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romanna [79]
3 years ago
9

three terms of an arithmetic sequence are shown. f(1)=3, f(3)=6, f(7)=12 what recursive formula could define the sequence ? A. f

(n+1)=2f(n) B. f(n+1)=f(n)+3 C. f(n+1)=f(n)+1.5 D. F(n+1)=0.5f(n)
Mathematics
1 answer:
WITCHER [35]3 years ago
8 0
an\ arithmetic\ sequence:\\\\ d\ \ \rightarrow\ \ the\ difference\\\\f(n)=f(1)+(n-1)\cdot d\\\\f(n+1)=f(1)+n\cdot d\\\\f(n+1)-f(n)=f(1)+n\cdot d-[f(1)+n\cdot d- d]=\\\\=f(1)+nd-f(1) -nd+d=d\\\\\Rightarrow\ \ \ f(n+1)=f(n)+d

f(1)=3\ \ \ and\ \ \ f(3)=6\\\\f(3)=f(1)+(3-1)\cdot d\ \ \ \Rightarrow\ \ \ 6=3+2d\\\\ \ \ \Rightarrow\ \ \ 2d=3\ \ \ \Rightarrow\ \ \ d=1.5\\\\ f(n+1)=f(n)+d\ \ \ \Rightarrow\ \ \ f(n+1)=f(n)+1.5\\\\\\Ans.\ \ \ f(1)=3\ \ \ and\ \ \ f(n+1)=f(n)+1.5
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a small plane lands at a point 324 miles east and 92 miles north of the point at which it took off. Find the distance the plane
Setler79 [48]

Answer: 336.80 miles, 15.85^{\circ} North of east

Step-by-step explanation:

Given

Plane lands at a point 324 miles east and 92 miles north

Distance is given by using Pythagoras theorem

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Direction is given by using figure i.e.

\Rightarrow \tan \theta=\dfrac{92}{324}\\\\\Rightarrow \tan \theta=0.2839\\\\\Rightarrow \theta=15.85^{\circ}

Direction is 15.85^{\circ} North of east

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2 years ago
Kate bought a T-shirt for $12.95 and a pair of shorts for $10.95. She paid 6.25% in tax. What is her total amount that she paid?
sergeinik [125]

Kate paid $25.39 for her purchases.

Kate will receive $24.61 in change.

Step-by-step explanation:

Given,

Cost of t-shirt = $12.95

Cost of pair of shorts = $10.95

Total = cost of t-shirt + cost of pair of shorts

Total = 12.95 + 10.95 = $23.90

Sales tax = 6.25% of total amount

Amount of sales tax = \frac{6.25}{100}*23.90=\frac{149.375}{100}

Amount of sales tax= $1.49

Total amount with sales tax = 23.90 + 1.49 = $25.39

Kate paid $25.39 for her purchases.

Amount paid = $50

Change received = Amount paid - Bill amount

Change received = 50 - 25.39 = $24.61

Kate will receive $24.61 in change.

Keywords: sales tax, addition

Learn more about addition at:

  • brainly.com/question/11584312
  • brainly.com/question/116059

#LearnwithBrainly

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Step-by-step explanation:

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Karolina [17]

Answer:

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Step-by-step explanation:

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Wilma can mow a lawn in 90 minutes. Bullwinkle can mow the same lawn in 60 minutes. How long does it take for both Wilma and Bul
boyakko [2]

Answer:

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