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jek_recluse [69]
3 years ago
10

Which is a point on the circle whose center is (0, 0) and whose radius is 5?

Mathematics
1 answer:
AleksAgata [21]3 years ago
5 0
Circle equation is given in the form of (x-a)²+(y-b)² = r²

Where (a, b) is the centre and 'r' is the radius

We have a circle with centre (0, 0) and radius of 5.

Substituting these value into the equation form, we have

(x-0)²+(y-0)² = 5²
x² + y² = 25

Hence, the equation of the circle is x² + y² = 25
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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

6 0
2 years ago
What 4 coins equal 90¢
N76 [4]

Answer:

half dollar, quarter, dime and nickel

Step-by-step explanation:

When you sum it up it will give you 90 cents.

3 0
4 years ago
Read 2 more answers
I need help with this please
enyata [817]

Answer:¿Qué es lo contrario de estos estadistas?

Step-by-step explanation:

What is the opposite of these statesment

5 0
3 years ago
Kiki's mother cooked a dinner that contained a total of 992 calories. She also prepared a dessert that contained a total of 846
PIT_PIT [208]

Answer: C

Step-by-step explanation:

992/4=165

846/6=141

165+141=306

(992/4) + (846/6) = 306 total calories consumed

3 0
3 years ago
How to do I solve this
padilas [110]
4. 2b-6+3b=
5b-6=143
5b=143+6
5b=149

b=149
    ------
       5
5 0
3 years ago
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