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zepelin [54]
3 years ago
5

The length of a rectangle is 3 less than twice the width. The perimeter is at least 210 cm. Find the smallest dimension of the r

ectangle.

Mathematics
2 answers:
SpyIntel [72]3 years ago
5 0

check the picture below

kotykmax [81]3 years ago
5 0

Answer:

w >= 36

L >= 69

See the image below...

Step-by-step explanation:

L = 2w - 3

P >= 210 cm  

P = 2L + 2w, then

2L + 2w >= 210  

Since L = 2w - 3, we have

2(2w - 3) + 2w >= 210  

Solving left side of the inequality,

4w - 6 + 2w >= 210  

6w - 6 >= 210

Adding + 6 in both sides,

6w - 6 + 6 >= 210 + 6

6w >= 216

we isolate w, dividing by 6 both sides,

6w / 6 >= 216 / 6

<h2>w >= 36</h2>

L >= 2w - 3  

L >= 2(36) - 3  

L >= 72 - 3  

<h2>L >= 69</h2>

Demonstrating,  

P >= 2L + 2w

P >= 2(69) + 2(36)

P >= 138 + 72

P >= 210

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Answer:

Part A

f(n)=52-12(n-1)

f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

Part B

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Part C

1/4,3/4,5/4,7/4,9/4

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Part D:

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Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12

<u>Explicit Formula</u>

To write an explicit formula is to write it as function.

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To write it as recursive formula, is to write it as recurrence given to some restrictions:

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Part B

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Part C

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Arithmetic Sequence, difference

d=\frac{2}{4}

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<u>Recursive Formula</u>

g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.

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h(n)=1.1+0.4(n-1)\\

<u>Recursive Formula</u>

h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.

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