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Lelu [443]
3 years ago
6

PROBLEM 6

Mathematics
1 answer:
Inessa [10]3 years ago
8 0

Answer:

See below.

Step-by-step explanation:

The nth triangular number is Tn = n(n + 1)/2, the nth square number Qn = n^2 and the nth pentagonal number Pn = (3n^2 - n) / 2.

(a.  Q6 + P5 = 6^2 + (3(5)^2 - 5)/2

= 36 + 35 = 71.

3T5 + Q5 + 1 =   3* 5(5 + 1) / 2 + 5^2 + 1

= 90 / 2 + 26

= 71.

So  Q6 + P5 = 3T5 +Q5 +1.

(b) Qn+1 + Pn  = (n + 1)^2 + (3n^2 - n) / 2

=  n^2 + 2n + 1 + (3n^2 - n) / 2

= n^2 + 2n + 1  + 1.5n^2 - 0.5n

= 2.5n^2 + 1.5n + 1.

3Tn +Qn + 1 = 3n(n + 1) / 2  + n^2 + 1

=  3n^2 + 3n / 2 + n^2 + 1

= 1.5n^2 + 1.5n + n^2 + 1

= 2.5n^2 + 1.5n + 1.

Therefore they are equal for all positive n.

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Answer:

30 oranges

Step-by-step explanation:

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how many oranges did Julissa give out in all?

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= 6 × 5

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What is the answer is it A. or B. or C. ?
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If the radius of a half-circle is 11...
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By giving just the radius and asking for the arc length of that circle your answer will be without math is 22
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But;

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Arc length = (()/360)⋅2⋅⋅
(
(
a
n
g
l
e
o
f
a
r
c
)
/
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)
⋅
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⋅
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⋅
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In this case angle of arc was not specified so: 360∘
∘
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(
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