplify your answer Use integers or fractions for any numbers in th B The domain of f o g is all real numbers b gof x 6 x 5 Simplify your answer Select the correct choice below and fill in any answer boxes within your choice A The domain of g of is x x20 Type an inequality Simplify your answer Use integers or fractions for any numbers in the OB The domain of g of is all real numbers c fof x x Simplify your answer

4x bx bx 8x d and the graph Suppose f x 4x of Y 4x bx 4 149 and 2 381 8x d passes through the points 3 2 Then f x 4x 2x 8x866 X

Let f be the function defined by f x x x If g x f x and g 2 1 what is the value of g 2 A B C 13 74

Which of the following is the solution to the differential equation x 2 y 2 for y 2 with the initial condition y 4 5 y 4 e 7 2 A B C D y 2 3e 5 22 Y y 4 16 4 z2 4z 5 2 2 42 5

A B C D 4 11 34 z 4 9 Shown above is a slope field for which of the following differential equations 4 u 17 zy 4 y 4 1 y 4 u 4 2 11X1 VL tell

What are all solutions to the differential equation dy dz A B D y y y 99 HIN C z 1 2 1 In 2 x In 2 C C y e In 2 C 1 z In 2

If xy 5y x 3 then find the equations of all tangent lines to the curve when y 1

nd the derivative of f x pressions and find x 61 3 x 213

OMMINU 50 F 32 F Frost JFMAMJ JASOND Earthquakes Volcanoes Tornadoes Heavy Snow 3210 Wh What does the line tell us the lire dels us the padden What are the patterns of weather in this location Hazards Where does each hazard occur in North America Write your answer and show on the maps below Hurricanes

where not met in 200 iterationswhere not met in 200 iterations Use synthetic division to factor f x 7x 8x A Fill in the table below to synthetically divide out the given 1 7 7 8 7 15 13 15 2 2 2 o 13x 8 B Write the polynomial in factored form based on the result

Femi and Paul s teacher has paired them together to investigate two right triangles Select a possible strategy that Paul and Femi could use to prove the two triangles are congruent

Use the half angle formulas to determine the exact values of the sine cosine and tangent of the angle 165 sin 165 cos 165 tan 165 cos 15

Use the figure to find the exact value of each trigonometric function a b cos c d cot e sec 2 f g 2 sin cos h 2 cos tan 8 A 6

Find all solutions of the equation in the interval 0 27 Enter your answers as a comma separated list If there is no solutio enter NO SOLUTION tan x sec x 1 x No Response

Match each function with its double angle formula a sin 2u 1 2 sin u 2 sin u cos u 2 tan u 1 tan u b cos 2u 1 2 sin u 2 sin u cos u 2 tan u 1 tan u c tan 2 1 2 sin u 2 sin u cos u 2 tan u 1 tan u

A vehicle travels a distance of miles in t 2 5t 4 10t 2 6 minutes

Find the exact value of the expression cos cos 5 sin TL 20 TT 20 sin A

20 points Consider the Helix given by a cost a sin t bt with a b 0 a sketch the graph label t 0 t 2 t 2 and the motion as t b Find the unit tangent vector r t r t c Find the unit normal vector T t T t d Find the curvature T t r t e Find the unit binormal B TX N T t N t K r r r

2 For the following quadric surface x 2 y z 2 0 a Sketch at least one non empty trace parallel to each of the coordinate planes Label the axes scale and intercepts b Sketch the surface in R Label the axes scale and intercepts c Identify the surface

Find the exact length of the curve in x y x x sin

Find the arc length function for the curve y 2x 2 with starting point Po 1 2 s x

Apply Green s Theorem to evaluate the integral fc 10y x dx y 3x dy C The circle x 3 y 6 6

A student wanted to determine if there was a difference in the price of a Big Mac in New York and West Virginia The student randomly selected 12 McDonald s restaurants in New York and 10 McDonald s restaurants in West Virginia and called them and asked about the current price of a Big Mac The data are shown below New York 5 12 4 10 4 95 4 75 4 55 4 50 5 05 5 00 3 99 4 25 3 90 4 75 West Virginia 4 00 4 25 3 90 4 05 4 10 4 25 3 45 4 35 3 70 4 50 The dotplots of the data are shown 3 8 3 4 T 4 4 6 4 2 4 4 Price of a Big Mac in New York dollars 4 8 5 3 6 3 8 4 4 2 4 4 Price of a Big Mac in West Virginia dollars 5 2 4 6 a Construct and interpret a 95 confidence interval for the true difference in the mean price of a Big Mac for all McDonald s restaurants in New York and West Virginia b Does the interval provide convincing evidence that the true mean price of a Big Mac for the two states are different Explain

an 4x xdy da Determine the equation of the line tangent to graph of x xy y 11 at the point 23 C ET

nsider the following functions Step 1 of 4 Find f g 2 Answer How to enter your answer opens in new window f 4 5 3 3 3 4 2 4 and 8 2 4 2 3 CEL yax

An independent group of food service personnel condu the bill left as a tip for 35 randomly selected bills The a normally distributed Construct an interval to estimate t necessary

Evaluate a c 8 3 518 1 dx 43 b d 1 3 dive

Function Operations Given the functions f x 4x 8 and g x 2x 10 determine each of the following Give your answers as simplified expressions written in descending order f g x Evaluate f g 1 Evaluate f g x Evaluate f g x Evaluate 9 f g x f g z 1 2

2 If 0 is an acute angle and cos 0 find sin 9 single fraction sin 0 3 Do not use a calculator and express each exact value as a