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decrease in temperature if you hike up the mountain 3000 meters is ° .
<u>Step-by-step explanation:</u>
Here we have , Hiking up a mountain, you notice that the air temperature drops 10 degrees every 1000 meters increase in elevation . We need to find Write a multiplication expression to represent the decrease in temperature if you hike up the mountain 3000 meters. Let's find out:
For every 1000 meters rise in elevation , there is decrease in 10° of temperature . So , For rise in n meters in elevation , there is decrease in n×10° of temperature i.e
Decrease in temperature = (n/1000)×(-10) i.e.
⇒ (n/1000)×(-10)
⇒
At n = 3000 meters:
⇒
⇒
⇒ °
Therefore , decrease in temperature if you hike up the mountain 3000 meters is ° .
Answer:
a. f(n) = n(n+1)/2
b. 351
c. 19
d. no; n would not be an integer for f(n) = 17.
Step-by-step explanation:
a. The terms are 1, 3, 6, 10, ...
Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.
When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.
For the polynomial ...
We can substitute values for n and f(n) to get 3 equations in 3 unknowns:
Solving these equations by your favorite method gives ...
(a, b, c) = (1/2, 1/2, 0)
That is, the function representing the relationship is ...
f(n) = n(n+1)/2 . . . . the function describing the relationship
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b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26
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c. The number of the term having 190 squares can be found by solving ...
n(n +1)/2 = 190
n(n +1) = 380 = 19(20)
The 19th term will have 190 squares.
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d. Terms 5 and 6 are 15 and 21.
17 is not the value of one of the terms in this sequence.