Geometry Questions

Find the surface area of the following cone OOO C A 9 7 km C 13 2 km OA OB O C UD 32 km 1 km B 6 5 km D 15 3 km

19 5 in 8 247 75 in 12 in The surface area is square inches round to the near

What is the surface area 4 3 mm 4 3 mm 4 3 mm O 101 94 mm O 110 49 mm O 110 94 mm O 101 49 mm

4 cm 5 cm 3 cm The surface area is

Find the surface area of the cone hint you must find the slant height first Round to the nearest hundredth 9 mm 20 mm mm

Which pairs of rectangles are similar polygons Select each correct answer 0 0 40 m 13 m 15 m 5 m 8m 5 2 m 3 m 2 5 m O 1225 m 18 m 144 m 6m 3 5 m 4 5 m 1 2 m 1 5 m

Find the value of x Round to the nearest tenth 1 3 5 60 m 40 22 18 900 ft 12 000 ft XXXXXX 4 6 X 1 000 ft 8 Two office buildings are 100 ft apart as shown From the edge of the roof of the shorter building the angle of elevation to the top of the taller building is 28 and the angle of depression to the bottom is 42 How tall is each building Round to the nearest foot 48 80 ft 7 Rachel is attempting to find the area of the triangle shown She remembers the formula A bh What line should she draw to apply the formula What is b What is h What is the area Round to the nearest tenth 2 800 ft 6 cm 28 70 100 ft 33 9 cm

Trigonometric Ratios For Exercises 1 3 find sin A cos A and tan A 9 1 2 C X45 4 Hap OPP X F 7 375 48 5 12 For Exercises 4 9 find the value of x Round to the nearest tenth 5 sin 45 W sin 35 odj B W X 5 5 W 5 5 sin 45 5 5 W X 5 5 sin 35 7 8 A 8 9 6 10 Skylar drew two triangles that share a side and labeled the two portions of the base w and x Then he solved for w and x as shown Are his calculations correct Explain 11 X 4 6 5 23 45 10 A OB 3 X 1 8 11 A wire makes a 70 angle with the ground and is attached to the top of a 50 ft antenna How long is the wire Round to the nearest foot 6 9 25 5 5 B W 60 70 8 54 47 45 B 35 x 50 ft

A patrol car is parked 30 feet from a long warehouse see figure The revolving light on top of the car turns at a rate of 34 revolutions minute How fast is the light beam moving in ft sec along the wall when the beam makes angles of 0 30 0 60 and 0 75 wi the line perpendicular from the light to the wall a 30 b 60 0 y ft ft sec ft sec c 0 75 Round your answer to two decimal places

Which equation shows a vertical stretch of 2 a reflection over the x axis then a shift left 3 units and down 4 units

atic aph each quadratic inequality Find the missing coordinates Ay x 6x 3 2 y x 3 x 5 vertex y int 0 41 point 5 0 7 6 5 4 3 2 1 1 2 3 5 6 0 1 2 x intercepts 0 0 vertex y int 0 point 2 7 6 5 3 2 1 0 6 5 4 3 2 1 2 1 2 3 3 y 2 x 2 6 vertex 2 6 y intercept 0 Circle each point that is a solution to the given system of inequalities and cross off those that are not 5 TERE 6 39 4 132 2 2 1 0 6 5 4 3 2 1 1234 0 1 2 3

Eetch the curve with the given polar equation by first sketching the graph of r as a function of 0 in Cartesian coordinates r 1 9 cos 0

For the parabola y 2 4y 8x 12 0 identify the Standard form equation Orientation Vertex Focus and Equation of the directrix

The cross section of a nuclear power plant s cooling tower is in the shape of a hyperbola Suppose the tower has a base diameter of 162 meters and the diameter at its narrowest point 40 meters above the ground is 54 meters If the diameter at the top of the tower is 108 meters how tall is the tower

lot each of the point which is the lowest and closest A 0 7 B 6 3 F 4 1 G 0 6

Given the plane r 2 1 5 s 3 2 0 t 1 1 5 s t R The plane cuts the x y and z axes to fo triangular pyramid Find the volume of the pyramid Vpyramid area of the base height

A bicycle wheel has radius R Let P be a point on the spoke of a wheel at a distance d from the center of the wheel The wheel begins to roll to the right along the the x axis The curve traced out by P is given by the following parametric equations x 0 70 5 sin 0 Ly 0 7 5 cos 0 What must we have for R and d R d

nd the exact value of each of the remaining trigonometric functions of 0 tan 0 15 8 and sin 0 0

ven that f x sin x g x cos x h x tan x F x csc x G x sec x and H x cotx Find f 135 What point is on the graph of f Find G 135 What point is on the graph of G Find h 135 What point is on the graph of h

K You have 204 feet of fencing to enclose a rectangular region What is the maximum area of the region OA 2 597 square feet OB 41 616 square feet OC 2 601 square feet OD 10 404 square feet

Determine the directrix of the conic with polar form r 6 3 cose

How many rectangles can you make that will fit on a 4 x 4 geoboard such that none of them are congruer 8 X rectangles

Plot the point whose coordinates are 3 0 5 Select one Oa O b 4 t A O C Od

etermine the directrix of the conic with polar form the directrix is x 1 3 3 cose

ch of the following is not a polar equation of a cc ect one a b C r 1 1 sin Oe r 1 2 cos r 3 d 1 1 2 cos 0 r 1 2 cos 0

suppose a certain baseball diamond is a square 86 feet on a side the pitching rubber is located 59 5 feet from home plate on a line joining home plate and second base how far is it from the pitting rubber to first base

Which of the following is the graph of the plane 2x 6y z 1 Select one Oa O b O C O d HHHH to Hy

A lamp has the shape of a parabola when viewed from the side The lamp is 24 centimeters wide and 18 centimeters deep How far is the light source from the bottom of the lamp if the light source is placed at the focus 24 cm 4 cm 18 cm Light source 18 cm 12 18 24 cm 0 0 cm 12 18

Set up the form for the partial fraction decomposition Do not solve for A B C and so on 4x 14 x 8 3x 4 010

The volume of the doorstep sketched below 4 inches 1 inch The side is y x

onstruct a simple graph with vertices T U V W X Y whose degrees are 2 2 1 1 2 2 That is the edge set

etric equations x x x x t y y y y t where 0 St 1 describe the line segment that joins the points P x y and P x Y Use a graphing calculator or computer to draw the triangle with vertices A 1 1 B 5 4 C 1 6 Find the parametrization including endpoints and sketch to check Enter your answers as a comma separated list of equations Let x and y be in terms of t from 0 1 4t 1 3t AB BC AC X ASK YOUR

valuate r v w 0 2 0 1 5 2 2 4 4 w 2011 10 RAMMERI ANT

Type the equation of the given graph in the form y Asin Bx or y Acos x 0 Type an equation Use integers or fractions for any numbers in the equation 4

equations x x x x t y y y y t where 0 st s 1 describe the line segment that joins the points P x Y and P x Y Use a graphing calculator or computer to draw the triangle with vertices A 1 1 B 5 4 C 1 6 Find the parametrization including endpoints and sketch to check Enter your answers as a comma separated list of equations Let x and y be in terms of t F AB BC

A ship leaves Port A and travels 73 km due west to Buoy C It then adjusts its course 66 northward It travels 123 km in that direction until it reaches Port B What angle with respect to due west could the ship have used to travel directly from Port A to Port 82 See the figure below The figure is not drawn to scale Port B 123 km 66 Buoy C 23 km Port A Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a degres

You are on a fishing boat that leaves its pier and heads east After traveling for 25 miles there is a report warning of rough seas directly south The captain turns the boat and follows a bearing of S35 W for 14 2 miles a At this time how far are you from the boat s pier b What bearing could the boat have onginally taken to arrive at this spot 142 MA

For the function f x 3 sinx 1 give the ampl midline vertical shift and graph the function Your graph should show at least one period with 5 accurately plotted points 3 Amplitude Period Horizontal shift Midline Graph Tr Lo 2111 20

Test the claim about the difference between two population means and 2 at the level of significance a Assume the samples are random and independent and the populations are normally distributed Claim 0 01 Population statistics 3 2 0 1 7 Sample statistics x 14 n 30 X 16 n 27 Ha H1 H Determine the standardized test statistic Z Round to two decimal places as needed Determine the P value P value Round to four decimal places as needed What is the proper decision OA Fail to reject Ho There is enough evidence at the 1 level of significance to reject the claim OB Reject Ho There is not enough evidence at the 1 level of significance to reject the claim OC Reject Ho There is enough evidence at the 1 level of significance to reject the claim OD Fail to reject Ho There is not enough evidence at the 1 level of significance to reject the claim

A tower that is 175 feet tall casts a shadow 151 feet long Find the angle of elevation of the sun to the nearest degree 151 ft 175 ft The sun s angle of elevation is Do not round until the final answer Then round to the nearest whole number

5 5 ft 74 10 ft feet zearn Richland School Di Find the height of the top of the goal post rounded to the nearest tenth of a foot

C 16 O O A 108 sin 108 40 sin 108 16 sin 108 40 sin 108 40 sin B 16 sin B 32 sin C 16 sin C 108 40 B

To calculate the cost of painting his silo a farmer must find its height The farmer uses a cardboard square to line up the top and bottom of the silo as shown in the diagram below Approximate the height of the silo DR

The vertices of AABC represent the buoy markers that form the legs of the course for a swim race What is the distance from marker C to marker A Round your answer to the nearest tenth of a meter 60 O 130 5 m O 148 4 m O 175 9 m O 269 5 m 200 m 40 B

In order to meet ADA Americans with Disabilities Act requirements a wheelchair ramp must have an angle of elevation of no more than 4 8 A builder needs to install a ramp to reach a door that is 2 5 feet off the ground 11 Is 20 feet long enough for the straight line distance of the ramp to meet the requirements What angle of elevation will this ramp have A 20 foot ramp will have an angle of elevation of approximately

You hike 210 meters up a steep hill that has a 31 angle of elevation as shown in the diagram A 210 m 31 b B a C Give each side and angle measure rounded to the nearest whole number a mZB III

3 7 01 You are planting a garden in the shape of an equilateral triangle as shown in the diagram You want to find the area of the garden to determine how much topsoil you will need 60 6 ft 6 ft 30 6 ft 19 Substitute the values of b and h in the formula A 2 b 1 b h for the area of the garden

A roof has a cross section that is a right triangle The diagram shows the approximate dimensions of this cross section Find the height h of the roof Round your answer to the nearest tenth 20 ft The height of the roof is about 23 9 ft feet h 13 ft

35 cos M cos N sin M 37 sin N N 12 HIII 1 T 1 1 1 T

You are holding a kite string in your hand The angle of elevation from your hand to the kite is 53 and the distance to the kite is 300 feet Your hand is 4 feet above the ground How high is the kite Round your answer to the nearest tenth of a foot feet