Calculus Questions

h 16t 2 48t 160 When will the object hit the ground

regulation size by the International Football Association FIFA field is variable if it is between 100 and 110 m long and between 64 and 73 m wide it is considered DA 50 Part a A particular field is 108 5 m long and 68 5 m wide What is the area of this field in square meters A sin cotan m cos asin tan 7 8 9 9 HOME acos E TAL 4 S 6 Grade Summary Deductions Potential 0 100 Submissions Attempts remaining 10

5 Find the coordinate matrix x given the coordinate matrix x B 1 1 9 9 1 1 1 9 1 B 3 0 3 3 3 0 0 3 3 x B 5 4

Given that cos 0 3 10 10 and is in Quadrant IV what is sin 0 Provide your answer below

Use a reference angle to write cos Provide your answer below 43 36 in terms of the cosine of a positive acute angle in radians

Given the triangle shown in the figure below find the value of sin t Give your answer as the ratio of side lengths 25 24

Given the triangle below find cos 0 Enter the answer as a fraction 24 7 25

Given that cot 0 and 0 is in Quadrant II find sec 0 and csc 0 12 Provide your answer below

0 Provide your answer below 65 ft A hiker is standing on the ground looking up to the top of a tree with an angle of elevation of 0 54 The figure shown above represents the situation where the base of the triangle is the eye level of the hiker and the vertical side is the tree Based on the dimensions shown in the figure what is the distance a in feet from the hiker to the base of the tree Rounc one decimal place

Write sec 325 in terms of the secant of a positive acute angl Sorry that s incorrect Try again

In terms of the cotangent of a positive acute angle what is the expression for cot 55

Provide your answer below B The figure above shows a right triangle with dimensions in inches Solve for c to the nearest inch Erlin 73 A 9 C

Compute the following using a calculator sin 13 Round your answer to two decimal places

1 x x 6x 9x 4 of the function What is are the local minimum minima Select the correct choice below and if necessary fill in the answer box to complete your choice A The local minimum minima is are atx Use a comma to separate answers as needed Type integers or simplified fractions B The function has no local minimum What is are the local maximum maxima Select the correct choice below and if necessary fill in the answer box to complete your choice A The local maximum maxima is areat x Use a comma to separate answers as needed Type integers or simplified fractions OB The function has no local maximum

Solve the following linear systems of differential equations Provide a sketch the phase portrait and classify the stability of the equilibrium solution as either stable unstable or unstable saddle x 1 3 X

Use the quotient to miu 8x 7 x y Choose the correct answer below OA 8 x 8x 7 OC 8x 7 2x x OB 7 2 xX x 7 OD 16 X 8 X X

Compute the following using a calculator cos Round your answer to two decimal places

the derivative of the function x 3 2x 5 5x 1 1 plify your answer

2 Evaluate cos 8 B where sine with in the second quadrant and tan with B in the fourth quadrant

What is the value of cot 0 if the terminal side of angle 0 intersects the unit circle in the first quadrant at x 45

Find the absolute extrema of the function f x x 72x 1296 on the interval 7 7 The function has an absolute minimum at x Simplify your answer Use a comma to separate answers as needed The function has an absolute maximum at x Simplify your answer Use a comma to separate answers as needed

the function using one or more of the differentiation rules 5 14

The function s t 612 91 2 gives the distance from a starting point at time t of a particle moving along a line Find the velocity and acceleration functions Then find the velocity and acceleration at t 0 and t 5 Assume that time is measured in seconds and distance is measured in centimeters Velocity will be in centimeters per second cm sec and acceleration in centimeters per second per second cm soc v t Do not factor a t v 0 cm sec v 5 cm sec a 0 cm sec a 5 cm sec EIIE

f x 14x 7 at 3 7 given point he equation of the tangent line to the graph of f x at the given point is

For the function f x x 5 find f x f 0 f 1 and f 2 f x Select the correct choice below and fill in any answer boxes within your choice OA f 0 OB f 0 is undefined Select the correct choice below and fill in any answer boxes within your choice OA f 1 OB f 1 is undefined Select the correct choice below and fill in any answer boxes within your choice OA f 2 OB f 2 is undefined

x 8 X 8 elect the correct choice below and if necessary fill in the answer box to complete your choice A The function f is discontinuous at x Use a comma to separate answers as needed B The function f is continuous for all x values

the derivative of the function 34x 2

Find the derivative of the function y 2 In 2x 2 3x

Find the derivative f x 4 9x 5

Given the triangle below find cos 0 Enter an exact answer in fraction form 7 24 25

Determine if the function f x is continuous at the values x 5 and x 9 X 5 Is the function continuous at x 5 Yes Is the function continuous at x 9 O Yes O No O No

Evaluate the volume of the following obje 2 3y 2z 6 3x 2 3 Ty 2 2x

Find i the net area and ii the area of the region bounded by the graph of f and the x axis on the given interval You may find it useful to sketch the region f x 5x 5x on 0 3 1 The net area is Type an exact answer using radicals as needed ii The area of the region bounded by the curve and the x axis is GITE

1 Proof the following a Tanx cotx secx cScx 1 cosx tanx b sinx 1 cosx sinx 2 Evaluate cos 0 B where sine with in the second quadrant and tan B wit in the fourth quadrant

Use the graph to find the following a the domain off G b the range of f c the x intercepts d the y intercept e intervals on which f is increasing f intervals on which fis decreasing g intervals on which f is constant h the number at which f has a relative minimum i the relative minimum of f 1 What is the relative minimum of f 1 f 2 k The values of x for which f x 3 1 Is f even odd or neither 5 00 Type your answer in interval notation f Over what interval is f decreasing 0 5 Type your answer in interval notation g Over what interval is f constant 0 0 Type your answer in interval notation h What is the number at which f has a relative minimum 1 What is f 2 1 2 21 k What are the x values where f x 3 The leftmost x value where f x 3 is when x What is the rightmost x value where f x 3

16 Round your answer to two decimal places 9 Compute the following using a calculator cos

A cold metal bar at 80 C is submerged in a pool maintained at a temperature of 40 C After 55 seconds the temperature of the bar is 20 C How long will it take for the bar to attain a temperature of 30 C Use decimal notation Give your answer to one decimal place Round any intermediate calculations if needed to no less than four decimal places t seconds

Find the value of each variable The dot represents the center of the circle Lines that appear tangent are tangent a 50 a 880 m b O O CO

4 Find the value of a The dot represents the center of the circle a CHEB L 66 20

Given the triangle below find csc 0 Enter your answer as a ratio of sides 3 5 0

s 16 Round your answer to two decimal places 9 Compute the following using a calculator cos

b 2V 105 3 0 6 rad 130 Show Transcribed Text This exercise involves the formula for the area of a circular sector Find the radius r of each circle if

5 8 sin270 sin120 2cos360 6 30 2 2 cos 330 cos 90

Determine the exact values of sin 0 and cos if the terminal side of angle intersects the unit circle in the first quadrant Provide your answer below

Find the coordinates of the point on the unit circle at an angle of 3 4 Give your answer in the form x y and leave any fractions in fraction form

1 2 cos 300 2 2 2 cos 210

9 Hint Let c x au y bv and z cw Then integrate over an appropriate region in uvw space Evaluate the given integral over the solid ellipsoid a b SSS3 xyz dx dydz x y z D HI

Evaluate the integral 6 0 2 SS 0 2x 4 Sp 3 p sin 20 d d0 dp 6 0 2 SS S 0 2 4 Type an exact answer using as needed p sin 2 dbd0 dp

Solve the system u 2x y v 2x 3y for x and y in terms of u and v Then find the x y value of the Jacobian Find the image under the transformation of the d u v triangular region with vertices 0 0 3 6 and 3 2 in the xy plane Sketch the transformed region in the uv plane The function for x in terms of u and vis x

Find the volume of the portion of the solid sphere p 2 that lies between the T 5 6 cones 6 and The volume is Type an exact answer using and radicals as needed