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Questions and Answers

What is the purpose of the MTH 103 course?

  • To introduce students to electrical engineering concepts
  • To provide an overview of the history of mathematics
  • To provide a general understanding of mathematics in everyday life
  • To teach students the skills required in Sciences, Technology and Engineering Professions (correct)

    • What is the recommended way to cite the course material if used as a bibliographic reference?

  • Course Title, National Open University of Nigeria
  • Course Code: Course Title, National Open University of Nigeria, 2014 at <a href="http://www.nou.edu.ng/index.htm#">http://www.nou.edu.ng/index.htm#</a> (correct)
  • Course Title, National Open University of Nigeria, 2001
  • MTH 103, Elementary Mathematics III, 2010

    • What is the number of study units in the MTH 103 course?

  • Ten
  • Thirteen
  • Eleven (correct)
  • Twelve

    • What is required to be included on every physical page of the textbook if it is redistributed in print format?

    <p>All of the above</p> Signup and view all the answers

    What is the title of the course MTH 103?

    <p>Elementary Mathematics III</p> Signup and view all the answers

    What is the purpose of the attribution statement when electronically redistributing the textbook?

    <p>To give credit to the original authors</p> Signup and view all the answers

    What is the URL mentioned in the attribution statement?

    <p><a href="http://www.nou.edu.ng/index.htm">http://www.nou.edu.ng/index.htm</a></p> Signup and view all the answers

    Who is responsible for the ideas and opinions expressed in the publication?

    <p>The authors</p> Signup and view all the answers

    What is the equation of an ellipse in its standard form?

    <p>x^2/a^2 + y^2/b^2 = 1</p> Signup and view all the answers

    What is the value of a in the equation 9x^2 + 4y^2 = 36?

    <p>3</p> Signup and view all the answers

    What are the coordinates of the foci of the ellipse 9x^2 + 4y^2 = 36?

    <p>F1 (0, 5) and F2 (0, -5)</p> Signup and view all the answers

    What is the length of the major axis of the ellipse 9x^2 + 4y^2 = 36?

    <p>6</p> Signup and view all the answers

    What is the definition of a hyperbola?

    <p>A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.</p> Signup and view all the answers

    What is the value of c in the equation 9x^2 + 4y^2 = 36?

    <p>$\sqrt{5}$</p> Signup and view all the answers

    What are the x-intercepts of the ellipse 9x^2 + 4y^2 = 36?

    <p>(2, 0) and (-2, 0)</p> Signup and view all the answers

    What is the length of the minor axis of the ellipse 9x^2 + 4y^2 = 36?

    <p>8</p> Signup and view all the answers

    What is the center of the circle x2 +y 2 +2x− 6x− 15 = 0?

    <p>(-1, 3)</p> Signup and view all the answers

    What is the radius of the circle x2 +y 2 +2x− 6x− 15 = 0?

    <p>5</p> Signup and view all the answers

    What is the equation of the circle with center (− 2, 3) and radius 6?

    <p>x2 + y2 + 4x - 6y - 23 = 0</p> Signup and view all the answers

    What is the radius of the circle with center (-3,4) which passes through the point (2,5)?

    <p>√26</p> Signup and view all the answers

    What is the equation of the circle with center (-3,4) which passes through the point (2,5)?

    <p>x2 + y2 + 6x - 8y - 1 = 0</p> Signup and view all the answers

    What is the method used to find the radius of the circle with center (-3,4) which passes through the point (2,5)?

    <p>The distance formula between two points</p> Signup and view all the answers

    What is the equation of the circle with center (h, k) and radius r?

    <p>(x - h)² + (y - k)² = r²</p> Signup and view all the answers

    What is the method used to find the equation of the circle with center (h, k) and radius r?

    <p>Using the formula (x - h)² + (y - k)² = r²</p> Signup and view all the answers

    What is the formula for the vector product of two vectors a = a1 i + a2 j + a3 k and b = b1 i + b2 j + b3 k?

    <p>(a2 b3 - a3 b2) i - (a1 b3 - a3 b1) j + (a1 b2 - a2 b1) k</p> Signup and view all the answers

    What is the vector product of a = 2i + 2j - k and b = 3i - 6j + 2k?

    <p>10i - 10j + 20k</p> Signup and view all the answers

    What is the meaning of the concept of Locus in geometry?

    <p>A set of points that satisfy a certain condition or description</p> Signup and view all the answers

    What is the algebraic expression of the Locus of points at a distance of 3 from the point (0, 0)?

    <p>x^2 + y^2 = 9</p> Signup and view all the answers

    What is the geometric representation of the equation x^2 + y^2 = 9?

    <p>A circle with centre at (0, 0) and radius of 3</p> Signup and view all the answers

    What is the objective of the unit on Loci?

    <p>To learn the concept of straight line</p> Signup and view all the answers

    What is the equation of the Locus of a point that satisfies the condition of being at a distance of 3 from the point (0, 0)?

    <p>x^2 + y^2 = 9</p> Signup and view all the answers

    What is the vector product of a = 3i + 2j - k and b = 2i + 3j - k?

    <p>7i - 7j + 13k</p> Signup and view all the answers

    What is the equation of a circle with center at (h, k) and radius r?

    <p>$(x - h)^2 + (y - k)^2 = r^2$</p> Signup and view all the answers

    What is the length of the hypotenuse of the right triangle in the Pythagoras theorem?

    <p>$ ceil{(x - h)^2 + (y - k)^2}$</p> Signup and view all the answers

    What is the condition for a second degree equation to represent a circle?

    <p>The coefficients of x^2 and y^2 are identical</p> Signup and view all the answers

    What is the center of the circle with equation x^2 + y^2 + 8x + 6y = 0?

    <p>(-4, -3)</p> Signup and view all the answers

    What is the radius of the circle with equation x^2 + y^2 + 8x + 6y = 0?

    <p>5</p> Signup and view all the answers

    What is the equation of a circle with center at (-g, -f) and radius r?

    <p>x^2 + y^2 + 2gx + 2fy + c = 0</p> Signup and view all the answers

    What is the value of c in the equation x^2 + y^2 + 2gx + 2fy + c = 0?

    <p>g^2 + f^2 - r^2</p> Signup and view all the answers

    What is the center of the circle with equation x^2 + y^2 - 4x + 2y - 4 = 0?

    <p>(2, -1)</p> Signup and view all the answers

    Study Notes

    Course Introduction

    • The course is designed to teach students how mathematics is used to solve problems in the scientific world.
    • The course aims to equip students with the skills required to attain proficiency in sciences, technology, and engineering professions.

    Mathematics in Problem-Solving

    • The course is structured to expose students to the skills required to solve scientific problems.

    Course Objectives

    • There are eleven study units in the course, each with its objectives.
    • The course aims to teach students the basics of mathematics required to solve scientific problems.

    Vector Product of Two Vectors

    • The vector product of two vectors a and b is given by the formula: a x b = (a2b3 - a3b2)i - (a1b3 - a3b1)j + (a1b2 - a2b1)k
    • Examples of vector product calculations are provided.

    Loci

    • Loci is a concept that combines algebraic expressions with geometric interpretations.
    • The concept of loci involves finding the algebraic expression of a locus given its condition or description.
    • Examples of loci include the equation of a circle, which is given by the formula: x2 + y2 = 9.

    Coordinate Geometry (Circle)

    • The equation of a circle is given by the formula: (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius.
    • The equation of a circle can be derived from the Pythagorean theorem.
    • Examples of finding the center and radius of a circle are provided.

    Coordinate Geometry (Circle) - General Equation

    • The general equation of a circle is given by the formula: x2 + y2 + 2gx + 2fy + c = 0, where the center is (-g, -f) and the radius is r = √(g2 + f2 - c).
    • Examples of finding the center and radius of a circle using the general equation are provided.

    Ellipse and Hyperbola

    • The equation of an ellipse is given by the formula: x2/a2 + y2/b2 = 1, where a and b are the lengths of the semi-axes.
    • The equation of a hyperbola is given by the formula: x2/a2 - y2/b2 = 1, where a and b are the lengths of the semi-axes.
    • Examples of finding the points of intersection of a circle with a line and the length of the major and minor axes are provided.
    • The concept of hyperbola is defined as a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

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    Description

    This publication outlines the terms of use and attribution for academic content, including proper citation and credit to the National Open University of Nigeria.

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