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beks73 [17]
2 years ago
5

Dan is fourteen years older than Marge. Eight years ago, Dan was three times as old as Marge. Find their present age.

Mathematics
1 answer:
34kurt2 years ago
5 0

Answer:

<u>Marge's</u> present age = 14 ; <u>Dan's</u> present age = 29

Step-by-step explanation:

  • Present age

Let Marge's present age be = M

Dan's present age [D] : 14 years elder than Marge = M + 14

  • 8 years ago  

Marge Age = M - 8

Dan's Age = D - 8 = (M + 14) - 8 = M + 6  

{Given} : Dan's age = 3 times Marge's age

M + 6 = 3 (M - 8)

M + 6 = 3M - 24

6 + 24 = 3M - M

30 = 2M

M = 30/2

M = 15 [Marge's present age]

Dan's present age [D] = M + 14 = 29

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1 year ago
Use Lagrange multipliers to find three positive numbers whose sum is 210 and whose product is maximum. (Enter your answers as a
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Step-by-step explanation:

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Lets ( x, y, z ) be the three positive numbers

such that

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what is the maximum of xyz

take f(x,y,z) = xyz

Q(x,y,z) = 0

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consider the function

F(x,y,z) = f(x,y,z) + λQ(x,y,z)

F = xyz + λ(x+y+z-210)

dF/dx = 0 ⇒ yz + λ(1) = 0 ⇒ λ = -yz   ..............equ(1)

dF/dy = 0 ⇒ xz + λ(1) = 0 ⇒ λ = -xz.................equ(2)

dF/dz = 0 ⇒ xy + λ(1) = 0 ⇒ λ = -xy...............equ(3)

Now

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⇒ y = z = x

by substitution

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1 year ago
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Step-by-step explanation:

Given,

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Formula

Probability of an event = number of required outcomes ÷ the total number of outcomes.

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Now,

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Hence, the probability of the pointer lands on red(R) both spin = \frac{1}{36}

4 0
2 years ago
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