Application of derivatives Questions and Answers

Factor the trinomial 4x 21x 5 ALICATES ht

x 2x 24 Select the correct choice below an O A x 2x 24 Simplify B The trinomial is not factora

IC Equations by I by Using the K Factor the given trinomi x 2x 8

Observe that r t a cos t b sin t defines an ellipse a Find the arclength of r t b Find the curveature of r t

Solve the initial value problem 4 2 dr 1 1 x dY dt where the initial condition Yo is a Yo 1 0 Y Y 0 Yo b Yo 2 1 c Yo 1 2

225 ft X 0 104 0 A building that is 225 feet tall casts a shadow of various lengths as the day goes by An angle of elevation is formed by lines from the top and bottom of the building to the tip of the shadow as seen in the figure above Find the rate of change of the angle of elevation do dx when x 104 radians per foot Round to five decimal places

Identify any extrema of the function by recognizing its given form or its form after completing the square Verify your results by using the partial derivatives to locate any critical points and test for relative extrema If an answer does not exist enter DNE 14y 1 f x y x y 4x relative minimum relative maximum x y z x y z

1 Let f x 2 sin x 9 cos x tan J f x

1 Points A B and C are three vertices of a parallelog complete the parallelogram A 1 2 B 7 10 C 11 10

3x 10 8 3x 10 8x 9

vFind the slope of the line joining the points 0 5 and 2 2

Graph the solution set of the inequality where x X 2 Oc

Use the slope intercept form to graph the ed

Graph the solution set of the inequality where 3 x2 1

Graph the equation and state the slope of t y 3 alto graph the linear ed

aphing Linear Equations he equation and state the slope of the line if the B graphing tool to graph the linear equation Click to enlarge graph

39 Surveying To find the distance across a small lake a sur veyor has taken the measurements shown Find the distance across the lake using this information 2 82 mi 40 3 B 3 56 mi A

53 Land Value Land in downtown Columbia is valued at 20 a square foot What is the value of a triangular lot with sides of lengths 112 148 and 190 ft

Solve An investment is worth 2877 in 1992 By 1997 it has grown to 5547 Let y be the value of the investment in the year x where x 0 represents 1992 Write a linear equation that models the value of the investment in the year x

33 36 Heron s Formula Find the area of the shaded figure rounded to two decimals 33 4 3 6 34 5 5 5 2 2

29 32 Heron s Formula Find the area of the triangle whose sides have the given lengths folly Srebre el 29 a 9 b 12 c 15

5 Compute the Riemann Sum for f x x 4 on the interval 2 3 with five subintervals 1 7 2 X1 4 1 2x 0 x3 1 x4 X5 3 with the sample points in each subinterval x 1 x 2 x3 x4 x3 determined by the partition xo

47 54 Values of Trigonometric Functions Find the values of the trigonometric functions of from the information given Thaboven Sne Joyche Im 47 sin 0 0 in Quadrant IV 4 4 48 tan 0 0 in Quadrant III 49 cos 0 12 sin 0 0

57 60 Area of a Triangle Find the area of the triangle with the given description 57 A triangle with sides of length 7 and 9 and included angle 72

Give an equation of the form f a A esc Br C D which could be used to represent the given graph Note U U a Of z 2csc z 7 1 b Of z 2csc z 1 c Of x 2 csc z x d Of x 4 csc z 1 e Of z 4 csc 2 x 1 3m 2x

Use differentials to approximate the number 3 022 1 972 5 992 Round your answer to five decimal places

Graph the solution set of the inequality where x is

4 One of the roots of the polynomial P z z 4z3 3z 10z 50 is i 3 a Find a quadratic factor of P z with real coefficients b Find the other roots of P z

State whether the expression is a monomial binomial or trinomial 3ab 4 Obinomial trinomial O monomial

Write fractions as N D or N D with no spaces In the expression 6r the variables are the constants are 1 5 and and

4 a Find the intersection point of the line L x 3 t y 1 2t 2 1 2 with the planes x 2y 2z 11 and x 2y 2z 7 call them P and Q Find the distance D from P to Q Is D the distance between the planes Why c Find the midpoint R of the segment from P to Q d Find the equation of the plane that contains R and is parallel to the plane x 2y 2z 7

Consider the following position function a Find the velocity and speed of the object b Find the acceleration of the object 1 r t 1 1 8 1 12 1 fort 20 b What is the acceleration of the object a t

At the beginning of an experiment a scientist has 188 grams of radioactive goo After 165 minutes her sample has decayed to 2 9375 grams What is the half life of the goo in minutes Find a formula for G t the amount of goo remaining at time t G t How many grams of goo will remain after 41 minutes

5 12 Given the data X 3 6 0 83 with missing components use the prediction estimation algorithm of Section 5 7 1 estimate and E Determine the initial estimates and iterate to find the first revise estimates

ework 2 1 Element 1 16 0 15 answered estion 11 slope of the tangent line to

hework 2 1 Elementar 0 16 0 15 answered Question 7 x x 2x 7x 2x en f x is 4 is

n 2

15 When a cold drink is taken from a refrigerator its tempera ture is 5 C After 25 minutes in a 20 C room its temperature has increased to 10 C a What is the temperature of the drink after 50 minutes b When will its temperature be 15 C

3 A roast turkey is taken from an oven when its temperature has reached 185 F and is placed on a table in a room where the temperature is 75 F a If the temperature of the turkey is 150 F after half an hour what is the temperature after 45 minutes b When will the turkey have cooled to 100 F

1 Let q x 1 2 Use the graph of k x and the table of p x shown below and the equation of q to answer the following questions k x 5 5 0 5 4 2 0 2 4 3 4 5 I p x 1 2 10 X a Let f x kop x Evaluate f 2 b Solve f x 4 for x c Let g x q k x Evaluate g 0 d Solve g x 1 for x e Let a x p x 2q x Evaluate a 4 f Let b x k x g x Evaluate b 6

83 If V is the volume of a cube with edge length x and the cube expands as time passes find dv dt in terms of dx dt

Evaluate the following integrals S 1 2 3 1 x 25 x dx 1 SD VD x x 9 e 1 e2r da use the substitution e tan 0 da

rgian College Accelerate you X Carb Diyeti Ne Content gc blackboard com ultra courses 323494 1 cl outline 10 Benefits of Onlin QUESTION 3 ProQuest Ebook Ce Expand each of the following 3 5 x 105 X d Error DOI Prefix ht Note Do not include spaces for your zeros or number Conversely if you have 2 5x 10 5 0 000 025 do not

Suppose a point moves along a circle with radius r as shown in the figure below The point travels a distance s along the circle in time t a The angular speed of the point is S b The linear speed of the point is V c The linear speed v and the angular speed are related by the equation V

Find the exact value of the expression cos tan 40 9

Rewrite the expression as an algebraic expression in x sin tan x

Find the radius r of the circle if an arc of length 28 m on the circle subtends a central angle of 7 8 rad Round your answer to two decimal places r m

Find the exact value of the trigonometric function If an answer is undefined enter UNDEFINED cot 120

Solve the following equation for x X log 9x 11 3 log x 5

Solve the following equation for x Round your answer to three decimal places X log 9x 14 log x 8 2 log 3x