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 The volume under an an uneven surface 2020-05-01 From Solon:I am trying to fill an area of floor which has an uneven surface. I need to know the volume of fill. If you imagine a rectangular room (4 corners) that measures 189 inches by 240 inches and the depth at each corner is different. Let us say corner #1 has a depth of 1", corner #2 has a depth of 0", corner #3 has a depth of 2" and corner #4 has a depth of 4". How would i find the volume of said floor area? Any assistance would be greatly appreciated!Answered by Harley Weston. The angle between two planes 2017-09-12 From Arthi:Hello. hope you are having a good day. I am stuck on a maths question in which it is asking, how to find the angle between two given planes. These planes are in a 3D shape such as a prism. How can I do this? Please reply as soon as possible Thank YouAnswered by Penny Nom. An airplane schedule 2016-10-14 From Stephanie:Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time?Answered by Penny Nom. Sierpinski Pyramid 2015-12-14 From victor:Is a tetrix (a Sirpienski Pyramid/Tetrahedron) its own hyperplane?...alternatively, is it a hyperplane?Answered by Robert Dawson. The line of intersection of two planes 2015-12-09 From Rabz:Determine the vector equation for the intersection between the two given planes 2x+7y equal to 14,x+z equal to 7Answered by Penny Nom. The intersection of a plane and a cone 2015-05-16 From Tom:Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known.Answered by Chris Fisher. Meetings for 77 students 2014-09-18 From Adam:We have a new group of students starting, and would like to set up a series of small group meetings so each student meets each other, hopefully without meeting the same people twice. We have 77 students. In theory I would like to have 11 meeting slots, with 10 groups in each slot, with up to 8 students in each group. Is there a way to do this? I have wondered if it might be easier to do 9 meeting slots, with 9 groups per slot, with 9 students per group. Thanks!Answered by Victoria West. If x+y+z=1 then x^2 + y^2 + z^2 = ? 2014-04-30 From Nitin:If x+y+z=1 then x^2 +y^2+z^2 = ? ?Answered by Robert Dawson. A plane 2013-10-27 From Thomas:Why is this 3d plane flat? if m ≠ n arcsin(sin(m*arctan(x/y))), arcsin(cos(n*arctan(x/y))), Pi-arcsin(sin(m*arctan(x/y)))-arcsin(cos(n*arctan(x/y))) This is using radians. These are angles of a triangle, when m and n are the same it is a right triangle. All three inputs are not equal to each other. The last input is pi minus the first two inputs, which makes a complete triangle. I was kind of hoping to find more lissajous curves. It doesn't make sense to me that this is a flat plane, a diagonal one at that. I'm not a student or anything. I'm just wasting time.Answered by Chris Fisher. Dropping supplies from an airplane 2013-02-14 From Claire:An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph. a) write the parametric equations that represent the path of the supplies c)How long will it take for the supplies to reach the ground? d) how far will the supplies travel horizontally before they land?Answered by Penny Nom. Is a line lying in a plane an open or a closed region? 2013-02-13 From pardeep:please help with this question on the open and closed intervals :: Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so?Answered by Harley Weston. How fast is the distance between the aircraft and the car increasing? 2012-10-24 From Steven:At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car?Answered by Penny Nom. A plane travelling with the wind and against the wind 2012-08-03 From Gwen:The time of a plane trip of 450 miles, with the wind is 3/5 the time of the return trip against the wind. If the plane travels 120 mph in still air, what is the wind speed?Answered by Penny Nom. The position of an aircraft relative to the airport 2012-06-08 From Dennis:"Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing.  Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north.  What are the x,y, and z components (in meters) of the position vector. The x-axis is east, the y-axis is north and the z-axis is vertical.Answered by Penny Nom. Two line segments in the plane 2011-08-15 From Tim:For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin. Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value. Prove that these segments have no common points.Answered by Chris Fisher. Points with distance 5 from the point (-2, -1) 2011-01-19 From Alexa:Find all points having a x-coordinate of 2 whose distance from the point (-2, -1) is 5.Answered by Penny Nom. The angle between a line and a plane 2011-01-12 From tom:what are the angles of the diagonal of a rectangular parallelepiped 2in by 3 in by 4 in makes with the faces... You know this is a problem that I can't figure out ...I don't know where the angle and the diagonals where? can you help me with this one?Answered by Penny Nom. What is its speed in still air? 2010-11-28 From Shelby:An Airplane flies a certain distance in 3 hours going WITH a 40km/hr wind. It travels the same distance in 5 hours when going against the wind. What is it's speed and how long would it take to travel the same distance in still air? Distance = speed x timeAnswered by Penny Nom. Two jets leave denver at 9 am. 2010-10-15 From Carl:two jets leave denver at 9 am. One flying east at a speed of 50 km per hour greater than the other which is traveling west. At 11 am the planes are 2500 km apart. Find their speeds.Answered by Stephen La Rocque. Graphical Representation of Complex Numbers 2010-06-08 From Anas:why do we write complex number a+ib as (a,b)?Answered by Janice Cotcher. Can a line segment curve over two planes? 2010-02-14 From Graham:I am working on a math fair project. Can a line segment curve over two planes? Such as, if I had a three dimensional L bracket and I drew a line segment on it with a marker starting on the bottom of the L and had it curve around the corner and up the top, would it still be considered one line segment? Or is that two line segments? Is there a rule that a line segment can only occupy one plane? Thank you. GrahamAnswered by Chris Fisher. Two jets are traveling towards each other 2009-10-05 From jake:two jets are traveling towards each other and are 4000 km apart. the rate of one jet is 100 km/h faster than the rate of the other. if the jets pass each other after 2.5 hrs what is the rate of speed of the faster jet?Answered by Penny Nom. At what speed does an automobile start to hydroplane? 2009-06-03 From Don:How do you figure at what speed does an automobile start to hydroplane when driving on a wet surface.Answered by Robert Dawson. An aeroplane flying in a wind 2009-06-02 From Maria:The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air, are such that its resultant speed and direction are 800 kph, and direction N71.6◦E I need to find the size of the angle between v and vw, in degrees to one decimal place, and find the speed at which the aeroplane would fly if the air were still, to the nearest kph. It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane would have if the air were still, the velocity vw of the wind, and the resultant velocity v of the aeroplane (diagram should be in the form of a triangle illustrating how one velocity vector is the sum of the other two) ThanksAnswered by Harley Weston. A plane cuts a line segment 2009-03-17 From Manis:Find the ratio in which the line joining (2,4,16) and (3,5,-4) is divided by the plane 2x-3y+z+6=0.Answered by Robert Dawson. A slopped table top 2009-03-16 From anthony:A perfect circle with radius 100m is supported by four legs, 50m long. The circle is flat when all four legs are 50m long, and tilted when the legs are different in length. The four legs are spread evenly 90 degrees apart at 0, 90, 180, and 270. Find the high and low points in degree and height when the legs are 55m at 0 degree, 70m at 90 degree, 45m at 180 degree, and 30m at 270 degree. Not sure if they can be calculated using only 2 or 3 legs. I have tried by picking the two adjacent highest legs (55m and 70m) so I know the high point falls into the first quadrant. Then I tried using ratio to determine where the high point is, which I think high point should be closer to the 70m leg, I am not sure. If I can find the high point, the low point should be opposite to it.Answered by Chris Fisher and Harley Weston. Related rates 2009-03-09 From Megan:A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later?Answered by Harley Weston. How fast is the visible surface of the earth decreasing? 2009-01-24 From Ray:A dive bomber loss altitude at a rate of 400 mph. How fast is the visible surface of the earth decreasing when the bomber is one mile high?Answered by Harley Weston. How far is the airplane from the control tower? 2009-01-17 From Murtaza:An aircraft is vertically above a point which is 10 km west and 15 km north of a control tower. The aircraft is 4000 m above the ground, how far is it from the control tower?Answered by Penny Nom. The area of a region in the plane 2009-01-03 From Rogerson:Find the area, S, of the shaded region enclosed by the given cureve, the given line and the x-axis. y = -x^2 + 1 line x = 2Answered by Harley Weston. What is i^i? 2008-12-27 From randomness:i have learnt that 'i' is square root of -1. What is then i^i ? It baffles my maths teacher...Answered by Robert Dawson and Penny Nom. How fast is the distance between the airplanes decreasing? 2008-11-10 From Crystal:At a certain instant, airplane A is flying a level course at 500 mph. At the same time, airplane B is straight above airplane A and flying at the rate of 700 mph. On a course that intercepts A's course at a point C that is 4 miles from B and 2 miles from A. At the instant in question, how fast is the distance between the airplanes decreasing?Answered by Harley Weston. The flight of an airplane 2008-08-29 From kobina:You are traveling on an airplane that is moving at 500 mph in a direction 40deg north of west.Therefore , You are travelling (due to the plane ) at how many mph toward the west.Answered by Stephen La Rocque. What is the altitude of the plane? 2008-04-23 From tiana:If a plane is taking off and its climbing at 380 feet per minute at 205 MPH, what is the altitude of the plane after it traveled 115 miles?Answered by Penny Nom. A package of supplies is dropped from a plane 2008-02-29 From beth:An airplane flies west at a speed of 200m/s. A package of supplies is dropped from the plane to some campers. if the plane is at an altitude of 1000meters, how far from the campers should the package be dropped to land near them? ignore wind resistance.Answered by Stephen La Rocque. Forces on an inclined plane 2008-01-10 From Ron:A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body?Answered by Stephen La Rocque. The radius of a planet 2008-01-06 From Ben:Two people who are both h feet tall are standing on a spherical planet. One person walks a distance d in feet away from the the other person. At this point, the person walking turns around and can no longer see the top of the other persons head. What is the radius of the planet?Answered by Stephen La Rocque and Harley Weston. What is the speed of the plane in still air? 2008-01-05 From oscar:A plane flies 400 miles with the wind and 340 miles against the wind in the same length of time. If the speed of the wind is 24mph, what is the speed of the plane in still air?Answered by Penny Nom. Points that are 15 units from the origin 2007-09-20 From Paula:Find the coordinates of any point(s) 15 units away from the origin with an x-coordinate of 9. I was given the answer: (9,12) and (9,-12), but I do not understand how these numbers were calculated. Thank you for your help!Answered by Stephen La Rocque. Points in a plane 2007-06-01 From Gabrielle:In general how many planes are there which contain two given points, three given points, and four given points?Answered by Steve La Rocque and Walter Whiteley. The intersection of two planes 2007-05-31 From Sarim:How to find a intersection of two planes?Answered by Penny Nom. The velocity of an aircraft 2007-03-22 From William:Hello, I don't understand how to work this problem. Thanks in advance for your help! A jet moving at 500.0 km/h due east moves into a region where the wind is blowing at 120.0 km/h in a direction 30.0 degrees north of east. What is the new velocity and direction of the aircraft relative to the ground?Answered by Penny Nom. Cut a given sphere by a plane 2007-03-14 From Rory:Cut a given sphere by a plane so that the volumes of the two segments formed shall be in a given ratio. Show that in modern notation, this leads to the cubic equation m(r+x)^2(2r-x)=n(r-x)^2(2r+x) where r is the radius of the sphere, x is the distance of the cutting plane from the centre of the sphere, and m/n < 1 is the given ratio. Can you help me show the solution to this question. Thank you.Answered by Penny Nom. The distance from a point to a line in 3 space 2006-10-29 From Marie:find the distance from the point (1, -2, -3) to the line x = y = z-2Answered by Penny Nom. Computing gravity 2006-09-27 From Patricia:What is the gravity of planet z in inch/hr squared if the weight of an element with mass of 45000 oz on planet z is 2N?Answered by Stephen La Rocque. Plotting co-ordinates on a number plane 2006-09-08 From Victor:I need to plot co-ordinates (0,2), (2,-2), (-2,0), and (0,0) on a number or co-ordinates plane, I am not sure how to do this, and get lost after the first point, can you please help? Answered by Penny Nom. Flying with and against the wind 2006-07-06 From Tim:When a plane flies with the wind, it travels 800 miles in 4 hours. Against the wind it takes 5 hours to cover the same distance. Find the rate of the plane in still air and the rate of the wind.Answered by Stephen La Rocque. A line parallel to a plane 2006-03-28 From Ryan:I was wondering how I would prove the following theorem. I am completely lost at this point and all my other ideas have been extremely complicated and somewhat blurry. "Through a point outside a given plane, there is at least one line parallel to the given plane." Answered by Chris Fisher. Find the ground speed and the planes true heading. 2006-02-05 From Jimmie:An aircraft going from city A to city B on a bearing of S69E (degrees) is traveling at a speed of 430 mph. The wind is blowing out of the north to south at a speed of 25 mph. Find the ground speed and the planes true heading.Answered by Penny Nom. How many passengers boarded the plane in Phoenix? 2005-11-03 From Vish:Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix?Answered by Penny Nom. What is the radius of this planet 2005-08-05 From Kelly:Assuming that a North-South line has been established, you set up two camps that are 67 miles apart. You now set up poles at each camp perpendicular to the ground. On a certain day at "noon" the pole at the South camp casts no shadow, while at the North camp a shadow is cast. The shadow makes an angle of 89 degrees with the horizontal. What is the radius, diameter, and circumference of this planet?Answered by Chris Fisher. An aircraft is flying directly from airport A to airport B 2004-10-22 From A student:In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from airport A to airport B, which is 2000 km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i-30j)km/h. Calculate (i) the time of flight, to the nearest min (ii) the direction of the wind.Answered by Penny Nom. The intersection of planes 2004-09-07 From Joshua:I was wondering about the intersection of planes. Can planes intersect? Answered by Penny Nom. Two line segments and a plane 2003-09-11 From Laura:Do all figures made up of two segments lie in a plane?Answered by Penny Nom. Can 2 vertical planes intersect? 2003-09-06 From Erin:My question is can 2 vertical planes intersect?Answered by Penny Nom. A triangle in the complex plane 2003-07-10 From Scott:The vertices O and A of an EQUILATERAL triangle OAB in the complex plane are located at the origin and 3 + 3i. Find all possible values for the complex number representing the vertex B. Give the location of B in both polar and cartesian form (to 2.d.p)Answered by Penny Nom. Two trig problems 2003-06-10 From Bett:I have this ongoing trouble with trig and solving triangles with laws of cosines and sines!! For example if it asks to solve triangle FGH, given angle G=102.7 , side f=14.2, and h=18.6. Now do I use law of cosines because I don't have the measure of an angle and length of the opposite side??I don't know where to go from here,I am totally confused!!! I also have a problem with this word problem I have been doing. It asks: An airplane flies 847.5 km at a bearing of 237.3 degrees. How far south and west fo its original position is it? Huh? Please help! Answered by Penny Nom. Two airplanes leave Dallas 2003-02-06 From A student:TWO AIRPLANES LEAVE DALLAS AT THE SAME TIME AND FLY IN OPPOSITE DIRECTIONS. ONE AIRPLANE TRAVELS 80 MILES PER HOUR FASTER THAN THE OTHER. AFTER THREE HOURS, THEY ARE 2940 MILES APART. WHAT IS THE RATE OF EACH AIRPLANE?Answered by Penny Nom. Two rate problems 2002-09-30 From Rebecca: There are two small holes in the bottom of a tub filled with water. If opened, one hole will empty the tub in three hours; the other will empty it in six hours. If both holes are opened at the same time, how long will it take to empty the tub? An airplane flies 400 miles per hour in calm air. It can cover 900 miles flying with the wind in the same time that it can cover 700 miles against the wind. What is the speed of the wind? Answered by Penny Nom. The radius of a planet 2001-07-30 From Jessica:A satellite is orbiting the earth at an altitude of 100 miles. If the angle of depression from the satellite to the horizon is 50 degrees, what is the radius (to the nearest mile) of the planet?Answered by Harley Weston. How many planes contain a line and a point? 2000-08-30 From Harold:How many planes contain each line and point?Answered by Harley Weston. Uniting algebra and geometry 2000-04-16 From Beth:Who is the mathmatician that united algebra and geometry???Answered by Claude Tardif. Parallel planes 2000-01-10 From Hugo Alvarez:When two parallel planes are cut by a third plane, the lines of the intersection are? Answered by Claude Tardif. An airplane problem 1999-03-08 From B.M.R.:A plane left New York and headed East to its destination 3600 miles away across the Atlantic. On the way back its speed was boosted by a 50 mph tail wind and it arrived an hour early. What was its normal speed?Answered by Jack LeSage. Intersection of Planes 1998-12-03 From Lindsay Fear:My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is: Prove that a necessary condition that the three planes ` -x + ay + bz = 0 ax - y + cz = 0 bx + cy - z = 0 ` have a line in common is that a^2 + b^2 + c^2 + 2abc = 1Answered by Walter Whiteley. Intersection of planes 1998-11-22 From Dave Rasmussen:I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Co-ordinate Geometry. I have been teaching my students to write equations of planes and lines, - to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me?Answered by Walter Whiteley and Harley Weston.

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