Application of derivatives Questions and Answers

Convert each radian measure into degrees 5 18 1 Convert each degree measure into radians 3 45 2 10T 3 4 300
Calculus
Application of derivatives
Convert each radian measure into degrees 5 18 1 Convert each degree measure into radians 3 45 2 10T 3 4 300
A 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 derivatives
A 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
Use the Laws of Logarithms to combine the expression 7 log x 8 log x 1
Calculus
Application of derivatives
Use the Laws of Logarithms to combine the expression 7 log x 8 log x 1
Find 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 derivatives
Find 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
Use the Laws of Logarithms to expand the expression log V 7x y HODINY FR
Calculus
Application of derivatives
Use the Laws of Logarithms to expand the expression log V 7x y HODINY FR
Use 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 derivatives
Use the elimination method to solve the following initial value problem dR dt dJ dt J R R 0 1 J 0 0
Find the sum 7 1 0
Calculus
Application of derivatives
Find the sum 7 1 0
A 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 derivatives
A 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
The 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 derivatives
The 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
Rewrite 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 derivatives
Rewrite 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
Use the product to sum formulas to write the product as a sum or difference 2 sin 20 sin 50
Calculus
Application of derivatives
Use the product to sum formulas to write the product as a sum or difference 2 sin 20 sin 50
Use 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 derivatives
Use 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
Use 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 derivatives
Use 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
The 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 derivatives
The 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
Use 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 derivatives
Use the properties of logarithms to expand the expression as a sum difference and or constant multiple of logarithms Assume all variables are positive
Rewrite 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 derivatives
Rewrite 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
Rewrite the expression in terms of In 2 and In 3 In 108
Calculus
Application of derivatives
Rewrite the expression in terms of In 2 and In 3 In 108
Consider 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 derivatives
Consider 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
Complete 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 derivatives
Complete 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
Find 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 derivatives
Find 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
1 If x 0 and y 0 then 2x y al X
Calculus
Application of derivatives
1 If x 0 and y 0 then 2x y al X
Graph 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 derivatives
Graph 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
Use 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 derivatives
Use 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
150 180 210 120 240 90 270 60 30 2 3 4 300 330 0
Calculus
Application of derivatives
150 180 210 120 240 90 270 60 30 2 3 4 300 330 0
Solve the triangle with the given angles and sides 6 points B 52 C 28 a 43 c
Calculus
Application of derivatives
Solve the triangle with the given angles and sides 6 points B 52 C 28 a 43 c
Find 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 derivatives
Find the area of the parallelogram whose vertices are given below A 1 4 B 4 0 C 11 3 and D 6 7
Find 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 derivatives
Find the volume of the parallelepiped box determined by u v and w u 4i 2j V 3i j 3k w i 3k
0 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 derivatives
0 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
The 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 derivatives
The 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
18 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 derivatives
18 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
The 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 derivatives
The 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
Given 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 derivatives
Given 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
5 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 derivatives
5 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
Find the solution to the equation given below Exact values only Try again 4x 5 x 0 4024
Calculus
Application of derivatives
Find the solution to the equation given below Exact values only Try again 4x 5 x 0 4024
What is the conjugate of b if a 3 4i and b 2 3i
Calculus
Application of derivatives
What is the conjugate of b if a 3 4i and b 2 3i
Question What is a b if a 3 4i and b 2 3i
Calculus
Application of derivatives
Question What is a b if a 3 4i and b 2 3i
X Given the two points A 2 3 and B 3 9 Find the mid point
Calculus
Application of derivatives
X Given the two points A 2 3 and B 3 9 Find the mid point
If 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 derivatives
If 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
The 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 derivatives
The 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
Find the area of the largest rectangle that can be inscribed in the ellipse 2 y 1 a 62
Calculus
Application of derivatives
Find the area of the largest rectangle that can be inscribed in the ellipse 2 y 1 a 62
Find 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 derivatives
Find 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
A 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 derivatives
A 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
15 Given a 3 B 5 and a b 7 determine a b
Calculus
Application of derivatives
15 Given a 3 B 5 and a b 7 determine a b
11 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 derivatives
11 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
Suppose 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 derivatives
Suppose 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
Question 6 Solve the rational inequality Write your answer in interval notation 4 3 C 2 0
Calculus
Application of derivatives
Question 6 Solve the rational inequality Write your answer in interval notation 4 3 C 2 0
Solve 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 derivatives
Solve 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
Solve 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 derivatives
Solve 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
In 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 derivatives
In 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
Watch 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
Calculus
Application of derivatives
Watch 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