Differentiation Questions and Answers

Triangle ABC shown below has mZC 116 a 5 and b 12 Find the area of the triangle Round your answer to the nearest tenth and do not include units in your answer B 5 C 116 C 12

1 6 pts Solve each of the following triangles 85 B 3 50 A B C a b C

4 9 5x The angle of the direction opposite the point t 9 7 is o Submit Skip you cannot come back is o 5T 4 5A 4 Step 3 We have found that the angle of the direction opposite the point 9 4 9 is a S Therefore the point represents the same point as r 0 Therefore a pair of polar coordinates that represent the same point as 9 7 opposite Therefore the point opposite 9 5 9 1 s 9 5 9 7 should be our original point This is in fact an example of the general fact that r 8 9 7 but with r 0 is 5n 9 4 X

First we wish to find polar coordinates of the given point with r 0 To find the positive value of r we choose the positive square root to solve for r r 6 We are also asked to choose such that 0 02r As 3 3 3 is in the first quadrant we choose a value of 0 in the first quadrant with 0 0 2 such that tan 0 3 3 0 3 r 8 6 6 To finish we find that polar coordinates of the given point with the required conditions are as follows TL 3 r 8 film 13 6 k 3 Step 7 Now we must find polar coordinates for the point 3 3 3 with r 0 Recall that for a negative radius the resulting point is on the same line through the origin as the point with positive radius it is the same distance from the origin but it is on opposite sides of the origin That is r 0 represents the same point as r 0 We found that r 8 6 are the polar coordinates of the given point with a positive radius Therefore the polar coordinates of the given point with negative radius r 6 and 0 0 2r is as follows cannot come back

Triangle ABC shown below has m C 124 a 7 and b 9 Find the area of the triangle Select the correct answer below O24 4 34 5 26 3 A 28 7 9 C 124 C 7 B

is a significant difference in the mean GMAT score of students from different undergraduate backgrounds who apply to the MBA program The accompanying GMAT SCC data comes from a sample of students What conclusion can be reached using ANOVA Click the icon to view the GMAT Scores data Determine the null hypothesis and the alternative hypothesis Ho H H H H3 H1 H2 H3 at least one mean is different from the others GMAT Scores Data GMAT Scores by Undergraduate Major Liberal Arts Sciences 607 606 582 593 Business 578 593 583 585 583 592 568 567 599 603 593 572 589 562 576 583 570 562 575 571 608 592 595 593 604 582 616 588 595 616 585 600 X

Find the angles of AABC given that a 15 b 20 and c 25 Round your answers to the nearest tenth of a degree Provide your answer below 20 A 15 25 B

Find the missing side length and angles of AABC given that mZC 126 a 7 and b 11 A Select the correct answer below Oc 15 1 A 19 5 and B 34 5 Oc 16 1 A205 and B 33 5 Oc 16 1 A 19 5 and B 34 5 Oc 15 1 A 205 and B 33 5 11 C 126 C 7 B

List the first five terms of the sequence 1 a a3 4 a5 cos n an

Two lookout towers have been set up to keep a watch on forest fires The two towers are represented by the points X and Z in the figure A fire is spotted at point Y and each tower measures the angle from the opposite tower to the fire as shown in the figure If the distance between the two towers is 442 meters what is the distance in meters from the tower at point Z to the fire 600 1000 Y

Use the definition of Taylor series to find the Taylor series centered at c for the function f x COS X f x 8 n 0 C T 4 n X 4 cos n 2an COS n

Find y and y y y y In x 9 x 9 x 2 X 9 x 2

Solve the equation sin 20 given that 0 0 2m Select the correct answer below a 72 and 192 a 3 O a 7 5m 11x 19 12 12 12 x 2 5 a 2 3 4 5 6 3 6 W 23 12 7 4x 5 11 63 31 AT ST

Solve the equation 2cos 9cos 4 given that 0 2 Provide your answer below

Solve the following equation for x where S X T tan x tan x 0

Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative 2t 4 7 t t F t f t

Find an antiderivative of the function a h q sin q H q b f x 4ex F x

Find an antiderivative of the function a f x 7 F x b g t 18t G t

Solve for 0 if 10sin 0 8 5 3 8 and 0 0 2 Select the correct answer below 0 0 4 0 0 5 00 only only only 0 and 0 0 0 4 and 0 Sa 4x

Find the dimensions of a rectangle in m with perimeter 76 m whose area is as large as possible Enter the dimensions as a comma separated list m

Find two numbers whose difference is 46 and whose product is a minimum smaller number larger number

he sum and difference formulas are in section 5 2 of your textbook Example Find sin 105 According to section 5 2 of our textbook sin a sin a cos 6 cos a sin We know 150 45 105 so we can use a 150 and 3 45 We chose those two because we already know the sines and cosines of those two angles sin 105 sin 150 45 sin 150 cos 45 cos 1 3 1 2 2 2 2 2 6 2 4 6 4

What is the equation of the tangent line to the curve y arctan 2x at the point which x 1 Write the equation in point slope form Oy x arctan 2 Oy x arctan 2 O y x arctan 2 Oy x arctan 2

50 100 Select the correct answers 8 6 4 y f x 3 MAMM

Suppose that F x f g x and g 14 2 g 14 5 f 14 15 and f 2 12 Find F 14 Select the correct answer 24 60 15 12 017

Calculate y x4 x y x 3y Select the correct answer Oy y4 2xy 4x x 2 Oy 1 y 2xy 4x x 3 2 x 2x 3 x 4x 1 Oy 1 34 2x 4x x 3 3 Oy none of these

Find the derivative of the following function y 3 11X

The demand for a new computer game can be modeled by p x 43 5 3 In x for 0 x 800 where p x is the price consumers will pay in dollars and x is the number of games sold in thousands Recall that total revenue is given by R x x p x Complete parts through c below a Find R x R x b Find the marginal revenue R x R x c How many units will be sold if the price that consumers are willing to pay is 40 The number of units that will be sold is Round to the nearest whole number as needed

Find the derivative with respect to x if f x 6x 12x 12 ex The derivative with respect to x if f x 6x 12x 12 ex is f x

Considering only the values of for which Select the correct answer below 2tan cos B sin 2tan B 01 tan O cos sin cos 2B cos B is defined which of the following expressions is equivalent to cos s 2B cos B

Use implicit differentiation to find In xy 6x 35 dy dx dy dx

Use the Second Fundamental Theorem of Calculus to find F x dt ho 7 F x F x

You are given that tan A and tan B 2 Find tan A B Give your answer as a fraction

Considering only the values of a for which 1 sec a tan a Select the correct answer below O sin a sec a tan a tan a 1 sec atan a is defined which of the following expressions is equivalent to

Given that csc 0 5 and 0 is in Quadrant IV what is tan 0 Write your answer in exact form Do not round Provide your answer below

raph the following function Drag the black dot to shift your graph in the desired direction Use the blue draggable dot to change the period Drag the orange dot to change the amplitude and or reflect with respect to the x axis The horizontal distance between the vertica dotted green lines corresponds to one period Provide your answer below 6 5 4 3 2 2 1 0 0 y 3 sin 2x in 2x 2 2 TT 2n 0 21 3TT

Solve 2 sin t 5 sin t 2 0 for all solutions 0 t 2

a Find the solution to the initial value problem y e 6 y lim y t 1 00 6 y 0 1 b Discuss the behavior of the solution y t as t becomes large Does lim y t exist If the limit exists enter its value If the limit does not exist enter 1 00 DNE help numbers help equations

Apply Green s Theorem to evaluate the integral 8y x C x dx y 2x dy C The circle x 8 y 7 7 8y C x dx y 2x dy

A company manufactures and sells x television sets per month The monthly cost and price demand equations are C x 74 000 70x and p x 300 0 x 9000 X 30 A Find the maximum revenue B Find the maximum profit the production level that will realize the maximum profit and the price the company should charge for each television set C If the government decides to tax the company 5 for each set it produces how many sets should the company manufacture each month to maximize its profit What is the maximum profit What should the company charge for each set A The maximum revenue is Type an integer or a decimal

Now Step 3 dx dt dy et e t 2 te Submit Skip you cannot come back 2t e t 2 e 2t The simplified expression e2t 2 e 2t inside the radical can be re written as et 4

So dx dt Step 2 Now dx dt 4 dy dt et e t and et e 2 2 X

Find the exact length of the curve x et e t Step 1 For a curve given by parametric equations x f t and y g t arc length is given by dx L 2 dt dt We have x et et y 5 2t 0 t 3 So y 52t Osts 3 dx dt and dy 15 Submit Skip you cannot come back dt

1 Sketch a graph of the function Then sketch a graph of the inverse of each function Label each graph with its equation Lastly complete the table K a f x 2 x int y int Domain Range Asymptote f x 10 9 8 7 3 2 1 x int y int Domain Range Asymptote 10 9 8 7 6 5 4 3 2 0 4 2 3 4 5 6 7 8 9 10 2 3 f x 4 5 6 8 9 10

22 e Find the gradient field of the function g x y z 2 In x 3y The gradient field is Vg Oi Oj O k

Suppose that x 2y t and y tsin 8 Find 3 0 dy at and at

Suppose that x 2y and y tsin 9 Find 8 oy dy and

1 point Find a non constant solution to x x 4 using your knowledge of derivatives from basic calculus x t help formulas

2 dx 1 Enter your answers below in terms of the independent variable I in the order in which 1 point Show that y cos t is a solution to dt the terms were given Be sure you can justify your answer help formulas

A surveying team set up some equipment 133 ft from the base of a tree in order to sight the top of the tree From ground level they measure the angle of elevation to be 34 If the calculated height needs to be accurate to within 1 what is the allowed error in the angle measurement Assume the 133 ft measurement is 100 accurate The allowed relative error is The allowed percent error is Notor ontor on on OF DOOUroto to 4 decimal plagos