Math

posted by .

Clara measured the diameter of the circle.
How many centimeters is the diamter?
Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15.
Clue:The units digit and the hundreths digit are the same
Clue:If the diameter was 100 times longer, its measure would be a square number


Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15.
Clue:The units digit and the hundreths digit are the same
Clue:If the diameter was 100 times longer, its measure would be a square number.<<

it is betwen .90 and 1.35. The next clue means it is either .90 or 1.31, or 1.21, or 1.11.

MULTIPLY 100 to each of those, and see if you get a perfect square.


I have a question, Matt and Maggie were building a staircase from wooden cubes. The first step consisted of one cube, the second steop consisted of two stacked cubes, the third step had three stacked cubes, etc. The cubes were each 1/2 inch tall and were a variety of colors. Maggie asked matt, if we had 50 , I wonder how many blocks we would need?


It's a good idea not to pigyback questions like this John. You should start a new question so we don't miss your post.
If I understand the question correctly, we want each stack of cubes to be a different color and we want 50 steps, or stacks of cubes, then how many total cubes would we need?
The number of cubes for each step follows the sequence
1,2,3,...
Thus we want the sum of 1 + 2 + 3 + ... + 50
There are a number of ways to determine this sums. This is the method Gauss used for this problem.
Write the sum forwards then backwards directly beneath it like this
1 + 2 + 3 + ... + 49 + 50 = sum
50+49 +48 + ... + 2 + 1 = sum
Then add the rows to get
51+51+51 + ... + 51 + 51 = 2*sum
On the left hand side we have 50*51, so
50*51=2*sum Now divide both sides by 2 and find the sum.
In general the sum of the first positive n integers is (n(n+1))/2. Here n=50


From clue 1 you can see the number is between .90 and 1.35.
From clue 2 you can see the sumber looks like 1.d1. We need to check if it could be 0.d0 too.
From clue 3 100*d=x^2 so 1d1 is a square or d0 is a square. If you run through the numbers 1 to 9 you'll see whether d0 can be a square or not, i.e. check 10,20,30...,90. Now go through the number 0 to 9 for 1d1 for d, i.e. check if 101, 111, 121, 131 are squares.
I only found one answer. Remember the units too.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. arithmetic

    Clue 1: each digit increased by 1 and clue 2 add the numbers and the answer is 21. whats the six digit number?
  2. math

    how many two-digit primes have a ones digit of 1?
  3. 2nd grade

    Okay, my child is doing problem solving lesson 5-7 in scott foresman addison wesley book. The question that we are having a problem with is a number line. there are 10 spaces in the number line and the clues are: Clue 1: the number …
  4. 2nd grade math requestion post

    Okay, my child is doing problem solving lesson 5-7 in scott foresman addison wesley book. The question that we are having a problem with is a number line. there are 10 spaces in the number line and the clues are: Clue 1: the number …
  5. math

    what is my number? Clue 1 My number is a multiple of 5,but it does not end in 5. Clue 2 The prime factorization of my number is a string of three numbers. Clue 3 Two of the numbers in the prime factorizations are the same. Clue 4 My
  6. math

    clue#1 You will use exactly eleven base-ten blocks. Clue#2 The number is less than 300. Clue#3 The digit in the tens place is one less than the digit in the ones place. Who am I?
  7. Math

    Clue 1: I am less than 1,000. Clue 2: the sum of my 2 digits is 26 Clue 3: my ones digit is 8 Who am I?
  8. Math

    Whole Number Math Riddle Clue 1: Double my tens digit and get my ones digit. Clue 2: Double me and I am less than 50
  9. English

    State the meaning of the word eradicate as it is used in the following sentence. Then, identify the context clue that you used to understand the meaning: definition clue, synonym, example clue, contrast clue, or inference clue.
  10. English

    State the meaning of the word eradicate as it is used in the following sentence. Then, identify the context clue that you used to understand the meaning: definition clue, synonym, example clue, contrast clue, or inference clue. Researchers …

More Similar Questions