Is 5.18 rational or irrational
1 answer:
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Answer:
Tommy and Manuel are 16 ft apart
Step-by-step explanation:
The locations of all three players are shown in the image below
They form a right triangle where the hypotenuse is 20 ft, and one of the legs is 12 ft. We must find the other leg.
We must use Pythagoras's theorem. Being a and b the legs of a right triangle and c its hypotenuse, then
Knowing c and one of the legs, say b:
Using the values c=20, b=12 we find
So, Tommy and Manuel are 16 ft apart
Starting off with the polynomial in standard form would be extremely difficult, but we can construct one fairly easily with the zeroes we've been given.
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:
Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
=0\\ (x^2-x+2x-2)(x-2)=0\\ (x^2+x-2)(x-2)=0\\ (x^2+x-2)x-(x^2+x-2)2=0\\ x^3+x^2-2x-(2x^2+2x-4)=0\\ x^3+x^2-2x-2x^2-2x+4=0\\ x^3+(x^2-2x^2)+(-2x-2x)+4=0\\ x^3-x^2-4x+4=0\\](https://tex.z-dn.net/?f=%28x-1%29%28x%2B2%29%28x-2%29%3D0%5C%5C%0A%5Cbig%5B%28x-1%29x%2B%28x-1%292%5Cbig%5D%28x-2%29%3D0%5C%5C%0A%28x%5E2-x%2B2x-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29x-%28x%5E2%2Bx-2%292%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-%282x%5E2%2B2x-4%29%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-2x%5E2-2x%2B4%3D0%5C%5C%0Ax%5E3%2B%28x%5E2-2x%5E2%29%2B%28-2x-2x%29%2B4%3D0%5C%5C%0Ax%5E3-x%5E2-4x%2B4%3D0%5C%5C)
So, in standard form, our cubic polynomial would be
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:
Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
So, in standard form, our cubic polynomial would be