College Geometry Questions

In the year 2000 the population of a certain country was 285 million with an estimated growth rate of 0 5 per year a Based on these figures find the doubling time and project the population in 2150 b Suppose the actual growth rates are just 0 2 percentage points lower and higher than 0 5 per year 0 3 and 0 7 What are the resulting doubling times and projected 2

The population of a town with a 2016 population of 63 000 grows at a rate of 1 8 per year a Find the rate constant k and use it to devise an exponential growth function that fits the given data b In what year will the population reach 105 000

Devise an exponential decay function that fits the given data then answer the accompanying questions Be sure to identify the reference point t 0 and units of t The pressure of a certain planet s atmosphere at sea level is approximately 900 millibars and decreases exponentially with elevation At an elevation of 25 000 ft the pressure is one third of the sea level pressure At what elevation is the pressure half of the sea level pressure At what elevation is it 3 of the sea level pressure What is the reference point t 0 A the elevation at sea level 0 ft OB the elevation 25 000 ft OC 3 of the sea level pressure OD the pressure at sea level 900 millibars What are the units of t OA millibars B feet C pressure levels At what elevation is the pressure half of the sea level pressure feet

10 Locate the circumcenter of each triangle

For each triangle construct all three perpendicular bisectors to show they are concurrent 11 12

10 The graph of a function f is given Estimate f x dx using five subintervals with a right endpoints b left end points and c midpoints y 1 0 1 48 X milar

Locate the circumcenter of each triangle 7 8

Locate the incenter of each triangle 15 210 16

10 Locate the circumcenter of each triangle

13 14

Inscribe a circle in each triangle 17 18

For each triangle construct all three perpendicular bisectors to show they are concurrent 11 12

B A B Construct the perpendiculer bisector of side AB of each triangle

Find the magnitude and direction of each vector Round your answers to the nearest tenth 10 30

What is sin 60 3 B 3 O A Na Sl O C 1 O D 3 OE 1 2 E OF 5

In triangle ABC m A 35 mZB 65 and a 8 71 Use the law of sines to find b Round your answer to the nearest tenth A 8 7 B 9 5 C 13 8 D 23 7

Let v 2 6 and w 12 4 Which of the following is true A V and w are perpendicular B The x component of v is 6e C w 4 3 1 D v w 48

Parallelogram 1 2 3 5 the transformed parallelogram land in OAI OB II O c III OD IV is transformed using 1 0 Which quadrant does

Calculate the length a to two decimal places B 7 B 117 OA 13 68 OB 14 87 O C 187 2 OD 15 A 9 C

What is the approximate value of sin B B 7 A 17 46 16 OA 2 29 OB 1 09 OC 0 40 OD 0 92

O O 23 B S SS 13 12 67 90

An isosceles triangle has angle measures 40 40 and 100 The side across from the 100 angle is 10 inches long How long are the other sides OA 6 53 inches OB 6 43 inches O C 15 32 inches OD 10 inches

A 12 foot board rests against a wall The angle that the board makes with the ground is 60 How far is the base of the board away from the wall Select the correct trig ratio and distance from wall O A sin 60 12 x 13 85 feet B sin 60 x 10 39 feet O C C cos 60 12 X 6 feet x OD cos 60 12 x 24 feet

What is the length magnitude of the vector 6 3 A 3 B 2 OC 3 5 OD 53

A B C D 5 5 4 5 CE lockwise Identify the transformed vector

Use the law of cosines to find the value of cose Round your answer to two decimal places 5 7 9 8 OA 0 84 OB 1 23 OC 0 23 OD 0 35 10 2 8

The law of cosines reduces to the Pythagorean theorem whenever the triangle is acute OA True OB False

A boat is 400 feet away from one dock and 500 feet away from another dock The angle between the two paths is 45 What is the approximate distance between the docks OA 357 feet OB 166 feet OC 540 feet O D 695 feet

What is the best approximation of the projection of 5 1 onto 2 6 A 0 10 2 6 OB 0 10 5 1 O C 0 15 5 1 D 0 15 2 6

Knowing that sin 30 what is a A 7 OB 3 5 O C 12 12 OD 14 30 7 60

What is the approximate value of tan B B 7 A 17 46 16 20 A 0 40 OB 0 44 C 0 92 D 2 29 C

Use Pascal s Triangle to complete the expansion of t u 4 2 t6 6t u tu 20t u 15t u4 6tu5 u6

Use the law of sines to find the length of side A 38 b O A 21 28 OB 29 37 OC 38 06 D 25 B 31 6 25

Tiana would like to buy cone shaped hats for her birthday party She wants hats with the largest volume since they look bigger Which of the following brands of hat should she buy Brand A height of cone 15 in radius of cone base 6 in Brand B height of cone 18 in radius of cone base 5 in A Brand A OB Brand B O C Either the hats have equal volumes

What is the volume of the sphere shown below OA 4000 units OB 400 units 3 OC 400 units 4000 3 O D 3 units ww 10

The ratio of the lengths of corresponding parts in two similar solids is 2 1 What is the ratio of their surface areas OA 8 1 OB 2 1 O C 4 1 O D 6 1

What is the surface area of the right prism given below A 420 units OB 840 units2 C 480 units OD 298 units2 5 12 14

Question 15 38 118 NOTE The triangle is NOT drawn to scale Answer the following Round your answer to 3 decimal places as needed 31

A snack bag of potato chips is advertised as weighing 1 5 ounces Suppose a bag of potato chips is selected at random from a snack pack and weighs 1 7275 ounces Compute the percent error rounded to the nearest hundredth Simplify your answer completely PE Using the 5 guideline was the advertised weight an accurate estimate Since this percent error is less than 5 we see that the advertised volume was a good estimate Since this percent error is less than 5 we cannot determine if the advertised volume was or was not a good estimate Since this percent error is greater than 5 we see that the advertised volume was a good estimate Since this percent error is greater than 5 we see that the advertised volume was not a good estimate Since this percent error is less than 5 we see that the advertised volume was not a good estimate

Two similar cylinders have radii of 7 and 1 respectively What is the ratio of their volumes OA 49 1 OB 35 35 1 O C 112 1 OD 343 1

The two cones below are similar What is the value of x O OB 0 18 O O A 0 09 C 0 3 D 0 9 10 3 o d 3 x

Which of the following is a solid bounded by the set of all points at a given distance from a given point OA Cylinder B Cube C Cone D Sphere

The bases for a cylinder must be two discs that are parallel and O A similar B congruent C squares D have one lying directly above the other

A right cone has a slant height of 6 and a radius of 2 What is its surface area O A 48 units2 O B 16 units2 C 12 units D 24 units2

The ratio of the surface areas of two similar solids is 49 100 What is the ratio of their corresponding side lengths OA 7 10 OB 1 24 O C 10 10 OD 7 100

A geometric solid has only length and height O A True OB False

Which of the following is a solid consisting of a disc a point not in the same plane as the disc but directly above the center of the disc and all the points between them OA Oblique cone OB Oblique pyramid C Right cone D Right pyramid

A right cylinder has a radius of 5 and a height of 9 What is its surface area A 45 units2 B 140 units C 70 units D 90 units2

Which solid figure has a base that is a polygon and triangular faces that meet at a vertex A Cylinder B Prism C Cone D Pyramid

Which types of polygons are the faces of a tetrahedron O A Regular pentagons B Regular hexagons OC Squares OD Equilateral triangles