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mariarad [96]
3 years ago
10

The Martian monetary system uses colored beads instead of coins. A blue bead is worth 3 Martian credits, and a red bead is worth

7 Martian credits. Thus, three blue beads are worth 9 credits, and a blue and red bead together are worth 10 credits, but no combination of blue and red beads is worth 11 credits. Using Induction, prove that for all n ≥ 12, there is some combination of blue and red beads that is worth n credits. Clearly state the type of Induction you have used to prove the problem
Mathematics
1 answer:
GalinKa [24]3 years ago
5 0

Answer:

"a" is showing the number of blue beads

"b" represents the number of red beads in a combination

let "n" show the number of credits.

We get the following equation:

n = 3a + 7b.

Now, we want to prove that for all n ≥ 12, there is some combination of blue and red beads that is worth n credits, there are a, b in N such that:

n = 3a + 7b

Hence we will prove this by induction.

Base Cases: n = 12.

Applying the formula clearly 12 = 3*4+7*0.

n = 13

Applying the formula clearly 13 = 3*2+7*1.

n = 14.

Applying the formula clearly 14 = 3*0+7*2.

<u>Induction Step:</u> Assume that for all 12<=k<n there are x, y in N such that

k = 3x + 7y. We will now prove that there are a, b in N such that n = 3a + 7b.

By the induction hypothesis we know that there are x, y in N such that n-3 = 3x + 7y.

Hence n = n - 3 + 3 = 3x + 7y + 3 = 3(x + 1) + 7y, so choosing a = x + 1

and b = y we see that n = 3a + 7b.

Therefore by induction, the claim is true for all n ≥ 12

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vodomira [7]

Answer:

x= 5

Step-by-step explanation:

We are given;

  • Base of the triangle as x
  • Length of the leg is 4x-5
  • An isosceles triangle has two equal legs and a base.
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To get the perimeter of a triangle we add the lengths of all sides of the triangle.

Therefore;

x + 4x-5 + 4x-5  = 35

9x - 10 = 35

9x = 45

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Thus, the value of x is 5

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Answer:

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Step-by-step explanation:

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3 years ago
Diameter = 20.00, height = 10.00 what's the volume of cylinder ?
yanalaym [24]
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4 0
3 years ago
Paddy and Anna each invest $2000 for 5 years.
Serga [27]

Answer: r= 1.22

Step-by-step explanation:

Formula for amount with simple interest = P(1+rt)

, where

P= principal value , r= rate of interest , t = time.

Given: P=  $2000, t= 5 years, r= 1.25% = 0.0125

A=2000(1+0.0125\times5)\\\\=2000(1.0625)=2125

Formula to compute compound amount : P(1+r)^t

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When both have same worth then

2000(1+r)^5=2125\\\\\\ (1+r)^5=\dfrac{2125}{2000}\\\\\\ (1+r)^5=1.0625

taking log on both sides , we get

5\ln (1+r)=\ln 1.0625\\\\\\ 5\ln (1+r)=0.0606246\\\\\\ \ln (1+r)=0.012125\\\\\\ 1+r=e^{0.005266}\\\\\\ 1+r=1.0122\\\\ r=0.0122\\\\ \\ r=1.22\%

Hence, Value of r= 1.22

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3 years ago
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otez555 [7]

Answer:

The slope should be m= 4/7

Step-by-step explanation:

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2 years ago
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