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Anestetic [448]
3 years ago
10

Please help. I only need parts a and b.

Mathematics
1 answer:
Alex3 years ago
7 0

Answer:

oI know that for a they are pretty much the same shape im not sure how else to desribe it sorry

Step-by-step explanation:

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Work out the formula of the nth term in the following quadratic sequence:<br> 19, 15, 9, 1...
Butoxors [25]

In a quadratic sequence we'll get a linear first difference and a constant second difference.  Let's verify that.

n          1   2   3   4

f(n)       19  15  9   1

1st diff   -4  -6  -8

2nd diff     2   2

We see that we got a constant second difference.  We could just extend that and work back up to get more values.

n          1   2   3   4       5    6      7

f(n)       19  15  9   1      -9   -21   -35

1st diff   -4  -6  -8   -10  -12   -14

2nd diff     2   2    2     2    2

That's just an aside; we're after the general formula.  We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an²  + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c =  9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly.  Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

6 0
3 years ago
12. The Appalachian Trail is about 2,175 miles long.
spayn [35]
a. (2175 mi)/(18 mi/day) = 120.83... day ≈ 121 days

b.
120.83.../4 = 30.2083...
   Joelle will hike 30 full days and one partial day.
6 0
3 years ago
What is the median of this set of data?
Vladimir [108]

Answer:

The median would be 103.

8 0
3 years ago
Read 2 more answers
Britney has 50 beds 70% of the beds are gold how many beds are gold
belka [17]

Answer:

35 beds

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the conversion?
Gelneren [198K]

Answer:

  see below

Step-by-step explanation:

The conversion factor in the box is the product ...

  \dfrac{1\,\text{kPa}}{1000\,\text{Pa}}\cdot\left(\dfrac{1\,\text{m}}{100\,\text{cm}}\right)^3=10^{-9}\,\dfrac{\text{kPa m}^3}{\text{Pa cm}^3}

_____

The purpose of a conversion factor is to multiply by 1 in the form of a ratio that changes the units. We know that 1000 Pa = 1 kPa, so the ratio (1 kPa)/(1000 Pa) is the ratio of two equal quantities. It has the value 1 and will change units from Pa to kPa.

Likewise, 100 cm = 1 m, so (1 m)/(100 cm) will change the units from cm to m. However the given expression uses cm³, so we need to multiply by the conversion factor 3 times. That factor is ((1 m)/(100 cm))³ = (1 m³)/(10⁶ cm³).

To choose the appropriate conversion factor, look at the units you have (Pa, cm) and the units you want (kPa, m). Find the relationship these have to each other, and write the ratio so that it will cancel the units you have and leave the units you want.

When SI units are involved the prefixes help you out. k = kilo = 1000; c = centi = 1/100. It is worthwhile to get to know them.

8 0
3 years ago
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