Quadratic equation + expression of a variable from the formula - math problems

Number of problems found: 152

  • The pool
    The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom?
  • Find the 15
    Find the tangent line of the ellipse 9 x2 + 16 y2 = 144 that has the slope k = -1
  • Tangents to ellipse
    Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1].
  • Area and perimeter of rectangle
    The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
  • Isosceles triangle
    In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
  • Dimensions of the trapezoid
    One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2
  • Perimeter and diagonal
    The perimeter of the rectangle is 82 m, the length of its diagonal is 29 m. Find the dimensions of the rectangle.
  • Derivative problem
    The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
  • Roots and coefficient
    In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b.
  • Integer sides
    A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
  • On a line
    On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
  • Shell area cy
    The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
  • The cylinder
    The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder.
  • Lookout tower
    How high is the lookout tower? If each step was 3 cm lower, 60 more of them were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now.
  • 1 page
    One page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?
  • Two chords
    From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords.
  • Circle and square
    An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
  • Viewing angle
    The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
  • A map
    A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field?
  • Difference of legs
    In a right triangle, the length of the hypotenuse is 65 m, and the difference of legs is 23 m. Calculate the perimeter of this triangle.

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