College Geometry Questions

0 38 If the measure of angle A is 75 and the measure of angle C is 25 in a triangle ABC what is the measure of angle B

15 a 0 048 yards b 0 063 yards c 0 075 yards

21 The area of a triangle is 40 centimeters Find the length of the side included between the angles A 30 and B 50

Each problem below refers to a triangle ABC Any answers that involve angles should be rounded to the nearest tenth of a degree 1 If a 100 inches b 60 inches and C 60 find c 2 If a 100 inches b 60 inches and C 120 find c 3 If a 5 yards b 6 yards and c 8 yards find the largest angle 4 If a 10 yards b 14 yards and c 8 yards find the largest angle 5 If b 4 2 meters c 6 8 meters and A 116 find a

A window has the shape of a parabola above and a circular arc below Find the area of the window 10 7 10 ft 6 34 Use the dotted line as your y axis and the solid gray line as the x axis Find the distance from the z axis to the top of the circle Write the equation of the circle Write the equation of the parabola feet

B a Given triangle ABC and circle CA centered at A with radius AC and circle Cg centered at B with radius BC how many intersection points do the two circles have and where are the intersection point s located b If two circles centered at A and B intersect in a single point C then describe all of the possible relationships between AB BC and AC Explain your answer

y Find the value of the variable 450 450 y 60

d the value of each variable nesn srl 300 11 X

Find the value of each variable Express in simplest radical form 8 X 6 5

Find the value of each variable Express in simplest radical for 5 14 X ly

Find the value of each variable Express in simplest radical form 1 30 60 30 X y

SO 2004 12 21 to to slay s

In calculating the bank discount when discounting an interest bearing note which one of the following is not used in the calculation O Principal proceeds Maturity value Bank discount rate Discount period None of these

For both of the following problems identify the function whose level curve is the surface described and use it to solve the integration problem a Integrate f x y z 22 over the hemisphere given by the equation x y z 4 for z 0 Hint If you choose the circle x2 y 4 as R note that z 0 in R and plug that into the integral in that instance Answer 0 b Integrate f x y z x y z over the portion of the plane 2x 2y z 2 that lies within the first octant which means x y z 0 Hint If you choose the triangle in the x y plane as R note that 20 here so you can plug that into f in that instance Answer 1

LEM and b have a 0 68 angle between them The magnitude length of a is 142 and the magnitude of bis 207 We can write this as la 142 and 6 207 See Diagrams gmtobuz a Find la bl This means what is the magnitude of the sum of the two vectors Hint Law of Cosines 3 marks 68 b doing two tony 30 igen auli no id TB b a b b What angle does a b make with a Shown as on the diagram 3 marks Note this angle is NOT half of 68 To find this you will need to use the Law of Cosines or Law of Sines

A rapid transit service operates 189 trains along five routes A B C D and E The number of trains assigned to each route is based on the average number of daily passengers per route given in the following table Use Webster s method to apportion the trains The standard divisor is 58 13 Route A B C D E Average Number of Passengers 1098 1349 1548 1514 5478 Route Number of apportioned trains A

Tan STT 6

For each of the following graphs obtain a lower bound L A for the area enclosed by the curve by adding the areas of the squares enclosed completely by the curve Then obtain an upper bound U A for the area by adding the areas of the squares enclosed either partially or completely by the curve Notice the squares in the first graph are 1 by 1 squares and the squares in the second graph are 1 2 by 1 2 squares a L A b U A 2 1 0

C b a A C B If B 40 C 70 and c 82 km find A and then find a

2 In the adjacent figure x xOy is an angle Ox B C perpendicular to Ox and Oy perpendicular to O Oy A is a point of Ox and B is a point of Ox such that OA OB C is a y X point of Oy and D is a D point of Oy such that OC OD 1 Compare angles AOD and BOC 2 Prove that AD BC y 3 points 3 points

Find the circulation and the flux of the field F xi y j around and across the following curves a The circle r t cos t i sin t j 0 t 2 b The ellipse r t cos t i 2 sin t j 0 t 2 a The circulation of F around the circle is Type an exact answer

Find an equation for the conic section with the given properties The ellipse with vertices V1 1 9 and V 2 1 11 and foci F1 1 7 and F2 1 9

You may need to use the appropriate appendix table or technology to answer this question A simple random sample with n 58 provided a sample mean of 24 5 and a sample standard deviation of 4 4 Round your answers to one decimal place a Develop a 90 confidence interval for the population mean to b Develop a 95 confidence interval for the population mean to c Develop a 99 confidence interval for the population mean to d What happens to the margin of error and the confidence interval as the confidence level is increased As the confidence level increases there is a smaller margin of error and a wider confidence interval As the confidence level increases there is a larger margin of error and a wider confidence interval As the confidence level increases there is a smaller margin of error and a more narrow confidence interval As the confidence level increases there is a larger margin of error and a more narrow confidence interval

Two golf balls are hit into the air at 80 feet per second 60 mi hr making angles of 39 and 53 with the horizontal If the ground is level estimate the horizontal distance traveled by each golf ba The ball hit at 39 travels about feet Round to the nearest integer as needed

5 A square sheet of metal is sixteen inches on a side A square of side x inches is to be cut out of each corner of the metal sheet The sides of the sheet are then to be folded up to make a metal tray What should x be in order for the volume of the tray to be a maximum 6 There is a lamp on the ground exactly sixty feet from the vertical wall of a building A man six feet tall is walking away from the lamp in a

Macmillan Learning During a routine check of the fluoride content of Gotham City s water supply the given results were obtained from replicate analyses of a single sample 0 709 mg L 0 691 mg L 0 713 mg L 0 687 mg L and 0 717 mg L Determine the mean and 90 confidence interval for the average fluoride concentration in this sample mean 90 confidence interval mg L mg L

Solve triangle ABC If an answer does not exist enter DNE Round your answers to one decimal place Below enter your answers so that A is smaller than A2 b 126 c 164 2A1 2C1 a1 X zB 48 A C a2

Given ABCD is a parallelogram BEAC and DF 1 AC Prove ABEC ADFA Step 1 try Statement ABCD is a parallelogram BE AC DF 1 AC Type of Statement B E F C Re Gi

Ron Prentice bought goods from Shelly Katz On Sept 12 Shelly gave Ron a time extension on his bill by accepting a 2 700 8 190 day note On Dec 16 Shelly discounted the note at Roseville Bank at 8 Use Days in a year table What proceeds does Shelly Katz receive Note Use 360 days a year Do not round intermediate calculations Round your answer to the nearest cent Proceeds received

Complete the following table for the simple discount notes Use the ordinary interest method Note Round your answers to the nearest cent Amount due at maturity Discount rate Time Bank discount Proceeds 4 000 6 25 160 days

The capacity of an elevator is either 20 children or 15 adults If 14 children are currently in the elevator how many adults can still get in Your AncwoK

Let T R4 R3 be the linear transformation represented by T x Ax where 1 210 A 0 1 2 4 0 001 a Find the dimension of the domain 3 b Find the dimension of the range c Find the dimension of the kernel d Is 7 one to one Explain OT is one to one since the ker 7 0 OT is one to one since the ker 7 0 OT is not one to one since the rank 7 0 OT is not one to one since the ker 7 0 OT is not one to one since the ker 7 0 e Is T onto Explain OT is onto since the rank 7 is equal to the dimension of the domain OT is not onto since the rank 7 is not equal to the dimension of the domain OT is not onto since the rank 7 is equal to the dimension of the co domain OT is not onto since the rank 7 is not equal to the dimension of the co domain OT is onto since the rank 7 is equal to the dimension of the co domain f Is 7 an isomorphism Explain Select all that apply OT is not an isomorphism since it is not onto OT is not an isomorphism since it is not one to one

Let T R R be a linear transformation Use the given information to find the nullity of T rank 7 0 nullity 7 0 Give a geometric description of the kernel and range of T O The kernel of T is all of R3 and the range of T is all of R O The kernel of T is all of R3 and the range of T is the single point 0 0 0 O The kernel of T is the single point 0 0 0 and the range of T is all of R O The kernel of T is a line and the range of T is a plane The kernel of T is a plane and the range of T is a line

se the method of cylindrical shells to find the volume generated by rotating the region bounded by y e y 0 x 0 and x 1 about the y axis olume

K Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby This method is designed to increase the likelihood that each baby will be a gir assume that the method has no effect so the probability of a girl is 0 5 Assume that the groups consist of 44 couples Complete parts a through c below a Find the mean and the standard deviation for the numbers of girls in groups of 44 births The value of the mean is u 22 Type an integer or a decimal Do not round The value of the standard deviation is 3 3 Round to one decimal place as needed b Use the range rule of thumb to find the values separating results that are significantly low or significantly high Values of 10 girls or fewer are significantly low Round to one decimal place as needed Values of 26 girls or greater are significantly high Round to one decimal place as needed c Is the result of 31 girls a result that is significantly high What does it suggest about the effectiveness of the method The result Round to significantly high because 31 girls is as needed girls A result of 31 girls would suggest that the method is not

is discrete Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probabilit Probability of more than 5 passengers who do not show up for a flight Choose the correct answer below OA The area to the right of 4 5 OB The area to the right of 5 5 OC The area to the left of 5 5 OD The area to the left of 4 5 OE The area between 4 5 and 5 5

Return on Investment and Residual ome Johnson Company has two sources of funds long term debt and equity capital Johnson Company has profit centers in the following locations with the following net incomes and total assets Las Vegas Net Income Assets 1 310 000 4 000 000 1 550 000 8 000 000 Dallas Tampa 2 390 000 12 000 000 a Calculate ROI for each profit center and rank them from highest to lowest based on ROI Round ROI to the nearest whole percentage Las Vegas Dallas Tampa ROI Rank 0 0 0 b Calculate residual income for each profit center based on a desired ROI of 5 and rank them from highest to lowest based on residual income RI Rank

2 i Simplify each expression to a single term tn r in Pascal s triangle C 2 ii Find the numerical value of this term K U 2 a t32 20 32 21 b t40 12 139 12

5 4 3 2 1 13 12 11 10 9 8 7 6 5 4 B A2 1 5 6 7 1 2 3 4 The curve above is the graph of a sinusoidal function It goes through the points 7 0 and 3 0 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits

Graph one complete cyc 41 y sin x 4 43 y 3 sin 2x 7

A theater is presenting a program on drinking and driving for students and their parents or other responsible adults The proceeds will be donated to a local alcohol information center Admission is 2 00 for adults and 1 00 for students However this situation has two constraints The theater can hold no more than 240 people and for every two adults there must be at least one student How many adults and students should attend to raise the maximum amount of money To raise the maximum amount of money adults and students should attend

The graph of y f bx is a horizontal compression of the graph of y f x if b The graph of y f bx is a horizontal compression of the graph of y f x if b 1

Multiply Write your answer in simplest form 6 6k236k 54 k 6k 9

vide Write your answer in simplest f 75 5 6 s 1 3

Multiply Write your answer in simplest form 3 1 3 1

Multiply Write your answer in simplest form 2c 23c 12 2c 5 2c 5 C 12

Divide Simplify your ans 17p 2 17p 8np

Multiply Write your answer in simplest form y y 9y 6y 1 8

Divide Write your answer in simplest fo 1 n n 1

Multiply Write your answer in simplest form 12s s 1 s 2 3s 1 8s 16s