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Anit [1.1K]
3 years ago
9

In the xy−plane, the center of a circle has coordinates (6,10) and the circle touches the y−axis at one point only. What is the

radius of the circle?
A. 6
B. 10
C. 12
D. 16
Mathematics
1 answer:
lesya692 [45]3 years ago
5 0
It should be B. That would make it to where the circle touches the y axis at (6,0). I hope this helps.
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The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?
Amanda [17]

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

         1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm.  That's interesting.  64 happens to be the square of 8 . 
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3                                   Items = 2, Sum = 4
1, 3, 5, 7                           Items = 4, Sum = 16
1, 3, 5, 7, 9, 11                 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing !  The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the <em><u>first 20 consecutive odd numbers</u></em>.

I slogged through it on my calculator, and it's true.

I never knew this before.  It seems to be something valuable
to keep in my tool-box (and cherish always).


3 0
3 years ago
Here is questions for you because such thing as spring break is over ;)
zvonat [6]

Answer:

I don't now why but by seeing this photo my mouth is watery

6 0
3 years ago
Read 2 more answers
If f(1) = 7 and f(n) = 5f (n − 1) then find the value of f(5).
nevsk [136]

Answer:

f(5) = 4375

Step-by-step explanation:

Given f(n) = 5f(n - 1) and f(1) = 7

This allows us to find the next term in the sequence from the previous term

f(2) = 5f(1) = 5 × 7 = 35

f(3) = 5f(2) = 5 × 35 = 175

f(4) = 5f(3) = 5 × 175 = 875

f(5) = 5f(4) = 5 × 875 = 4375

3 0
2 years ago
Read 2 more answers
Gary wants to buy a bicycle that usually sells for $74.99. The store is having a sale and all merchandise is discounted by 25%.
marusya05 [52]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
Suppose you pick 6 different numbers in [10]. Prove that 2 of the numbers are next to each other. (Hint: use the pigeonhole prin
Masja [62]

Step-by-step explanation:

We are picking 6 numbers from the numbers 1,2,3,4,5,6,7,8,9,10. Since we care about numbers being next to each other, we might think of the 10 numbers as being distributed in 5 boxes (which you can think of as the holes):

|   1 2   |   3 4   |   5 6   |   7 8   |   9 10  |

So on the first box we have the numbers 1 and 2, on the second box we have the numbers 3 and 4, and so on. Since we are picking 6 numbers from those 10 numbers, that means we'll have to pick 6 boxes (and inside each box we pick a number), but we only have 5 available boxes, so by the pigeonhole principle, we'll have to pick 1 same box at least two times. Since on each picked box we'll need to pick a number, on this box which was picked two times, we will have to pick both of its numbers. And so those 2 numbers inside that box will be next to each other (meaning they're consecutive numbers).

4 0
3 years ago
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