Sue has baked 3 different types of circular cake, all measuring 8 inches across. There are equal numbers of coffee cakes and lem
on cakes, but just one carrot cake. She wants to arrange them on a rectangular table with area 576 square inches. Find the dimensions of the table. How many cakes has Sue baked? Sue would like to arrange her cakes to make an attractive display. She is a stickler for detail, so she won’t place lemon cakes directly next to the carrot cake; nor may cakes of the same flavour be next to each other. Show how she can achieve this
1) suppose for purposes of calculation that the cake is inscribed in a square of 8 by 8 the area of 1 cake=8*8=64 in² the rectangular table area=576 in²-----> I assume square table 24 in x 24 in 576/64= 9----------- > Sue has baked 9 cakes if just 1 carrot cake then (9-1)=8 ----------> coffee cakes and lemon cakes we know that equal numbers of coffee cakes and lemon cakes therefore coffee cakes=8/2=4 lemon cakes=4 carrot cake=1
the answer part 1) is the dimensions of the table are 24 in x 24 in
the answer part 2) is Sue has baked 9 cakes coffee cakes=4 lemon cakes=4 carrot cake=1
part 3) distribution of the cakes in the table 24 in x 24 in
answer
let Z------->carrot cake C------->coffee cakes L------->lemon cakes
![\sqrt[4][a^5 b^3]](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%5Ba%5E5%20b%5E3%5D)
) is the exponent.![\sqrt[][text]) symbol.\\a fourth root is a factor that was multiplied four times. ex: 2*2*2*2=16. the fourth root of 16 is two. \\when you do square roots, you take the number representing the factor out of the radical. anything else that is not a square root stays under. ex: \\([tex]\sqrt[9][text])\\([tex]\sqrt[3*3*3][text]) there is one set of two 3's so\\([tex]3\sqrt[3][text])\\with a fourth root, you look for groups of four. the symbol of that group is placed outside the radical. anything else stays in.\\ ([tex]\sqrt[4][a^5 b^3]](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%5Btext%5D%29%20symbol.%5C%5Ca%20fourth%20root%20is%20a%20factor%20that%20was%20multiplied%20four%20times.%20ex%3A%202%2A2%2A2%2A2%3D16.%20the%20fourth%20root%20of%2016%20is%20two.%20%5C%5Cwhen%20you%20do%20square%20roots%2C%20you%20take%20the%20number%20representing%20the%20factor%20out%20of%20the%20radical.%20anything%20else%20that%20is%20not%20a%20square%20root%20stays%20under.%20ex%3A%20%5C%5C%28%5Btex%5D%5Csqrt%5B9%5D%5Btext%5D%29%5C%5C%28%5Btex%5D%5Csqrt%5B3%2A3%2A3%5D%5Btext%5D%29%20there%20is%20one%20set%20of%20two%203%27s%20so%5C%5C%28%5Btex%5D3%5Csqrt%5B3%5D%5Btext%5D%29%5C%5Cwith%20a%20fourth%20root%2C%20you%20look%20for%20groups%20of%20four.%20the%20symbol%20of%20that%20group%20is%20placed%20outside%20the%20radical.%20anything%20else%20stays%20in.%5C%5C%20%28%5Btex%5D%5Csqrt%5B4%5D%5Ba%5E5%20b%5E3%5D)
)![\sqrt[4][a*a*a*a*a*b*b*b]](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%5Ba%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab%5D)
) there is one group of 4 a's so![a\sqrt[4][a* b^3]](https://tex.z-dn.net/?f=a%5Csqrt%5B4%5D%5Ba%2A%20b%5E3%5D)
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