Find an equation of a square root curve of the form

Mathematics

1 answer:

Vlad [161]3 years ago

3 0

Answer:

y = √(5x+34)

Step-by-step explanation:

The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...

y = √(5x+34)

If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:

y = √(ax +b)

7 = √(3a +b) ⇒ 49 = 3a +b

8 = √(6a +b) ⇒ 64 = 6a +b

Subtracting the first equation from the second, gives ...

(64) -(49) = (6a +b) -(3a +b)

15 = 3a ⇒ a = 5

49 = 3(5) +b ⇒ b = 34

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Step-by-step explanation:

The diagonal of any square with side length $s$ is equal to $s\sqrt{2}$ . Since the side length of the square is 10, the diagonal must be $\boxed{10\sqrt{2}}$ .

To support and prove this:

The diagonal creates two 45-45-90 triangles, with the diagonal being the hypotenuse of both of these triangles. The Pythagorean Theorem states that in any triangle, the sum of the squares of both legs is equal to the square of the hypotenuse ( $a^2+b^2=c^2$ ).

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