Use the result of Exercise 7 and the method of successive differences to find the first eight octagonal numbers Then divide each by 4 and record the remainder What is the pattern$$$ obtained?
Consider the following equations, where the left side of each is an octagonal number
Use the pattern established on the right sides to predict the next octagonal number What is the next equation in the list?
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- In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H. A margarine tub has the shape of a frustum of a cone. With the lower base having diameter length 11 cm and the upper base having diameter length 14 cm, the volume of such a container 623 cm tall can be determine by using H=3223 cm, h=26 cm. Find its volume. A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2arrow_forwardIn Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H. A container of yogurt has the shape of a frustum of a cone. With the lower base having diameter length 6 cm and the upper base having diameter length 8 cm, the volume of such a container 7.5 cm tall can be determined by using H=30 cm and h=22.5 cm. Find its volume. A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2arrow_forward
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