Answers:
Row 0: 1
Row 1: 1 1
Row 2: 1 2 1
Row 3: 1 3 3 1
Row 4: 1 4 6 4 1
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Explanation:
This is known as Pascal's Triangle. Each value, other than the '1's, is found by adding the values directly above it. For instance, the '4' is the result of 1+3, and the 6 is a result of 3+3, and so on.
You can use the nCr combination formula to find the same values.
Alternatively you can expand out binomials of the form (x+y)^n, for integer values of n, and you'll find the coefficients of the terms match perfectly with Pascal's Triangle.
Answer:
Ruby’s function notation V(h) describes the volume of the pool after h number of hours. Hours is the independent variable and the total volume is the dependent variable.
Step-by-step explanation:
sample response
Answer:
106.1 ft/s
Step-by-step explanation:
You know the diagonal of a square is √2 times the length of one side, so the distance from 3rd to 1st is 90√2 feet ≈ 127.2792 ft.
The speed is the ratio of distance to time:
speed = distance/time = 127.2972 ft/(1.2 s) ≈ 106.1 ft/s.
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In case you have never figured or seen the computation of the diagonal of a square (the hypotenuse of an isosceles right triangle), consider the square with side lengths 1. The diagonal will cut the square into halves that are isosceles right triangles with leg lengths 1. Then the Pythagorean theorem can be used to find the diagonal length d:
d² = 1² + 1²
d² = 2
d = √2
Since this is the diagonal for a side length of 1, any other side length will serve as a scale factor for this value. A square with a side length of 90 ft will have a diagonal measuring 90√2 ft.
Multiply the length*width*height to get the volume of the prism then, take out the difference between the volumes
Volume of the prism= 1018464
Then just subtract
