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Iteru [2.4K]
3 years ago
15

A 4ft piece of pipe needs to be divided into pieces that are 2/3ft long. How many pieces are made? How many remaining?

Mathematics
1 answer:
Katen [24]3 years ago
3 0
4ft divided by 2/3ft

4/1 divided by 2/3 

4/1 times 3/2 is 12/2 or 6 pieces, 0 remaining.
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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
The difference between three times a number and seven is twenty. What is the number?
Mama L [17]

Answer:

9

Step-by-step explanation:

(9*3) = 27 which is 20 more than 7

6 0
3 years ago
Can i have help with this please
gavmur [86]

Answer:

Your answer is 2c^{2}

4 0
2 years ago
Read 2 more answers
Jane Andre and Maria pick apples Andre pics three times as many pounds as Maria Jane pics to charge as many pounds as Andre the
Marta_Voda [28]
840 ÷ 3 = 280 

Andre picked 280 pounds of apples. 

Hope this helps and have a great day! :D 
7 0
3 years ago
a builder could get 6 sheets of sheetrock for $9 if he bought 12 sheets how much money would he have spent
SashulF [63]
He spent $18.
6=$9
12=$18

8 0
3 years ago
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