The Vector equation of a plane To find the vector equation of a plane a point on the plane and two different direction vectors are required. The equation is defined as: where a is the point on the plane and b and c are the vectors. This equation can then be written as: The Cartesian equation of a plane The cartesian equation of the plane is easier to use. The equation is defined as: One of the advantages to writing the equation in cartesian form is that we can easily find the normal
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Problem 705 Determine the centroid of the shaded area shown in Fig. P-705‚ which is bounded by the x-axis‚ the line x = a and the parabola y2 = kx. Solution 705 HideClick here to show or hide the solution At (a‚ b) Thus‚ → equation of parabola Differential area Area of parabola by integration Location of centroid from the y-axis (x-intercept of centroid) answer Location of centroid from the x-axis (y-intercept
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2-Variable Inequality Here is an example of a problem very similar to the one in the Week Three Assignment: Catskills Hammock Company can obtain at most 2000 yards of striped canvas for making its full size and chair size hammocks. A full size hammock requires 10 yards of canvas and the chair size requires 5 yards of canvas. Write an inequality that limits the number of striped hammocks of each type which can be made. (b) First I must define what variables I will be using in my inequality
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For those who are unaware‚ at least 1 and 2 are thanks to Georg Cantor and his invention of set theory. He had to endure a lot of resistance from the mathematical luminaries of his day - Kronecker and apparently‚ even Poincaré! Like Nietzsche‚ he died in a mental institution‚ the vicious attacks on his ideas (mostly by Kronecker) having supposedly played a part in Cantor’s breakdown. His mathematical ideas also ran afoul of some religious "philosophers" who‚ as is usually the case‚ are never ever
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SPM(U) 2006 : http://mathsmozac.blogspot.com Section A [52 marks] Answer all questions in this section. 1 The Venn diagram in the answer space shows sets P‚ Q and R such that the universal set‚ ξ = P ∪ Q ∪ R . On the diagram in the answer space‚ shade (a) the set P ∪ R ‚ (b) the set (P ∩ R ) ∪ Q ’ . [3 marks] Answer: (a) P Q R (b) P R Q 2 Diagram 1 shows a solid cuboid. A cone is removed from this solid. 12 cm 10 cm 15 cm DIAGRAM 1 The diameter of the base of the cone is 7 cm
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Unit 2 Homework - Template St Atanagio is a remote island in the Atlantic. The inhabitants grow corn and breed poultry. The accompanying table shows the maximum annual output combinations of corn and poultry that can be produced. Obviously‚ given their limited resources and available technology‚ as they use more of their resources for corn production‚ there are fewer resources available for breeding poultry. Maximum annual output options | Quantity of Corn(pounds) | Quantity of Poultry(pounds)
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Taviana Webb Period 1 Culminating Task #1 Rotation: The rotation transformation is where you turn a figure about a given point. The point that the obtated about can be inside the figure or anywhere outside it. The amount of rotation is called the angle of rotation and is measured in degrees. You can rotate shapes or figures on a coordinate grid. Each quadrant differs in degrees when working with rotations. Going clockwise the first quadrant is 90 degrees ‚ the second quadrant is 180 degrees
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UNIT ONE QUIZ MATH 110 Part 1 of 25 - 4.0/ 4.0 Points Question 1 of 25 4.0/ 4.0 Points ]WHERE THE QUESTION SAYS "FEEDBACK" THE ANSWER IS THE ONE ABOVE IT SO NUMBER ONE IS "B" NUMBER TWO IS "B" AND SO ON i DIDN’T MAKE ANY CORRECTION SO BE CAREFUL IN ANSWERING. I ALSO HAVE ANOTHER UNIT ONE QUIZ THAT IS DIFFERENT. I WILL POST THAT ONE TO Choose the location of the point (- 1‚ - 5) A.Positive x-axis B.Quadrant III In Quadrant III‚ both coordinates are negative. Feedback: Correct! C.Positive
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A movement is a self-contained part of a musical composition or musical form. While individual or selected movements from a composition are sometimes performed separately‚ a performance of the complete work requires all the movements to be performed in succession. A movement is a section‚ "a major structural unit perceived as the result of the coincidence of relatively large numbers of structural phenomena. Classification of Movements From a gymnastic point of view movements are divided into Active
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plot: creates 2d line plot axis: changes aspect ratio of x and y axis x label: annoted the x axis y label: annoted the y axis title: puts the title on the plot title of prog: title(’circle of unit radius’) print: prints the hardcopy of the plot EX: draw a circle of unit radius x and y co ordinates 100 points of the circle the parametric eq is x=cos(t) y=sin(t) theta=linspace(0‚2*pi‚100); axis=’equal’; xlabel(’x’) ylabel(’y’) 1. plot y=sinx range 0 x=linspace(0
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