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alina1380 [7]
3 years ago
13

Write a recursive formula and an explicit formula for the following arithmetic sequence.

Mathematics
1 answer:
Serjik [45]3 years ago
3 0

Answer:

Explicit: a₁=61    aₙ=a₁ -3ₓ(n-1)

Recursive: a₁=61    aₙ=aₙ₋₁ - 3

Step-by-step explanation:

Explicit: a₁=61    aₙ=a₁ -3ₓ(n-1)

Recursive: a₁=61    aₙ=aₙ₋₁ - 3

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After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F.
laila [671]

Answer:

  • Question 1: 0.081 min⁻¹
  • Question 2: 168ºF

Explanation:

The missing equation is:

             T=T_a+(T_0-T_a)e^{-kt}

You are given:

  • Ta = the temperature surrounding the object = 73ºF
  • T₀ = the initial temperature of the object = 204ºF
  • t = 2.5 min
  • T after 2.5 min = 180ºF

Question 1: Find the the value of k.

Substitute the data into the equation and solve for k:

          180\º=73\º+(204\º-73\º)e^{-k\cdot 2.5min}\\ \\ 107\º=131\ºe^{-k\cdot 2.5min}\\\\-k\cdot 2.5min=\ln (107/131)\\\\k=0.081min^{-1}

Question 2: Find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Subsititute into the formula and compute:

            T=73\ºF+(204\ºF-73\ºF)e^{-0.081min^{-1}\times 4min}\\ \\ T=73\ºF+(131\ºF)(0.72325024)\\\\T=168\ºF

4 0
4 years ago
When finding 433 - 249 using place value. What do you subtract first?
Ksenya-84 [330]
You subtract the ones place, then the tens, and lastly the hundreds place. Your answer will be 184 if you are looking for the answer as well.
5 0
3 years ago
A. 2x+5=23<br> B. x+2+5=23<br> C. x+x+5=23<br> D. 5x+2=23
storchak [24]

Answer:

b

Step-by-step explanation:

lucky guess

6 0
3 years ago
Read 2 more answers
1. A baseball player got a hit 19 times in his last 64 times at bat.
fiasKO [112]

A) Probability =0.297

B)In 200 times he can hit 59 times !

<u>Step-by-step explanation:</u>

Here we have , A baseball player got a hit 19 times in his last 64 times at bat. We need to find the following :

a. What is the experimental probability that the player gets a hit in an at bat?

According to question ,

Favorable outcomes = 19

Total outcomes = 64

Probability = (Favorable outcomes)/(Total outcomes) i.e.

⇒ Probability = \frac{19}{64}

⇒ Probability =0.297

b. If the player comes up to bat 200 times in a season, about how many hits is he likely to get?​

According to question , In 64 times he hit 19 times . In 1 time there's probability to hit 0.297 times! So ,In 200 times he can hit :

⇒ Hit =0.297(200)

⇒ Hit = 59.36

Therefore , In 200 times he can hit 59 times !

4 0
3 years ago
Gertrude cut a 76-meter rope into two pieces. the long piece was 12 meters longer than the short piece. how long was the short p
7nadin3 [17]
The shorter piece was 32 meters.
7 0
3 years ago
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