Ella Armstrong

Questions

• Point A is at #(-2 ,9 )# and point B is at #(-1 ,4 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
• The equation of line m is 4x + 5y = -2. What is the slope of a line that is perpendicular to line m?
• A triangle has vertices A, B, and C. Vertex A has an angle of #pi/6 #, vertex B has an angle of #(pi)/12 #, and the triangle's area is #12 #. What is the area of the triangle's incircle?
• An ellipsoid has radii with lengths of #15 #, #12 #, and #8 #. A portion the size of a hemisphere with a radius of #7 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
• A 30-60-90 triangle has a hypotenuse of length 9.8. What is the length of the longer of the two legs?
• The base of a triangular pyramid is a triangle with corners at #(5 ,1 )#, #(2 ,3 )#, and #(3 ,4 )#. If the pyramid has a height of #4 #, what is the pyramid's volume?
• A line segment has endpoints at #(7 ,6 )# and #(2 ,3 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
• What are regular polyhedrons? Give a few examples. Can we have general formula for finding their surface areas?
• The sun casts a shadow of a pine tree on the ground. The tree is 65 feet tall. The angle of depression is 53.4°. What is the length of the shadow?
• Using the Pythagorean Theorem, is a triangle with sides abc a right triangle? #a=12, b=9, c=15#
• The perimeters of two similar triangles is in the ratio 3:4. The sum of their areas is 75 sq cm. What is the area of the smaller triangle?
• What is the formula for surface area of a box?
• A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #33 # and the height of the cylinder is #14 #. If the volume of the solid is #225 pi#, what is the area of the base of the cylinder?
• If an angle is 30° more than half its complement what is its measure?
• A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #8 # and #6 # and the pyramid's height is #4 #. If one of the base's corners has an angle of #pi/3#, what is the pyramid's surface area?
• How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #6 #, and #5 #?
• An ellipsoid has radii with lengths of #8 #, #4 #, and #7 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
• A circle has a center that falls on the line #y = 2/9x +8 # and passes through # ( 3 ,1 )# and #(5 ,4 )#. What is the equation of the circle?
• The base of a triangle is 8 m, and the height is 10 m. How do you find the area?
• Two rhombuses have sides with lengths of #8 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?
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