<u>Anna:</u>
1st month = 18 + = 18
inches
2nd month = 18 +
= 19
3rd month = 19 +
= 20
4th month = 20 +
= 21
5th month = 21 + = 21
<u>Grace:</u>
Because Anna is inches shorter than Grace, we can start the count from the third month:
1st month = 20
2nd month = 21
3rd month = 21
4th month = 21 +
= 22
5th month = 22 +
= 23
Answer:
Step-by-step explanation:
We presume you want the values of x, y, and z.
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There are two "special triangles" in geometry and trigonometry. They are the 30°-60°-90° right triangle that is half of an equilateral triangle, and the 45°-45°-90° isosceles right triangle that is half a square (cut by the diagonal).
The side ratios of these special triangles are relatively easy to remember. It is useful to memorize them.
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For the isosceles right triangle, the side lengths are the same. The Pythagorean theorem tells you that if they are both 1, then the hypotenuse is ...
√(1²+1²) = √2
That is, the side lengths of the 45-45-90 triangle are in the ratio ...
1 : 1 : √2
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For the triangle that is half an equilateral triangle, you know the hypotenuse is twice the length of the shortest side (since we got that short side by cutting a long side in half). Then the longer side can be found from the Pythagorean theorem:
√(2²-1²) = √3
That is, the side lengths of the 30-60-90 triangle are in the ratio ...
1 : √3 : 2
_____
In this problem, we're given the hypotenuse of a 30-60-90 triangle, so we know the short side of it (x) will be half that length:
x = (16√3)/2
x = 8√3
The hypotenuse of the 45-45-90 triangle will be √3 times x, so will be ...
long side of small triangle = (√3)(8√3) = 24
The shorter sides of that 45-45-90 triangle will be this value divided by the square root of 2, so are ...
y = z = 24/√2
We can multiply this by (√2)/(√2) to "rationalize the denominator".
y = z = 12√2
Answer:
There are 199 pairs of consecutive natural numbers whose product is less than 40000.
Step-by-step explanation:
We notice that such statement can be translated into this inequation:
Now we solve this inequation to the highest value of that satisfy the inequation:
The Quadratic Formula shows that roots are:
Only the first root is valid source to determine the highest possible value of , which is
. Each natural number represents an element itself and each pair represents an element as a function of the lowest consecutive natural number. Hence, there are 199 pairs of consecutive natural numbers whose product is less than 40000.