Calculus Questions

4 Find the radius of gyration with respect to its axis of the solid generated by revolving the first quadrant region under the curve y 4 x about the y axis

2 Refer to the given vectors for the problems that follow 5 points each a Find v 3u u i 2j v i

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

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

Find the area of the triangle determined by the points P Q R P 1 1 2 Q 2 0 1 R 0 2 1

rms of Linear Equations Show all calculations in the space provided Please remember to indicate the formula s you use Describe the equations below List and identify the information provided by the equations 1 y 8 x 3 2 y x 3 Place the equation in slope intercept form 3 3x 2y 18 0 3 y 4x 4 y 2 x 5

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

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

A tree casts a shadow 6 feet long At the same time a person who is 4 feet tall casts a shadow that is 2 feet long How tall is the tree 19 feet 17 feet 15 feet 12 feet

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

VE vo X Simplify into a single log 2 log x log 4y

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

X Given f x x 3x 2x 1 What is the degree of the function As x approaches negative infinity f x is approaching

X Given that f x 3x 4 and g x x 1 find g f x 76 El

Find where x 2x 0 Write your answer in interval notation Round to one decimal place as needed Try again Left Interval 0 00 Right Interval undefined Edit my response

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

Question What is a b if a 3 4i and b 2 3i

Use a graphing utility to approximate the real solutions Round to two decimal places x 3x 6x 1 0 Solution 1 Solution 2

www Find the solution to the equation given below Exact values only e 5

Solve the equation 3x 1 10 Show your work Round to one decimal place as needed Solution 1 Solution 2

The graph of f is shown below Evaluate each integral by interpreting it in terms of areas 1 f x dx 1 5 2 f 2 dun 0 3 f x dx Note You can click on the graph to enlarge the image

X Given the two points A 2 3 and B 3 9 Find the mid point

Use the properties of logarithms to condense the expression Assume z 6 5 In z In z 5 2 In z 6

A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building Round your answer to two decimal places Enter an integer or decimal number more Question Help Message instructor

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

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

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

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

Find the number b such that the line y b divides the region bounded by the graphs of y 36x and y 9 into two regions wi equal area Round your answer to two decimal places b

Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle 2 4 x 4 y x y 4 y 4 4 y 2 2 Find the area of the region 2 X X 2 1 1 1 2 2 2 X X

Evaluate the integral and interpret it as the area of a region 2 1 14 sin x 4 cos 2x dx Sketch the region 1 KIN NTH T KI4 10 2 X a 2 416 412 kter X X

Y NOTES y Sketch the region enclosed by the given curves 2 y G 4 2 4 0 6 ASK YOUR TEACHER y 5 cos 6x y 5 sin 12x x 0 0 05 PRACTICE ANOTHER Find its area 0 10 0 15 0 20 0 05 0 10 0 15 0 20 0 25 0 25 X 0 30 X 12 y st 4 3 2 1 y 6 0 05 0 10 0 15 0 20 0 25 5 4 In 3 X 2 1 0 05 0 10 0 15 X 0 20 0 25 0 30 X

Sketch the region enclosed by the given curves 1 y 16x y X 0 16 10 8 y 10 8 aff 2 Find the area of the region Need Help Read It 10 Watch It 15 8 X X y 10 8 10 6 y 10 2 10 8 15 X X

Find the values of c such that the area of the region bounded by the parabolas y 4x c and y c 4x2 is 288 Enter your answers as a comma separated list C

14 sin A B 7 A 24 25 C

13 sin A B 9 A 40 41

12 sin X X 50 48 Z 14 Y

Find the value of each trigonometric ratic 11 cos X Y 27 36 45 X

Find the area of the shaded region 20 15 10 5 y 9x x 2 y 2x 4 6 7 14 00 8 10 X

MY NOTES 6 ASK YOUR TEACHER Sketch the region enclosed by the given curves y 14x1 y x 5 4 2 y 25 20 15 10 5 y 15 10 5 10 Need Help Read It 15 Find the area of the region PRACTICE ANOTHER 2 4 6 X 6 6 4 4 2 y 15 10 5 10 15 y 25 20 15 10 5 2 4 4 6 6 X X

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

Use a graphing utility to graph the function and find any asymptotes numerically by creating a table of values for the function 6 2 02 a Graph the function f x 15 10 10 15 10 5 10 10 15 10

All the necessary values have been found to calculate the margin of error We have Za 2 1 960 p 0 26 and E 0 05 Substitute these value rounding the result to four decimal places za 2 p 1 p E 1 96 2 0 26 1 0 26 n Since this value represents a sample size a whole number should be used Using the whole number smaller than this value will result in a larger than desired margin of error so the value should be rounded up to the nearest whole number Thus a sample size of should be used to ensure the margin of error of 0 05 is obtained