If you're a mathematician, you ask yourself: What's the largest sofa you could possibly fit around the corner?

It doesn't have to be a rectangular sofa either, it can be any shape. Here are the specifics: the whole problem is in two dimensions, the corner is a 90-degree angle, and the width of the corridor is 1.

All together, we know the sofa constant has to be between 2.2195 and 2.8284. The three letters correspond to the three sides of a right triangle. Just as there are some triangles where all three sides are whole numbers, there are also some boxes where the three sides and the spatial diagonal (A, B, C, and G) are whole numbers.

In a Pythagorean triangle, and all three sides are whole numbers. But there are also three more diagonals on the three surfaces (D, E, and F) and that raises an interesting question: can there be a box where all seven of these lengths are integers?

In Math-Only-Math you'll find abundant selection of all types of math questions for all the grades with the complete step-by-step solutions. So after completing the 1st week she will get $ (x 145). Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340. We know that, Interest = Principal × Rate × Time Interest = $ 160, Principal = $ 2500, Rate = r [we need to find the value of r], Time = 1 year. 160 = 2500r 160/2500 = 2500r/2500 [divide both sides by 2500] 0.064 = r r = 0.064 Change it to a percent by moving the decimal to the right two places r = 6.4 % Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year. Jones covered a distance of 50 miles on his first trip. So, times taken to covered a distance of 50 miles on his first trip = 50/x hr. Fahrenheit temperature F is a linear function of Celsius temperature C.

Parents and teachers can follow math-only-math to help their students to improve and polish their knowledge. Similarly after completing the 2nd week she will get $ (x 145) $ 145. Based on the cost, his profit one was 20% and his loss on the other was 20%. Income from $ 3500 at 4 % in one year = $ 3500 of 4 %. On a later trip he traveled 300 miles while going three times as fast. And times taken to covered a distance of 300 miles on his later trip = 300/3x hr. So we can clearly see that his new time compared with the old time was: twice as much. The ordered pair (0, 32) is an ordered pair of this function because 0°C is equivalent to 32°F, the freezing point of water. Write a formula that gives the length of x sports fields in feet.

Children can practice the worksheets of all the grades and on all the topics to increase their knowledge. = $ (x 145 145) = $ (x 290) So in this way end of every week her salary will increase by $ 145. The value of x x(x) = 2 2(2 × 2) = 2 2(4) = 2 8 = 10 Answer: (a) 3. On the sale of the pipes, he: (a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents 20 % profit on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Similarly, 20 % loss on $ 1.20 = $ 20/100 × 1.20 = $ 0.20 × 1.20 = $ 0.24 Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24. His new time compared with the old time was: (a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much Let speed of the 1st trip x miles / hr. The ordered pair (100, 212) is also an ordered pair of this function because 100°C is equivalent to 212° F, the boiling point of water. Then use this formula to determine the number of sports fields in 720 feet. A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes.

Since both profit and loss amount is same so, it’s broke even. The distance light travels in one year is approximately 5,870,000,000,000 miles. In order to have a yearly income of $ 500, he must invest the remainder at: (a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 % Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.

The goal is to find a box where A, and where all seven numbers are integers. Mathematicians have tried many different possibilities and have yet to find a single one that works.

But they also haven't been able to prove that such a box doesn't exist, so the hunt is on for a perfect cuboid. The loop doesn't have to be a circle, it can be any shape you want, but the beginning and the end have to meet and the loop can't cross itself.

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