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Rama09 [41]
3 years ago
10

Kam can make 72 cookies in 3 hours at his house, while Madison can make 120 cookies in 4 hours at her house. How long would it t

ake for them to make a total of 200 cookies together
Mathematics
1 answer:
DIA [1.3K]3 years ago
5 0

Answer:

The answer to your question is: 3.7 hours

Step-by-step explanation:

Kam can make 72 cookies/ 3 hours

Madison can make 120 cookies/4 hours

Time to make 200 cookies together = ?

First, calculate the number of cookies make per hour

Kam            72 ---------------- 3

                   x   ----------------  1 hour

  x = 72/3 = 24 cookies/h

Madison

             120 -------------   4 hours

               x ---------------      1 hour

x = 120 / 4 = 30 cookies

Now we write and equation where "t" will be time

         24t + 30t = 200      and solve it

         54t = 200

        t = 200/54

        t = 3.7 hours

 

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Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in t
nataly862011 [7]

Let (<em>x</em>, <em>y</em>, <em>z</em>) be a point on the plane in the first octant. The box formed by this point has volume <em>xyz</em>, and you want to maximize this subject to the equation of the plane.

Use the method of Lagrange multipliers: the Lagrangian is

<em>L</em>(<em>x</em>, <em>y</em>, <em>z</em>) = <em>xyz</em> - <em>λ</em> (<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6)

Find its critical points:

∂<em>L</em>/∂<em>x</em> = <em>yz</em> - <em>λ</em> = 0

∂<em>L</em>/∂<em>y</em> = <em>xz</em> - 2<em>λ</em> = 0

∂<em>L</em>/∂<em>z</em> = <em>xy</em> - 3<em>λ</em> = 0

∂<em>L</em>/∂<em>λ</em> = -(<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6) = 0

Solving the first three equations for <em>λ</em> gives

<em>λ</em> = <em>yz</em> = <em>xz</em>/2 = <em>xy</em>/3

Solve these equations for <em>y</em> and <em>z</em> :

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• <em>yz</em> = <em>xy</em>/3   =>   <em>z</em> = <em>x</em>/3   =>   3<em>z</em> = <em>x</em>

Substitute these solutions into the last equation and solve for <em>x</em>, then again for <em>y</em> and <em>z</em> :

<em>x</em> + 2<em>y</em> + 3<em>z</em> - 6 = 3<em>x</em> - 6 = 0   =>   3<em>x</em> = 6   =>   <em>x</em> = 2, <em>y</em> = 1, <em>z</em> = 2/3

At this critical point, the maximum volume is

<em>xyz</em> = 2*1*2/3 = 4/3

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The mass of mercury is 330,200,000,000,000,000,000,000 kilograms. how can this number be written in scientific notation?
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