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UNO [17]
3 years ago
7

At the deli, two smoked turkey subs and five veggie subs cost $29. Four smoked turkey subs and three veggie subs cost $30. (A) C

reate a linear system to model the equations. (B) Solve the system to determine the cost of a smoked turkey sub and the cost of a veggie sub.

Mathematics
1 answer:
horsena [70]3 years ago
5 0
For this case, the first thing we must do is define variables.
 We have then:
 x: cost of smoked turkey
 y: cost of veggie subs
 By writing the system of equations we have:
 2x + 5y = 29

4x + 3y = 30
 Resolving the system graphically we have the solution is:
 x = 4.5

y = 4
 See attached image for the graphic solution: You must observe the point of intersection of the lines.
 Answer:
 
smoked turkey = 4.5 $
 
veggie sub = 4 $

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4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t
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First part of question:

Find the general term that represents the situation in terms of k.

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a_{n}=a_{1}r^{n-1}

a_{1} = the first term of the series

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a_{1} would represent the height at which the ball is first dropped. Therefore:

a_{1} = k

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

r=\frac{3}{4}

Our general term would be:

a_{n}=a_{1}r^{n-1}

a_{n}=k(\frac{3}{4}) ^{n-1}

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

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k = 235\ ft

n represents the number of times the ball bounces:

n = 6

Plugging this back into our general term of the geometric series:

a_{n}=k(\frac{3}{4}) ^{n-1}

a_{n}=235(\frac{3}{4}) ^{6-1}

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Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. ​

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

S_{n}=\frac{a_{1}(1-r^{n})}{1-r}

We already know these variables:

a_{1}= k = 235\ ft

r=\frac{3}{4}

n = 12

Therefore:

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }

S_{n}=(4)(235)(1-\frac{3}{4} ^{12})

S_{n}=910.22\ ft

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3 years ago
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