Caroline Aucoin
Geometry teacher | Verified Expert
I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.
Questions
Circle A has a radius of #4 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #8 # and the triangle has an area of #32 #. What are the lengths of sides A and B?
The North Campground (3,5) is midway between the North Point Overlook (1,y) and the Waterfall (x,1). How do I use the Midpoint Formula to find the values of x and y and justify each step? Please show steps.
Sherry spots a car as she is looking down at a 70° angle from the top of the Eiffel Tower, which is 1063 ft tall. How far away from the base of the tower is the car?
Is the answer choice I selected right?!
How would I find the area of a 45-45-90 triangle with one side of length 73?
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 #21 # and the height of the cylinder is #2 #. If the volume of the solid is #90 pi#, what is the area of the base of the cylinder?
A line segment has endpoints at #(2 , 3)# and #(5 , 2)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #3#, and reflected about the y-axis, what will the line segment's new endpoints be?
How many sides do these regular Polygons have if their interior is 30?
A composite geometry is made up of cube and a square pyramid frustum. The slanted side AK stretch a side lengths of 5.62 forming an isosceles triangle. Calculate the volume, surface area and sketch the net of the surface area?
A line passes through #(5 ,8 )# and #(2 ,9 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?
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 #42 # and the height of the cylinder is #1 #. If the volume of the solid is #225 pi#, what is the area of the base of the cylinder?
An ellipsoid has radii with lengths of #8 #, #8 #, and #12 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?
Circle A has a center at #(1 ,5 )# and an area of #18 pi#. Circle B has a center at #(8 ,4 )# and an area of #66 pi#. Do the circles overlap?
Two corners of an isosceles triangle are at #(2 ,4 )# and #(8 ,5 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?
There is a rectangle with width #4x# and height #(7/3)x#. What is the area of the rectangle when #x = 6#?
A circle's center is at #(7 ,5 )# and it passes through #(5 ,8 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?
A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #( pi)/4 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?
A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #3 #, its base has sides of length #6 #, and its base has a corner with an angle of # pi/3 #. What is the pyramid's surface area?
A line segment has endpoints at #(8 ,4 )# and #(3 ,7 )#. The line segment is dilated by a factor of #1/2 # around #(3 ,2 )#. What are the new endpoints and length of the line segment?