Calculus Questions

Recall the equation for a circle with center h k and radius r At what point in the first quadrant does the line with equation y 0 5x 1 intersect the circle with radius 3 and center 0 1 y

A sector of a circle has a central angle of 135 Find the area of the sector if the radius of the circle is 14 cm cm

Write the equation of the circle centered at 1 6 with radius 15

69 The angle between 0 and 27 in radians that is coterminal with the angle Tin radians is 10

Use Cramer s rule to solve the system The solution set is 5x 2y 30 4x 2y 6

Use Cramer s rule to solve the system x y 8 x y 6 The solution set is Simplify your answer Type an ordered pair using integers or fractions

Find if possible a AB and b BA if A AB 15 5 17 3 5 5 3 2 4 2 15 4 5 3 3 2 3 a Select the correct choice below and if necessary fill in the answer boxes to complete your choice 7 Simplify your answers and B OA BA Simplify your answers B This mix operation is not possible 1 5 21 01 5 33 B This matrix operation is not possible b Select the correct choice below and if necessary fill in the answer boxes to complete your choice

low has mZB 36 a 5 and c 13 Find the area of the triangle Select the correct answer below O 22 1 O 19 1 O 18 3 21 2 O 16 2 B 5 C 36 13 b A

Triangle ABC shown below has mZA 92 b 10 and c 14 Find the Round your answer to the nearest tenth and do not include units in your an A 10 92 14 a

Use Cramer s rule to solve the system 9w 8x 10y z 37 w x y z 6 w x y z 6 4w 9x 10y z 70 Find the determinants Let A be the coefficient matrix of the given system of equati A Pw D W Dx

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

X Find an equation of the curve that passes through the point 0 6 and whose slope at x y is 2 x y 6 X Need Help Read It

Triangle ABC shown below has mZB 38 a 8 and c 16 Find the area of the triangle Round your answer to the nearest tenth and do not include units in your answer A b C 16 38 8 B

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

Solve the differential equation dy dx 1 3 2n C 6x y for y 0 ANSWERS SCALCET9

Solve the differential equation dy 7x Y dx 7n 2 K SE x for y 0 5

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 mZB 94 a 9 and c 13 Find the area of the triangle Round your answer to the nearest tenth and do not include units in your answer 13 B 94 b C

Step 6 We have found the following values to use for the parametric coordinates of the given point 2 36 3 3 3 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 re tan 8 We are also asked to choose 0 such that 0 0 2 As 3 3 3 is in the first quadrant we choose a value of 0 in the first quadrant with 0 8 2r such that tan 0 3 3 3 0 To finish we find that polar coordinates of the given point with the required conditions are as follows r 0 VISIE

Triangle ABC shown below has mZA 147 b 6 and c 16 Find the area of the triangle Round your answer to the nearest tenth and do not include units in your answer B a 16 147 A 6 C

b 3 3 3 We are now given the Cartesian coordinates 3 3 3 and must convert this point to polar coordinates Again recall that to find polar coordinates r 0 we use the following equations 2 x y y X We can use these equations to find the following values for x y 3 3 3 tan 0 tan 0

Given AABC below with m B 100 a 6 and c 12 find the area of the triangle Round your answer to the nearest tenth and do not include units in your answer C B 100 b 12 A

Direct Materials Purchases Budget Pasadena Candle Inc budgeted production of 785 000 candles for January Wax is required to produce a candle Assume 10 ounces of wax is required for each candle The estimated January 1 wax inventory is 16 000 pounds The desired January 31 wax inventory is 12 500 pounds It candle wax costs 1 24 per pound determine the direct materials purchases budget for January One pound 16 ounces For those boxes in which you must enter subtracted or negative numbers use a minus sign Pasadena Candle Inc Direct Materials Purchases Budget For the Month Ending January 31 Pounds of wax required for production Total units available Total pounds to be purchased Unit price per lb Total direct materials to be purchased in January 604 035 Feedback Check My Work

Convert 19 40 27 to a decimal number of degrees Do not round any intermediate computations Round your answer to the nearest thousandth 0 X

Find an equation of the parabola with focus 3 1 and directrix x 5 0 0 0

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

he nearest tenth and do not include units in your answer 12 14 16

Triangle ABC shown below has mA 104 b 8 and c 10 Find the area of the triangle Round your answer to the nearest tenth and do not include units in your answer C A 104 a 10 B

A circle has a radius of 4 5yd A sector of the circle has a central angle of 2 9 radians Find the area of the sector Do not round any intermediate computations Round your answer to the nearest tenth yd X S

A vector is described Express the vector in terms of i and j A quarterback releases a football with a speed of 38 feet per second at an angle of 30 with the horizontal V Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type your answer in the form Rationalize all denominators

Use Heron s formula to find the area of the triangle with side lengths 9 16 and 18 as shown below Round your answer to the nearest tenth and do not include units in your answer 9 18 16

Jean needs to cut a triangular piece of tile for a mosaic In unknown angle as shown in the figure The lengths of PQ QR and PR are 90 millimeters 77 millimeters and 151 millimeters respectively What is the value of the unknown angle R Select the correct answer below 23 27 39 50 051 77 Q 151 90 P

Let u 5i 6j and v 2i 2j Find u v

uppose a boat leaves port travels 10 miles turns 20 degrees and travels another 8 miles as shown in Figure How far fi port is the boat Round your answer to the nearest tenth and do not include units 8 mi 20 10 mi

Let u 2i 2j and v 6i 9j Find u v U V Type your answer in terms of i and j

A ship starts at point P travels 170 miles to point Q adjusts its route according to the angle shown and continues another 199 miles to point R To the nearest mile what is the distance from the starting position of the ship to its current position a point R R P 170 114 Q 199

Two ships leave a harbor at the same time One ship travels on a bearing 15 W at 18 miles per hour The other ship travels on a bearing N75 E at 9 miles per hour How far apart will the ships be after 2 hours accom The distance is approximately miles Round to the nearest tenth as needed

Consider the following curve 2 sin 20 S Set up an integral that can be used to find the shaded region A Find the area of the shaded region de

A ship starts at point X travels 200 miles to point Y adjusts its route according to the angle shown and continues another 194 miles to point Z To the nearest mile what is the distance from the starting position of the ship to its current position at point Z Z X 200 108 194

Fill in the blanks If v a i b j v w v w kv and w a i b j then the following are true i j i j j i

Find the area of the shaded region r 1 cos 0 Q r 3 cos 0

Graph the curve r 6 sin 40 6 4 2 Need Help y 6 4 2 2 4 6 Find the area that it encloses Read It 2 4 Watch It 6 X 6 4 2 y 6 4 2 2 2 4 6 1 6 4 2 4 4 2 21 y 2 4 6 Xx 4 2 2

Sketch the curve O r 7 6 cos 0 5 y 5 12 10 8 6 4 2 2 Find the area that it encloses Read i Watch It 5 DSC X 12 12 10 8 6 4 2 5 5 2 4 6 8 10 o 2 X O 5 4 0 8 2 10 12

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

9 5x is a The angle of the direction opposite the point 9 is 5x OF Step 3 We have found that the angle of the direction opposite the point 9 7 is a ST 4 Submit Skip you cannot come back r 8 Therefore a pair of polar coordinates that represent the same point as Therefore the point opposite 9 5 9 n s but with r 0 is should be our original point This is in fact an example of the general fact that r 6 represents the same point as

Find the area of the region enclosed by one loop of the curve sin 40 r

Sketch the curve r 2 2 sin 8 O y 1 X Co90 1 3 2 Find the area that it encloses Need Help Read It 1 y 2 y 1 2 MY NOTES 3 3 ASK 2

unknown angle as shown in the figure The lengths of KL LM and MK are 105 millimeters 123 millimeters and 182 millimeters respectively What is the value of the unknown angle Round your answer to the nearest degree if necessary M 123 L 182 105 K

r 0 50 TH 4 5 2 50 77 Step 3 We are asked to find a second pair of polar coordinates for the Cartesian coordinates 5 5 We have found the following point with the required conditions are as follows We must now find polar coordinates with r 0 To find the negative value of r we choose the negative square root to solve for r r 5 2 5 2 Step 4 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 8 represents the same point as r 0 m We found that r 8 5 2 74 are the polar coordinates of the given point with a positive radius Therefore the polar coordinates of the given point with negative radius r 5 2 and 0 8 2 is as follows r 0 Submit Skip you cannot come back