Geometry Questions

In a right triangle the side adjacent to angle has length 3 79 meters and the hypotenuse has length 6 19 meters What is the cosine of the angle cose i e Textbook and Media

Some questions make use of the Interactive Graphing Tool in order to draw a parabola using two points Click the icon to view instructions for the Interactive Graphing Tool Draw a solid vertical parabola overlaying the dashed parabola on the graph Use the vertical parabola tool button on the graphing palette to draw a solid vertical parabola Place the first point at the vertex of the parabola shown as the solid dot on the graph and place the second point at another location on the parabola shown as the dashed curve on the graph Click to enlarge graph Careful Be sure to use a second point that is exactly on the parabola causing the dashed curve to be completely covered 8 6 A 4 P 8 Ay 6 9 1 2 14 6 48 40

2 Find the values of the six trig functions whose terminal ray passes through point Q 2 21 10 points Sin B Cos B Tan B Csc B Sec B Cot B

Show that the equation sin x X x 0 has a solution Provide all the necessary ju

For the function find the points on the graph at which the tangent line is horizontal If none exist state that fact y 2x 8 List all the points where the tangent line is horizontal Select the correct choice below and if necessary fill in the am A The point s at which the tangent line is horizontal is are Type an ordered pair Use a comma to separate answers as needed B The tangent line is horizontal at all points of the graph C There are no points where the tangent line is horizontal

8 A girl 160 cm tall stands 360 cm from a lamp post at night Her shadow from the light is 90 cm long How high is the lamp post 6104

5 Your new job requires you to calculate the material costs for manufactured goods One of goods you manufacture is a fabric sample in the shape of a circle Given the formula A Tr find the 2 area A of the fabric sample whose radius r is 6 2 x 105 m Write your answer in scientific notation Use 3 14 for T A m

If you already know lal and lvl then the formula a xv2 gives a convenient way to ind the curvature Use it to find the curvature and radius of curvature of the curve r t cost t sin t i sin t t cos t j t 0

O GRAPHS FUNCTIONS AND SYSTEMS Finding the slope and y intercept of a line given its equation in Find the slope and the y intercept of the line 7x 2y 10 Write your answers in simplest form slope 0 y intercept 8 08 X Undefined

A car has wheels with a 8 inch radius If each wheel s rate of turn is 3 revolutions per second find the angular speed in units of radians second 3 n 8 24 3 n 6 3r

Find a solution to the equation sec B 12 csc 29B 10

A Bolat leaves a port traveling due east at 12 mi hr At the same time another boat leaves the same port traveling northeast at 15 mi hr The angle of the line between the boals is measured relative to due north see the figure to the right What is the rate of change of this angle 30 min after the boats leave the port 3 hr after the boats leave the port Purt Let x be the distance from the port to the eastbound boat and let z be the distance from the port to the northeast bound boat Write an equation relating x z and 2 2 x Z 2 tan 2 Type an exact answer Type any angle measures in radians The rate of change of this angle 30 min after the boats leave the port is Round to the nearest thousandth as needed 15 mih 12 mih

In the diagram below of circle O GO 8 and m GOJ 60 8 G 60 What is the area in terms of 7 of the shaded region

A circle with a diameter of 10 cm and a central angle of 30 is drawn below 10 cm 30 What is the area to the nearest tenth of a square centimeter of the sector formed by the 30 angle 1 5 2 2 6 5 3 13 1 4 26 2

Find the angle of the sector below if the area of the sector is 36T P 18 Q

Find the area of the sector created below Round to the nearest tenth 120 4 cm B

1 Find the length of arc s in the diagram below To the nearest tenth 8 in 60 S

3 A ball is rolling in a circular path that has a radius of 10 inches as shown in the accompanying diagram What distance has the ball rolled when the subtended arc is 54 F Express your answer to the nearest hundredth of an inch 10 in 54

2 Find the length of minor arc AB to the nearest tenth The diagram below shows circle O with radii OA and OB The measure of angle AOB is 120 and the length of a radius is 6 inches O 120 6 B

1 If DE is the perpendicular bisector of AC which of the following statements is not true A BD BE OZABD CBD OAB BC AD CD D B E C

4 Find the height in centimeters of a square pyramid with a volume of 455cm and a base edge length equal to the height Give the approximate answer rounded to 2 decimal places

ect the correct answer from each drop down menu BC has vertices at A 11 6 B 5 6 and C 5 17 YZ has vertices at X 10 5 Y 12 2 and Z 4 15 NO has vertices at M 9 4 N 3 4 and O 3 15 KL has vertices at J 17 2 K 12 2 and L 12 7 PQR has vertices at P 12 3 Q 12 2 and R 3 2 can be shown to be congruent by a sequence of reflections and transl can be shown to be congruent by a single rotation

2 A tent is in the shape of a right pyramid with a square floor The square floor has side lengths of 8 feet If the height of the tent at its center is 6 feet what is the volume of the tent in cubic feet

Complete the wage table for an employee who receives time and a half overtime pay after 40 hours of work Hours Worked Money Earned Hourly Pay Table 10 140 00 280 00 420 00 560 00 A 770 00 B 650 00 C 840 00 D 1020 00 20 30 40 50

3 The volume of a triangular prism is 70 in The base of the prism is a right triangle with one leg whose measure is 5 inches If the height of the prism is 4 inches determine and state the length in inches of the other leg of the triangle

1 The Pyramid of Memphis in Tennessee stands 107 yards tall and has a square base whose side is 197 yards long What is the volume of the Pyramid of Memphis to the nearest cubic yard

Find the distance from the point to the plane 2 4 1 x 4y 4z 18 The distance is

Determine the graph of the equation 2 2 4 Choose the correct graph of the equation OA O C B O D G 0 y

Determine the graph of the ellipsoid 36x y 2 36 Choose the correct graph of the equation OA OB O C

5x 2z 133 hes Identify the surface by type paraboloid ellipsoid etc Choose the correct graph of the equation below OA O B HID O C

graph of the hyperbolic paraboloid 2 x 9z Choose the correct graph of the hyperbolic paraboloid OA O C OB O D y

Determine the graph of the paraboloid z x 9y Choose the correct graph of the equation OA B O C Y

Find the equation for the plane through the point Po 0 5 5 and normal to the vector n 7i 2j k Choose the correct answer below OA 7x 2 y 5 z 5 0 OB 7x 2y z 5 OC 7x 2y z 0 O D x 7 5 y 2 5 z 1 5

Find the angle between the vectors u 6i 6j v i 3j 5k The angle between the vectors is 0 Round to the nearest hundredth as needed radian s

Nora leans a 24 foot ladder against a wall so that it forms an angle of 76 with the ground How high up the wall does the ladder reach Round your answer to the nearest hundredth of a foot if necessary

5 In the diagram below a plane intersects a square pyramid parallel to its base Which two dimensional shape describes this cross section 6 A solid metal prism has a rectangular base with sides of 4 inches and 6 inches and a height of 4 inches A hole in the shape of a cylinder with a radius of 1 inch is drilled through the entire length of the rectangular prism Find the volume of the entire rectangular prism Find the volume of the cylinder 4 in 4 in What is the approximate volume of the remaining solid in cubic inches 6 in

A person is standing at the edge of the water and looking out at the ocean see figure The height of the person s eyes above the water is h 1 7 m and the radius of the Earth is R 6 38 x 106 m a How far is it to the horizon In other words what is the distance d from the person s eyes to the horizon Note At the horizon the angle between the line of sight and the radius of the earth is 90 b Express this distance in miles a Number i Units 90 Horizon

find the area of segment coloured in red A D 400m A B 340m B D 260m triangle is above centre point G A weat wosk

m 1 N L Find the measure of each marked angle in the figure when m1 3x and m2 2x 10 2 u m t C O S

Find the volume of the solid 20 5 in 7 in 21 2 cm 6 cm 4 cm 22 11 24 ft 4 ft

B a 80 b 120 16z 12 E 2z 4 D c 12 d 141

9 Which is mVXU a 15 W a 105 b 120 9x 18 X V T 15x U 3x 21 c d 122 5 126

anu 0 H Not drawn to scale Given m HJF 84 are shown Which statement if true would help prove that quadrilateral FGHJ is inscribed in Circle O and why a m JFG 84 for a quadrilateral inscribed in a circle adjacent angles are congruent b m JFG 96 for a quadrilateral inscribed in a circle adjacent angles are supplementary c m FGH 84 for a quadrilateral inscribed in a circle opposite angles are congruent d m FGH 96 for a quadrilateral inscribed in a circle opposite angles are supplementary

12 What is m XYZ a 83 166 b 979

16 Write the equation of a circle with center M 7 10 and radius 2 a x 10 y 7 4 b x y 7 10 4 c x 7 10 4 d x 7 10 2

14 Which statement below correctly relates BDC and ZBAC B A a ZBDC and ZBAC are complementary ZBDC and ZBAC are supplementary b c ZBDC and ZBAC are congruent d It is impossible to determine a relationship between ZBDC and ZBAC

ven the following sets find the set A n BUC U 1 2 3 8 A 1 2 4 6 B 1 2 3 C 1 2 3 4 5

The circle in the figure below has a radius of r and center at C The distance from A to B is x Redraw the figure below label as indicate in the problem and then solve the problem If C 70 and x 27 find r Round your answer to the nearest whole number r Xx D B X A

could be used to show that Circle A is similar to Circle B 2 and radius 1 0 0 and scale hat sequence of transformations a a translation of the center 5 units to the right and 2 units up then a dilation with center 0 0 and scale factor 3 b a translation of the center 5 units to the right and 2 units down then a dilation with center 113 C a translation of the center 5 units to the left and 2 units up then a dilation with center 5 2 and scale factor 3 d a translation of the center 5 units to the left and 2 units up then a dilation with center 5

what is the equation for the parabola with a focus f 0 16 7