A Sense of Proportion: Jupiter is about 71,000 km in radius.  The innermost Galilean moon, Io, orbits 420,000 km from the center of the planet, and the outermost Galilean moon, Callisto, orbits 1,900,000 km from the planet's center.  Design a model with Jupiter 5 inches in radius.  Where would the two moons orbit?

Q: The measures of corresponding angles of two similar figures can be compared using a scale factor. O…

A: It is False that the measure of corresponding angles of the similar triangles can be compared by…

Q: A tinsmith wants to make a small windowsill planter from a 40cm×16cm40⁢cm×16⁢cm sheet of copper.…

A: We will calculate height first from given ratio in question. PFA Given dimension of sheet 40 cm×16…

Q: If the ratio of the areas of two figures is . What is the scale factor of the figures?

A: We have to choose correct option

Q: The volume of Prism A is 1, 536 m and the volume of Prism B is 375 m. What is the ratio of their…

A: Given :                 The volume of prism A is 1536 m3                 The volume of prism B is…

Q: Find the ratio of perimeter to area of a regular octagon whose edge is 1 unit. a. 1.657 b. 1.245 c.…

A:

Q: A manufacturer needs to decide which container to use for packaging a product. One container is…

A: For the first figure,  V1=πr12h1 and V2=πr22h2 It is given that r1r2=21  and h1h2=12

Q: If two prisms are similar and their surface areas are in a ratio of 9:25, what is the ratio of their…

A: For two similiar  prisms their ratios of volumes are equal to their surface area.

Q: Two similar cones have heights of 4m and 12m. What is their scale factor? What is the ratio of their…

A: Given: Both cone are similar

Q: what is the scale factor of the dilation if the pre-image of triangle ABC has the side length AB of…

A: Given Data: The length of side AB of pre-image triangle ABC is: AB=10 cm The length of side A'B' of…

Q: The corresponding medians of two similar triangles are 2 cm and 5 cm. What is the ratio of their…

A: Given that the corresponding medians of two similar triangles are 2 cm and 5 cm. To find the ratio…

Q: the instructions for a model car show a scale of 1 inch to 48 inches how long is the actual car if…

A: According to the scale 1 inch represents  48 inches , So this implies , if the drawing is 4 inches,…

Q: On a scale drawing, the scale is - inch = 1 foot. What are the 2 %3D dimensions on the scale drawing…

A: Given scale drawing, the scale is 12 inch = 1 foot We have to convert the dimensions of the room…

Q: The rectangular front windshield of the bus has the length of 1.5V3 m and the width of 1.5 m. The…

A: Given data: Length of windshield=1.53 m. Width of the windshield=1.5 m. Area of the windshield =…

Q: In the diagram, the cylinder and the hexagonal prism have the same height, h = 12 centimeters, and…

A: Given: The height of the cylinder and and the hexagonal prism, h = 12cm In the diagram, Any…

Q: which calculation should be made: Perimeter, Area, Lateral Area, Total Surface Area, or Volume.…

A:

Q: If the cones below are similar, what is the ratio of the surface area of Cone A to the surface area…

A:

Q: If a point on the pre-image has coordinates (3, -4), and the coordinates of its image are (12, -16),…

A: Given: A point on the pre-image has coordinate (3,-4), and the coordinate of its image are (12,-16)…

Q: The areas of two similar triangles are equal to 64 cm2 and 81 cm2. What is the ratio of their…

A: Let's find ratio of their corresponding altitudes.

Q: Given the edge of a square is about 100 cm, by how to measure it such that the

A:

Q: The composite figure below contains a rectangle, an isosceles trapezoid, and two equal parts of a…

A:

Q: A can of soda is 4.8 inches tall and 2.5 inches in diameter. What 2-dimensional shape would be…

A: After doing a vertical cross section it will be a

Q: The cage containing exotic birds is in the shape of a pentagonal prism. If the side length is 17…

A: We will solve the following.

Q: If Gabby wants to make a regular octagon with a side length of 20 inches using wire, how much wire…

A: Given: Length of one side of octagon 20 inches. The number of sides of the octagon, n=8. The…

Q: For a crane to lift the beam shown to the right, the beam and the two support cables must form an…

A: Given that the distance between the cables along the beam is 18 ft and the height h is 8 ft. The…

Q: The pitch of a roof is the ratio of the rise to the half-span. If a roof has a rise of 5 feet and a…

A: Given that rise is 5 feet and span is 50 feet .

Q: What is the ratio of the volume of a cone to the volume of a cylinder, if both have a radius of 8…

A:

Q: Find the scale factor and the ratio of perimeters for each pair of similar figures. 4. two regular…

A:

Q: An athletic field is a 40 yd​-by-80 yd ​rectangle, with a semicircle at each of the short sides. A…

A:

Q: arry and Gary are trying to solve for the height of the oblique regular pentagonal prism below. What…

A:

Q: A computer monitor is 20 inches wide. The aspect ratio, which is the ratio of the width of the…

A: width = 20 inch width/height = 16:9 20*9/16 = height 45/4 = height rectangle screen  diagonal = 202…

Q: The pitch of a roof is the ratio of the rise to the half-span. If a roof has a rise of 32 feet and a…

A: Given: A roof has a rise of 32 feet and a span of 40 feet.

Q: From the similar triangles in the diagram, write a proportion using the ratio BC DC В A C А. ВС АВ…

A:

Q: A silo consists of a right circular cylinder surmounted by a hemisphere. Find the most economical…

A: The question is to find the proportions of the silo such that the total cost for making the silo is…

Q: The areas of two similar triangles are equal to 25 cm2 and 81 cm2. Find the ratio of a pair of…

A:

Q: What would be the best (most specific) name for the shape that has the following ratios for its…

A: Given : The ratio of sides of a triangle is 3:4:3

Q: A rectangular open tank has a total surface of 720 square cm. If the ratio of the length, width and…

A:

Q: The exterior dimensions of a freezer are 48 inches by 36 inches by 24 inches, and it is advertised…

A: Given :   The exterior dimensions of a freezer are 48 inches by 36 inches by 24 inches, and it is…

Q: The scale on a map indicates that 1 centimeter on the map corresponds to an actual distance of 30…

A: Solution : 1cm=30km  .. 15.6cm=x km  say ... 2from the equation 121cm5.6cm=30kmx km5.6cm1cm=x km30…

Q: Mr. Malone plans to construct a walkway through his rectangular garden, as shown in the drawing. -11…

A: Rectangle is a plane figure with four straight sides and four right angles. It's two sides meet at…

Q: For the pair of similar figures, give the ratios of the perimeter & area of the first figure to the…

A: Answer

Q: You and your friends order an extra large pizza, which has a diameter of 24 in. If you eat a 117…

A: SOME FORMULAS: 1.) Area of the circle = πR2 , where R is an radius of the circle. 2.)Area of the…

Q: The primary bedroom is 5 m by 4 m with a height of 2.5 m. Given that paint costs $1.39 per square…

A:

Q: 5. An 80-ft flagpole has upper and lower diameters of 4 and 16 in., respectively. Find the cost of

A: 4. Given that, R=Radius of sphere, slant height of cone =12 inch l= altitude =38 inch Let r be the…

Q: If carpeting costs $32.95 per square yard and is available in WHOLE SQUARE YARDS ONLY, find the cost…

A:

Q: In a pair of similar triangles, the lengths of corresponding sides are in proportion.

A:

Q: The composite figure below contains a rectangle, an isosceles trapezoid, and two equal parts of a…

A: Area of trapezoid = Sum of parallel sides2× height Area of rectangle = Base x Height Area of circle…

Q: A living room is 7.2 m long and 4.5 m wide. What size would it be on a plan drawn to a scale of…

A: This is a problem of counting.

Q: You reduce a sphere in surface area to make a new sphere that is equal to 676Tt cm2. If the ratio of…

A: Here we use the formula of surface area of sphere =

Q: Consider the parallelogram shown below whose area is 40 square centimeters and height is 8 c…

A:

Q: If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a2:b2,…

A: Given two similar solids have a scale factor of a:b, so it may be cube , sphere , cone what ever.…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.