In constructing a golden section, if b =5, what is a?  Give answer in three or four significant figures.?
352741
The golden section phi= 0.5 + 0.5 root 5 = 1.619...\n\nThe question is not very precise, but if you want phi=a/b,\nthen a=8.095...
785535
Multiply both sides by a. Then divide both sides by 9. You should get a=5.
81890
it's not factored completely if you leave it as a^2-25 so the proper answer is 5(a-5)(a+5)
201205
One such nuber is phi, the golden ratio, equal to (1+sqrt(5))/2.\nIt is the most pleasing ratio for the human eye and also when you take Fibonacci's series, going: 1, 1, 2, 3, 5, 8...\ngenerally f(n)=f(n-1)+f(n-2) you will see that it often appears in the numbers of petals on flowers, seend in rows on a sunflower and others. for a large n, f(n)/f(n-1) --->phi
754998
a 4\nb 5\nc 3\nd 2\ne 3\nf 4\ng 3\nh 5\ni 5\nj 5\nk 3\nl 5\nm 5\nn 5
1149183
Good question.   I think 3 or 4.
143210
fancy description of a rectangle.\n\nIf it had four congruent sides, it would be a square.
344212
At first glance, if the top left times the bottom right is A, and the other cross is B, then A > B, means the right fraction was larger.\n\nI couldn't come up with a quick counter.  Maybe you can.
830486
..... ^\n... / .. &#92;\n.. / A1 &#92;\n../-------&#92;\n./ .. A2.. &#92;\n/______&#92;\n\nIs this what you mean (where A1/A2 = 1/φ; and φ = golden ratio = ½(1 + √5))?\n\nIt is my understanding.\n\nSo the two triangles are similar \n\nArea = ½ base * height\n\nA1 / A2 = 1/φ\nThus A1/ (A1 + A2) = 1/(1 + φ)\nie A1 /A = 1/(1 + φ)\n\nThus corresponding sides are in the ratio 1/√(1 + φ) \nNow √(1 + φ) = φ \n(since φ - 1 = 1/φ then φ² - φ = 1 so φ² = φ + 1)\nSo the top base = 1/φ * 8 inches ≈ 4.94 inches\nand the top side walls = 1/2 * 8/φ * tan 52°\n≈ 3.16 inches\nThus the bottom side walls are 8 - 1/2 * 8/φ * tan 52°≈ 4.84 inches
975944
5 would be (a)\n6 would be (b)\n7 would be (c)\n8 would be (b)
413999
In step 4 you divided by (a-b) which is zero.\n\nIf you could do this you could just say that 5 times 0 = 8 times 0 means that 5 = 8, by dividing both sides by 0 and canceling it.
969791
For question 1, think about the fraction. It's 9/24. A pie chart shows a fraction visually. Imagine a pie cut into 24 identical pieces. One piece for each student. Now color 9 of the pieces (all together) a different color from the rest of the pie to represent the newspaper only pupils.  Now measure the angle formed by the section of newspaper only). What is the angle of a sector of a circle that is 9/24 of the circle?\n\nFor question 2, a mixed number means there is a whole number and a fraction. What is .25?? It's 25 percent or one quarter of a dollar... so the fraction is 1/4. 2.25 is the same as 2 1/4... those digits add up to 7.
172593
#3 is 4?\nI mean it might be 1??
983331
a.\n\n   5 =            4 16/16\n - 2 5/16\n________________\n                   2  11/16
2009
It is the Fibonacci sequence, called the "golden ratio" - it is a fractal sequence found in nature, everywhere - the arrangements of flower petals, pine cones, the arrangements of seeds in a fruit. It is an unsolved mystery of science, a sort of design pattern for life.
810871
the golden ratio = 1.61803399\n\nHere is a 'Fibonacci series'.\n\n0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ..\n\nIf we take the ratio of two successive numbers in this series and divide each by the number before it, we will find the following series of numbers.\n\n1/1 = 1\n2/1 = 2\n3/2 = 1.5\n5/3 = 1.6666...\n8/5 = 1.6\n13/8 = 1.625\n21/13 = 1.61538...\n34/21 = 1.61904...\n\nThe ratio seems to be settling down to a particular value, which we call the golden ratio(Phi=1.618..).\n\n\n\nGolden Rectangle is a rectangle with proportions that are two consecutive numbers from the Fibonacci sequence.\n\nThe Golden Rectangle has been said to be one of the most visually satisfying of all\ngeometric forms. We can find many examples in art masterpieces such as in edifices of ancient Greece.\n\n\nit's even important in Mona Lisa! InWe can draw a rectangle whose base extends from the woman's right wrist to her left elbow and extend the rectangle vertically until it reaches the very top of her head. Then we will have a golden rectangle.\nAlso, if we draw squares inside this Golden Rectangle, we will discover that the edges of these new squares come to all the important focal points of the woman: her chin, her eye, her nose, and the upturned corner of her mysterious mouth.\nIt is believed that Leonardo, as a mathematician tried to incorporate of mathematics into art. This painting seems to be made purposefully line up with golden rectangle.\n\n\ni hope this has helped!\n\n~MathWhiz~
389991
height times the base area. divided by three.