# Application of derivatives Questions and Answers

Calculus

Application of derivativesConvert each radian measure into degrees 5 18 1 Convert each degree measure into radians 3 45 2 10T 3 4 300

Calculus

Application of derivativesA cell receives nutrients through its surface and its surface area is proportional to the two thirds power of its weight Therefore if w t is the cell s weight at time t then w t satisfies w aw2 3 where a is a positive constant t Solve this differential equation with the initial condition w 0 7 initial weight 7 units w t 3 at 7 X

Calculus

Application of derivativesUse the Laws of Logarithms to combine the expression 7 log x 8 log x 1

Calculus

Application of derivativesFind the function of the form y log x whose graph is given y II 1 0 0 5 0 5 1 0 2 3 1 3

Calculus

Application of derivativesUse the Laws of Logarithms to expand the expression log V 7x y HODINY FR

Calculus

Application of derivativesUse the elimination method to solve the following initial value problem dR dt dJ dt J R R 0 1 J 0 0

Calculus

Application of derivativesA weight is oscillating on the end of a spring see figure The position of the weight relative to the point of equilibrium is given by y cos 8t 3 sin 8t where y is the displacement in meters and it is the time in seconds Find the times at which the weight is at the point of equilibrium y 0 for 0 sts 1 Round your answers to two decimal p Enter your answers as a comma separated list t H Equilibrium 4x4

Calculus

Application of derivativesThe length of each of the two equal sides of an isosceles triangle is 10 meters see figure The angle between the two sides is 0 10 m a Write the area of the triangle as a function of 0 2 A 0 2 0 10 m b Write the area of the triangle as a function of and determine the value of 0 such that the area is a maximum A 0 radians

Calculus

Application of derivativesRewrite the expression in terms of the first power of the cosine Use a graphing utility to graph both expressions to verify that both forms are the same 3cos 2x

Calculus

Application of derivativesUse the product to sum formulas to write the product as a sum or difference 2 sin 20 sin 50

Calculus

Application of derivativesUse inverse functions where necessary to solve the equation Use n as an integer constant Enter your answers as a comma separated list 2 cos x 13 sin x 8

Calculus

Application of derivativesUse the properties of logarithms to verify the equation In 18 2 In 3 In 2 In 18 In 32 2 In 32 2 2 In 3 In 2 X In 3 X

Calculus

Application of derivativesThe relationship between the number of decibels and the intensity of a sound S in watts per square meter is given by 10910 10 12 B 10 log10 a Use the properties of logarithms to write the formula in a simpler form B b Use a graphing utility to complete the table Verify your answers algebraically 10 4 10 6 10 8 S n X DO so Po 100 10 10 n 10 12 an 10 14

Calculus

Application of derivativesUse the properties of logarithms to expand the expression as a sum difference and or constant multiple of logarithms Assume all variables are positive

Calculus

Application of derivativesRewrite the logarithm as a ratio of common logarithms and natural logarithms 9 lage 0 10 a common logarithms k 9 log 10 log a b natural logarithms

Calculus

Application of derivativesConsider the function f x x e6 f x has two inflection points at x C and x D with C D 3 6 where Cis 3 and Dis 3 6 3 Add Work X X retry this question below Finally for each of the following intervals tell whether f x is concave up type in CU or concave down type in CD C C D D

Calculus

Application of derivativesComplete the table to determine the balance A for 10 000 invested at rate r 2 for t years compounded continuously Round your answers to two decimal places 1 t 1 10 20 30 40 50

Calculus

Application of derivativesFind the x and y intercepts of the graph of the circle If an answer does not exist enter DNE x 10x y 2y 19 0 STEP 1 Consider the equation for the circle x2 10x y2 2y 19 0 Let y 0 Give the resulting equation below 10x 19 0 STEP 2 Solve your equation from Step 1 for x If one or more solutions exist these values are the x coordinates of the x intercepts of the graph of the circle Enter your answers as a comma separated list x x STEP 3 Consider once again the equation for the circle x 10x y 2y 190 Now let x 0 Give the resulting equation below 2y 19 0 STEP 4 Solve your equation from Step 3 for y If one or more solutions exist these values are the y coordinates of the y intercepts of the graph of the circle Enter your answers as a comma separated list y x STEP 5 Complete the problem by listing the x and y intercepts x intercepts x y y intercept x y x y x x smaller x value larger x value

Calculus

Application of derivativesGraph the function not by plotting points but by starting from the graph of y e in the figure below 10 range O 10 O y 10 10 y 10 10 y 2 10 10 X 10 O 10 State the domain and range Enter your answers using interval notation domain y 10 10 10 10

Calculus

Application of derivativesUse transformations of the graph of y 1 x to graph the rational function as in Example 2 domain 10 range 10 5 5 10 X 10 X 10 State the domain and range Enter your answers using interval notation 10 5 5 2

Calculus

Application of derivativesSolve the triangle with the given angles and sides 6 points B 52 C 28 a 43 c

Calculus

Application of derivativesFind the area of the parallelogram whose vertices are given below A 1 4 B 4 0 C 11 3 and D 6 7

Calculus

Application of derivativesFind the volume of the parallelepiped box determined by u v and w u 4i 2j V 3i j 3k w i 3k

Calculus

Application of derivatives0 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 2 3 3 81 9x x 3 cos 0 0 1 1 Then find sin 0 and

Calculus

Application of derivativesThe price of a home is 180 000 The mortgage on the hous a 30 year fixed rate mortgage at 4 Use this information to fin the amount of the monthly payment Round your answer to the nearest cent Use the formula below to solve the problem P 1 1 xt PMT 859 35 954 83 012 54

Calculus

Application of derivatives18 Estimate to the hundredth the area from 1 to 5 under the graph of f f x approximating rectangles and right endpoints 2 x using four

Calculus

Application of derivativesThe population of a colony of mosquitoes obeys the law of uninhibited growth If there are 1000 mosquitoes initially and there are 1200 after 1 day what is a The growth rate Round to three decimal places b The population of mosquitoes after 6 days Round to the nearest whole number c When will the population double Round to the nearest whole number

Calculus

Application of derivativesGiven that 2 is a zero find the remaining real zeros Show work WILL be required on the exam No approximate answers will be accepted 3 x 4x 3x 2 Solution 1 Solution 2

Calculus

Application of derivatives5 10 5 5 5 10 For which values in the domain is this graph increasing Give your answer in interval notation Assume the graph extends to finity in both directions Submit

Calculus

Application of derivativesFind the solution to the equation given below Exact values only Try again 4x 5 x 0 4024

Calculus

Application of derivativesIf 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

Calculus

Application of derivativesThe 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

Calculus

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

Calculus

Application of derivativesFind 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

Calculus

Application of derivativesA 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

Calculus

Application of derivatives11 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

Calculus

Application of derivativesSuppose 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

Calculus

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

Calculus

Application of derivativesSolve 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

Calculus

Application of derivativesSolve 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

Calculus

Application of derivativesIn 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

Calculus

Application of derivativesWatch 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