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What would the ratio of a two rectangles be if one rectangles width is 24Cm and length 30Cm the other rectangle is width of 36 Cm length of 42 Cm?
These are not similar rectangles so there is no obvious candidate for the ratio. Is it ratio of lengths (sides, perimeter, diameter), or ratio of area?
Can someone explain Newton's Lemma 2 and 3 from Book I Section 1 of Principia Mathematica in English?
Lemma 2 says that if the curved area is approximated by inscribed and also by exscribed rectangles, where all rectanlges are of equal width, then the ratio of the exscribed areas summed up, to the curved area will be 1 as the number of rectangles tends to infinity. Also, the ratio of the sum of the area of the inscribed rectangles to the curved area to the curved area will be equal to 1 as the number of rectangles tends to infinity. In less technical language, the rectangles approximate the area under the curve, and as we use more and more (and thus thinner and thinner) rectangles, the approximation will get better and better; in fact we can make it as accurate as we want to. Lemma 3 says the same as the above, but drops the requirement that the rectangles all be of equal width.
The length of rectangle A is 24 cm and the length of rectangle B is 96 cm The two rectangles are similar Find the ratio of the area of B to the area of A?
8:32
Is the area the same on all rectangles with the same perimeter?
No, it is not. I'll give you two examples of a rectangle with a perimeter of 1. The first rectangle has dimensions of 1/4x1/4. The area is 1/16. The second rectangle has dimensions of 3/8x1/8. The area is 3/64. You can clearly see that these two rectangles have the same perimeter, yet the area is different.
How do you find the are of a cross?
You could consider the cross as two intersecting rectangles. Calculate the area of both rectangles and the area of the intersection (overlap). Then area of cross = sum of the areas of the rectangles minus the area of the overlap.
What would the ratio of a two rectangles be if one rectangles width is 24Cm and length 30Cm the other rectangle is width of 36 Cm length of 42 Cm?
These are not similar rectangles so there is no obvious candidate for the ratio. Is it ratio of lengths (sides, perimeter, diameter), or ratio of area?
What is its the width of 2 rectangles that the areas are 15cm2 and 60cm2 the lengt of the first rectangle is 5cm?
I can give the width of one of the rectangles. The first rectangle of area 15 cm2 and length of 5 cm has width of 3 cm. It is impossible to know the width of the other rectangle of area 60 cm2. However, if you had said that the two rectangles were similar, then the dimensions of the second rectangle would be 10 cm X 6 cm. But you didn't say that the two rectangles were similar; so there are infinite possibilities of what the dimensions of the second rectangle might be.
Can someone explain Newton's Lemma 2 and 3 from Book I Section 1 of Principia Mathematica in English?
Lemma 2 says that if the curved area is approximated by inscribed and also by exscribed rectangles, where all rectanlges are of equal width, then the ratio of the exscribed areas summed up, to the curved area will be 1 as the number of rectangles tends to infinity. Also, the ratio of the sum of the area of the inscribed rectangles to the curved area to the curved area will be equal to 1 as the number of rectangles tends to infinity. In less technical language, the rectangles approximate the area under the curve, and as we use more and more (and thus thinner and thinner) rectangles, the approximation will get better and better; in fact we can make it as accurate as we want to. Lemma 3 says the same as the above, but drops the requirement that the rectangles all be of equal width.
The length of rectangle A is 24 cm and the length of rectangle B is 96 cm The two rectangles are similar Find the ratio of the area of B to the area of A?
8:32
Is the area the same on all rectangles with the same perimeter?
No, it is not. I'll give you two examples of a rectangle with a perimeter of 1. The first rectangle has dimensions of 1/4x1/4. The area is 1/16. The second rectangle has dimensions of 3/8x1/8. The area is 3/64. You can clearly see that these two rectangles have the same perimeter, yet the area is different.
How do you calculate surface area to volume ratio?
You measure or calculate the surface area; you measure or calculate the volume and then you divide the first by the second. The surface areas and volumes will, obviously, depend on the shape.
How do you find the are of a cross?
You could consider the cross as two intersecting rectangles. Calculate the area of both rectangles and the area of the intersection (overlap). Then area of cross = sum of the areas of the rectangles minus the area of the overlap.
What is the area of a L shaped room?
An L-shaped area can be divided into two rectangles. The total area is the sum of the areas of the two rectangles.
How many rectangles can be made with an area of 10 square inches?
The answer is Infinite...The rectangles can have an infinitely small area and therefore, without a minimum value to the area of the rectangles, there will be an uncountable amount (infinite) to be able to fit into that 10 sq.in.
What is the difference between inscribed and circumscribed in integration?
When rectangles are inscribed, they lie entirely inside the area you're calculating. They never cross over the curve that bounds the area. Circumscribed rectangles cross over the curve and lie partially outside of the area. Circumscribed rectangles always yield a larger area than inscribed rectangles.
How many rectangles have the same area and perimeter of 18?
thare is only 1 differint rectangles
How are rectangles related to the distributive property?
Rectangles are related to the distributive property because you can divide a rectangle into smaller rectangles. The sum of the areas of the smaller rectangles will equal the area of the larger rectangle.
