Heights & Distances Questions and Answers

What is the volume of this cone Use 3 14 and round your answer to the nearest hundredth 20 in 30 in cubic inches

What is the volume of this triangular pyramid 6 ft 5 ft 10 ft cubic feet

1 Write the side ratios for the following trig functions sine cose tano

ircle A center 12 32 and radius 15 ircle B center 1 4 and radius 10 Which of the following is the necessary transformation translation dilation from A to B to prove that the two circles are similar O Translation 13 units left 28 units down Scale factor reduction ratio 2 3 Translation 13 units left 28 units up Scale factor enlargement ratio 2 3 O Translation 13 units left 28 units down Scale factor reduction ratio 3 2 Translation 13 units right 28 units down Scale factor enlargement ratio 3 2

Find the missing lengths O a b a b a b 15 2 15 2 15 2 2 15 2 2 5 6 2 5 6 2 15 6 4 15 6 4 a U b 45 15

Find the missing length indicated 15 O 10 O 20 O 16 O 100 9 None of the other answers are correct

A 35 foot ladder is leaning against the side of a building and is positioned such that the base of the ladder is 21 feet from the base of the building How far above the ground is the point where the ladder touches the building feet

8 The bottom of a ladder must be placed 3 ft from a wall The ladder is 12 feet long How far above the ground does the ladder touch the wall Round your answer to the nearest tenth 4 points

Solve the following Proportions by cross multiplying 11 13 7 b 9 b 10 For 13 and 14 Find the value of the missing variable 3x S 28 10 8 12 14 9 k 7 16 ft 6 k 149 x ft 9 ft

A ship leaves its port and sails on a bearing of N22 20 E at speed 21 6 mph Another ship leaves the same port at the same time and sails on a bearing of S67 40 E at speed 8 9 mph How far apart are the ships after 5 hours miles Round to the nearest integer as needed 22 26 67 40

Is the 3 yd of this figure Submit 4 yd cubic yards 2 yd 1 yd 2 yd 1 yd

Independent Events The probability of winning the shell games if you randomly pick is 1 in 3 What would be the approximate probability of winning 4 games in a row O O 1 2 1 5 16 7 33 3

Question 6 Jen is on the platform of her boat She sights the top of a lighthouse at an angle of 30 as shown bel She knows that the height of the lighthouse is 50 meters B N How far is Jen from the base of the lighthouse in meters A 25 B 25 3 C 50 3 B D 100 30 Figure to not drawn to cel

A 60 60 The string makes an angle of 60 with the ground If the length of the stringi height of the kite above the ground in feet B 60 3 C 120 D 120 3 B low cos inth 48 120 feet

Evaluate the following expression for z 3 z 6

16 Find the angle e to the nearest minute cos8 0 3094 A 71 59 B 71 51 C 71 58 D 71 52 A

In a certain college dormitory 108 students are assigned dorm rooms The dormitory has 26 dorm rooms each of which is assigned 3 or 5 students How many of the dorm rooms will be assigned 3 students

Frequency 208 12 10 6 4 2 0 40 50 B 71 C 77 D 84 60 70 Score 80 90 no list The histogram above shows the distribution of the scores of 22 students on a recent biology test Which of the following could be the median score of the 22 students represented in the histogram A 68 10

2 In the diagram above MN 8 a Determine the length of RM and RN FAMNR 30

1 In the diagram below AB 4 2 Determine the length of AC and CB C 30 60 B

A rectangular plot of land is to be fenced in using two different kinds of fencing materials Two opposite sides will use a material that costs 3 per foot The remaining two sides will use a material that costs 5 per foot The available budget for this project is 30 000 Find the dimensions z and y that will maximize the area that can be fenced in Show your work

Solve for x Round to the nearest WHOLE NUMBER 12 S X T 20 16 R

Solve for x Round to the nearest WHOLE NUMBER X 26 3 ft 23 ft 12 8 ft

IS 1 05 shadow to be 26 45 meters She stands 21 4 meters away from the tree so that the tip of her shadow meets the tip of the tree s shadow Find the height of the tree to the nearest hundredth of a meter 26 45 m Type your answer 18 ft 1 65 m 7 ft 21 4 m 6 1 point A pole 7 feet tall is used to support a guy wire for a tower which runs from the tower to a metal stake in the ground After placing the pole Rashaad measures the distance from the pole to the stake and from the pole to the tower as shown in the diagram below Find the length of the guy wire to the nearest foot DO

4 couple landmarks at points V and W She measures UX XY as marked Find the distance across the lake VW rounding your answer to the nearest hundredth of a meter Type your answer 1 65 m 70 m 1 15 m 120 25 m 130 m 1 point For a project in his Geometry class Nathaniel uses a mirror on the ground to measure the height of his school s flagpole He walks a distance of 7 95 meters from the flagpole then places a mirror on flat on the ground marked with an X at the center He then steps 1 15 meters to the other side of the mirror until he can see the top of the flagpole clearly marked in the X His partner measures the distance from his eyes to the ground to be 1 65 meters How tall is the flagpole Round your answer to the nearest hundredth of a meter U 7 95 m DO

P Classic Probability There are 20 random box lunches at a conference for teachers They are all the same except 10 of the lunches have peanut butter cookies 5 have snicker doodle cookies and the last 5 boxes have chocolate chip Knowing this a math teacher realizes that he has a 25 chance of randomly picking a box with a chocolate chip cookie What type of probability did the teacher use Subjective Probability Empirical Probability Theoretical Probability Authentic Probability AFMOR Tw MO N MAR CHIRIN

Mr Smith asked all of his 2nd period students what type of social media accounts they had 22 24 How many students does Mr Smith have in his 2nd period class 34 Facebook 0 39 Google Twitter

A Cliff at point A Elevation At a point B on the ground the angle of elevation is 30 At point C which is 20m closer to the base of the cliff the angle of elevation is 45 What is the elevation of point A

9 Find the length of the hypotenuse a 2 6 b 2 5 c 2 3 C d 6 a 45 2 3

Six friends share a 15 ounce bag of nuts equally Between what two whole numbers of ounces will each person get 3 and 4 2 and 3 1 and 2 0 and 4

A graphical representation of a linear program is shown below The shaded area represents the feasible region and the dashed line in the middle is the objective function line If this is a maximization problem which extreme point is the optimal solution 14 120 10 8 0 OA E O B C OC A D B OE D A 8 10 12 14

The conical tank shown here is filled with olive oil weighing 41 lb ft How much work does it take to pump all of the oil to the rim of the tank W 20 y ft lb Round to the nearest whole number as needed y 5x orx 3y 4 20

1 2 x y y x about the y axis 2 Method Used

crate of medicine with a density of 2 200 kilograms per cubic meter will be shipped from Israel to the U S What is the crate s density in pounds per cubic ot rst fill in the two blanks on the left side of the equation using two of the ratios Then write your answer rounded to the nearest hundredth on the right side e equation Ratios 35 3 ft 3 1 m 3 2200 kg 1 m 3 1 m 35 3 ft 2 2 lb 1 kg 1 kg 2 2 lb lb 133 ft kg m X lb 00 S ft 5

uppose ABC is a right trangle with sides a b and c and right angle at C Use the Pythagorean theorem to find the unknown side length Then find the values of the skingonomet unctions for angle B Rationalize the denominators when applicable Complete the table by using the names of the sides to express each trgonometric function as a ratio sin cosi tan csc 5 sec B cot What is the length of side O Sampity your answer excluding any radicals Use vitegers or fractions for any numbers in the expression sin s Simplify your answer includeg any radicals Usedegers or tractions for any numbers in the expression cos 1 Cieplity your ans vicuding any radicals the vegers of actions for any numbers in the expression tan imply your answer including any radicals Use integers or acions for any members in the expression exc

A farmer builds a trough to fit in a corner The trough is made from rectangular prisms Use the diagram to find length A What is length A 8 ft 9 ft 3 ft 2 ft 3 ft 4 ft 5 ft 7 ft A B 2 ft

Hint s 2 3 z 3 3 HIDE HINT 52 12 52 7372 H A possible sot 3 1 3 3A quadratic equation in standard form has the form az bx c 0 Rewrite the equation in this form 5 177 Given a quadratic equation in standard form the quadratic formula Stat

2 In the diagram above mZBAC 90 and mzDCA 90 AD 6 and CD 4 Determine the length of AC A

b Find f 4 y intercept 0 1 f 4 2 y intercept 1 0 f 4 2 y intercept 0 1 f 4 2 y intercept 1 0 f 4 2

4 A student wants to know how tall the flagpole at her school is her eye level is 5 5 feet above the ground and she stands 36 feet from the base of the flagpole If the angle of elevation is 25 what is the height of the flagpole draw your own picture

The legs of a right triangle are represented by a and b and the hypotenuse of the right triangle is represented by c Which equation is not equivalent to the Pythagorean Theorem O O C q 3 1c a 3 None of the other answers are correct

In the triangle below with right angle C suppose that m B m2 D 5x 17 Find the degree measure of each angle in the triangle D 5x 17 2x 37 mz B mz C m2 D 0 0 0 2x 37 and X

X y 12 Question 4 a 9 TV a X 12 The two triangles below are similar Find the values of a and b 12 18 6 15 9 10

13 From the hay loft door Ted sees his dog on the ground The angle of depression of the dog is 40 Ted s eye level is 16 feet above the ground How many feet must the dog walk to reach the open barn door directly below Ted to the nearest foot

he target heart rate during moderate activity R in beats per minute for an adult who is y years old can be estimated using the equation R 3 220 y 5 According to this estimate for every increase of 2 years in age by how many beats per minute will the target heart rate for adults engaged in moderate activity decrease

At 1 00 P M a truck driver is 200 miles into a long journey to make a delivery The driver continues on the journey and travels at an average speed of 60 miles per hour How many total miles into the journey will the driver be at 8 00 P M

1 Two congruent pieces of glass whose areas are described by the region bounded by both axes y 4 and the graph of x g y see right are to be glued together Let A h be the area of the pieces of glass covered by glue when the glue is at height y h from the bottom of the pieces The glue is injected at a constant rate R that is R dA dt 3 1 0 ii iii iv A h a Intuitively for what approximate height hy is the glue level changing most rapidly What does this mean about Give reasons for your answer dt c We now want to mathematically find the heights hy and hm i x g y b Intuitively for what approximate height hm is the glue level changing most slowly Give reasons for your answer What integral describes the area A h when the glue is at a height y h How does the Fundamental Theorem of Calculus help you compute dA dh How can you computed in terms of What other term is involved Why can you conclude that is inversely proportional to g h For what approximate value of his g h minimal What does that say about Does this agree with your answer to part b What can you say when g h is maximal Estimate the values of h and hm

Mariah is visiting the Jefferson Memorial with her family She wants to estimate the height of the statue of Thomas Jefferson Mariah stands so that her line of vision to the top and base of the statue form a right angle as shown in the diagram below Approximately how tall is the statue Round to the nearest inch x in 68 in 104 in

A flute case is shaped like a rectangular prism The case is 5 inches tall 3 inches wide and has a volume of 255 cubic inches What is the length of the flute case 15 inches 17 inches 51 inches 240 inches

5 24x 3y 63 y 8x 21 A No solution B 6 2 C 6 2 D Infinite number of solutic