Mathematics, 12.12.2019 05:31 ryliefitz32

The simple town bakery has a cake that has a length twice as long as the width and a height 1 inch less than the width. if the volume is 1800 in cubed, what should the dimensions of the cake be?

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Answer from: isabellam646

Length = 20 inches

Width = 10 inches

Height = 9 inches

Step-by-step explanation:

Assume the width to be equal to 'w' inches.

It is given that the length of the cake to be twice of width. So,

Length of cake = 2 × (width of cake) = 2w

It is also given that the height of cake to be 1 inch less than the width of cake. So,

Height of cake = (width of cake) - 1 = w-1

Volume of cake = (Length) × (Breadth) × (Height)

Volume of cake is given to be as 1800 inch cube.

Therefore, 1800 = (2w) × (w) × (w-1)

900 = (w) × (w) × (w-1)

$900=\textrm{w}^{3}-\textrm{w}^{2}$

$\textrm{w}^{3}-\textrm{w}^{2}-900=0$

To solve cubic equation there is only one way is to get the first root* by hit and trial. (you will hit the bulls-eye only by practice)

Let w=10 So,

$(10)^{3}-(10)^{2}-900=0\\1000-100-900=0\\1000-1000=0\\0=0$

So the solution is w=10.

Therefore the width = w = 10 inches

Length = 2w = 20 inches

Height = w-1 = 9 inches

(*As you know that a cubic equation have three roots. In them there are two cases possible: one root is real and rest two imaginary or all the three are real. Here in this case only one root is real and other two are imaginary.In this question the factorized form of this cubic equation is $(w-10)(w^{2}+9w+90)=0$ . By this factorized form you can conclude that one root is 10 and the roots of the quadratic equation are imaginary (as $D=9^{2}-4\times1\times90$ ). In this only real root can become solution as the solution gives width which is a real quantity. So, the only real solution is w=10 )

Answer from: Quest

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y

Answer from: Quest

60.9774

step-by-step explanation:

because when you add 47.6 plus 7.32 equals 54.92

and when you add .0574 + 6= 6.0574

and when you add 54.92 and 6.0574 you get the answer of 60.9774.

plzz mark brainlest last one got deleted. cause i didn't explain it but i did but i understand what the mod meant

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