Application of derivatives Questions and Answers

Two cars are moving towards an intersection One car is 170 meters north of the intersection and moving towards the intersection at 11 m s while the other is 200 meters west of the intersection and moving towards the intersection at 10 m s How rapidly are the cars approaching each other 5 seconds later The cars are getting Select an answer 3 decimal places at m s Enter your answer rounded to

In 2005 the world population was 6 4 billion The exponential growth rate was 1 2 per year Fin the exponential growth function

Two variable inequalities from their gr Google Classroom 5 4 3 2 5 Y 3 2 L 2 3 4 cr 1 2 3 4 5 Find the inequality represented by the graph

The population of a small town in central Florida has shown a linear decline in the years 1994 2004 In 1994 the population was 45200 people In 2004 it was 36300 people A Write a linear equation expressing the population of the town P as a function of t the number of years since 1994 Answer B If the town is still experiencing a linear decline what will the population be in 2009

and work When you are completed take a picture and upload it to Schoology 1 f x x 5x 2x 8 Degree 3 odd ends go opposite L C 1 Right Side Goes y intercept 0 5 092 260 8 0 0 08 Potentiol zeros 1 2 4 2 2 5 2 2 2 2 f 1 1 5 1 26 0 111 5 2 8 0 8 8 1 680 1x 6x 8 x 4 x 2 X 4 0 X 4 2 f x 2x x 6x 7x 2 Degree 4 X 2 0 x 2

Quilt squares are cut on the diagonal to form triangular quilt pieces The hypotenuse of the resulting triangles is 36 cm long What is the side length of each piece Round your answer to he nearest hundredth

Find the equation in factored form and sketch the graph of a polynomial function with an inflection point at 0 1 and is tangent to the x axis at 2 The point 0 12 is on the function

1 10 A curve is given by the parametric equations below A Graph x vs t and y vs t then sketch the curve in the x y plane B Sketch the line tangent to the curve at the point corresponding to t 3 and calculate its slope If you lack drawing skill carefully label some important points in your graph to make u for it X cost y sin t 1 0 t 2

The graph of which function has a minimum located at 4 3 f x x 4x 11 Of x 2x 16x 35 Of x x 4x 5 O f x 2x 16x 35

160 B gure below the a g x 2 sin x 2 b g x sin x 2 c g x 2 sin 2x d g x 2 sin x e g x 2 sin 2x 2 f g x sin 2x 2 g g x sin 2x plotted using a blue line while the red corresponds to graph the listed Mark this Tu

13 Use an Addition or Subtraction Formula to write the expression as a COMBINED trigonometric function of one number and then find its exact value Round to 2 decimal places if needed LOS 3T 27 21 7 3 sin sin 7 COS 27 21 tan tan 18 1 tan kla kla TT tan 18

What is the net outward flux of the rotation field F z 9y 6x 7x across the surface that encloses any region D in R www What is the net outward flux Select the correct choice below and fill in any answer boxes within your choice A The net outward flux is Type an exact answer using as needed OB The net outward flux cannot be determined for an arbitrary surface

Use Stokes Theorem to find the circulation of the following vector field around any simple closed smooth curve C F y z 2xyz 3xy z The circulation is

21 Solve the logarithmic equations for x apo shtronomo log x log x 3 2 log x 5 logo x 3 1 X 5 x 3 1 X 5 1 5 5 x 6 x 3 1 3 3 X 4

Simplify 82 1 212 A x 82 1 OC 2x x 18 O E 22 8 24 13 OB 8x x4 D 2x z 1

Given that cot 0 7 sec 0 0 for the angle 0 0 0 2 find the exact value of each trigonometric functi 0 a sin 20 b cos 20 c sin d cos 2 a sin 20 Type an exact answer using radicals as needed 0 b cos 20 Type an exact answer using radicals as needed c sin Type an exact answer using radicals as needed 0 d cos Type an exact answer using radicals as needed e tan 20 Type an exact answer using radicals as needed f tan 0 2 Tyno an exact answer using radicals as pooded Y 0 e tan 20 f tan 2

a Sketch 0 in standard position Then sketch an angle between 0 and 2x that is coterminal with 0 L

Solve for x to the nearest 10th 320 6790 0 88 3 2 450 MED samanl

Solve for the exact value of x 21n 1x 1 10 14

Write the expression below as a single logarithm in simplest form 3 log 4 log 4

10 For the function f x e8 find f x

What is the value of log6 6 5

Express the following fraction in simplest form only using positive exponents 3d 4n5 3 19 33 4

Expand the binomial by using Pascal s Triangle to determine the coefficients 2v 3 6

Use Pascal s Triangle to find the binomial coefficient 6 3

Use the Binomial Theorem to expand the complex number Simplify your result Remember that i 1 2 1 5

8 Find fxe 2 dx a c x x e x C xe 2x e 2x C b d xe 2x e 2x C xe 2 2x C

17 Find the radius of convergence for 1 k 1 xk k a c R 1 R 2 b 3 R 0

12 Find the slope of the tangent line to the curve x t 1 y 2t t 1 at t 1 a c 5 1 b d 4 3

Consider the vector field 2 5 3 xr where r x y z a Compute the curl of the field and verify that it has the same direction as the axis of rotation b Compute the magnitude of the curl of the field a The curl of the field is i k

3 3 points Find an equation of the tangent line to the graph of the function at the given point y ln 2 1 227 1 2 2 1

4 3 points Find the particular solution of the differential equation that satisfies the initial condition s f x sinx f 0 1 f 0 6

Find dy by implicit differentiation x y y x da

7 Z4 74 OA OB 24 10i 24 10i C 24 10i OD 24 10i

49 If 3 identical prizes are available for a contest with 50 entrants in how many ways can the prizes be distributed What is the answer A 3 260 OB 117 600 C 9 800 D 19 600

37 2n lim n n 2 A 2 The limit B B does not exist C 1 2 D 0

32 For the geometric sequence with a 5 and ag 405 find the common ratio OA B 119 113 C 9 D 3

12 Find the roots of this function f x x 2x 2 A 1 2 and 1 2 OB 1 i and 1 i OC 1 2 2 and 1 2 2 OD 1 2i and 1 2i

Find the lengths of the circular arc Assume r 9 and 0 132 6 6T X S S 0

Determine the amplitude range period and phase shift and then sketch the graph of the function using the quarter points y 5 sin 4x x 1 The amplitude of y 5 sin 4x x 1 is Type an exact answer using as needed Use integers or fractions for any numbers in the expression The range of y 5 sin 4x 1 1 is Simplify your answer Type your answer in interval notation Type an exact answer using it as needed Use integers or fractions for any numbers in the expression The period of y 5 sin 4x x 1 is Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression The phase shift of y 5 sin 4x 1 is Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Use the coordinates of the five quarter points of y sinx to determine the corresponding quarter points on the graph of y 5 sin 4x x 1 Quarter points of y sin x 0 0 I 2 B x 0 3x Quarter points of y 5 sin 4x x 1 Simplify your answers Type ordered pairs Type exact answers using as needed Use integers or fractions for any numbers in the expressions Choose the correct graph of y 5 sin 4x 1 below O A 2 0 O C O D

Consider the following region R and the vector field F a Compute the two dimensional divergence of the vector field b Evaluate both integrals in Green s Theorem and check for consistency F 2y 5x R is the triangle with vertices 0 0 4 0 and 0 4 a The two dimensional divergence is 0 b Set up the integral over the region SS 0 0 Type exact answers dy dx

Solve each trig equation below All angles are in radians 17 cotxsinxsec x cscx for 0 x 2 58 18 4sin2x 4cosx 5 0 for 0 x 27 58 19 sin x 2sinxcosx 0 for 0 x 2 58

5 Solve the initial value problem y 2y y 2y y 2y 2y y y 0 1 y 0 0 y 0 3 y 0 2

1 pt Given the logistic function f t 3 function is maximum Leave your answer with 3 decimal places 1 2e 05 find the value of t where the growth rate of the

Graph the function and label all key points and aymptotes y 2 tanx 2 x

5 Solve the triangle Round your anwer to the nearest tenth wer in the space provided 3 B 110 C 4 a

Let s solve the exponential equation 4e 80 a First we isolate e to get the equivalent equation b Next we take in of each side to get the equivalent equation c Now we use a calculator to find x Round your answer to three decimal pla

a Most calculators can find logarithms with base following Round your answers to three decimal places logs 16 log log and base e To find logarithms with different bases we use the Change of Base Formula b Do we get the same answer if we perform the calculation in part a using In in place of log O Yes the result is the same No the result is not the same 8 To find logs 16 we wn

The logarithm of a product of two numbers is the same as the sum of the logarithms of these numbers So log2 4 8 log2 4

Use the Laws of Logarithms to expand the expression log3 2x