Answer:
whats the question?
Step-by-step explanation:
Answer:
The length of the width is 1
Step-by-step explanation:
Since we are not finding the hypotenuse and we are given it, we have to rearrange the a² + b² = c² equation because that equation is to find the hypotenuse of a right - angled triangle and we are not asked to find the hypotenuse but the width so
a² + b² = c²
→ Substitute in the values
( √3 )² + b² = 2²
→ Simplify equation
3 + b² = 4
→ Minus 3 from both sides to isolate b²
b² = 1
→ Square root both sides to isolate b
b = 1
Answer:
It means that the whisker is shorter in the data
Step-by-step explanation:
Answer:
![\large \boxed{\sf \ \ k=1 \ \ }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Csf%20%5C%20%5C%20k%3D1%20%5C%20%5C%20%7D)
Step-by-step explanation:
Hello,
First of all, let's notice that even if we do not know the zeros of P(x) we can say that
![(1) \ \alpha + \beta =\dfrac{5}{6} \\ \\ (2) \ \alpha * \beta =\dfrac{k}{6}](https://tex.z-dn.net/?f=%281%29%20%5C%20%5Calpha%20%2B%20%5Cbeta%20%3D%5Cdfrac%7B5%7D%7B6%7D%20%5C%5C%20%5C%5C%20%282%29%20%5C%20%5Calpha%20%2A%20%5Cbeta%20%3D%5Cdfrac%7Bk%7D%7B6%7D)
<u>But, why !?</u>
As they are the zeros of P(x), we can write:
![P(x)=6(x^2-\boxed{\dfrac{5}{6}}x+\boxed{\dfrac{k}{6}})=6(x-\alpha)(x-\beta)=6(x^2-\boxed{(\alpha +\beta)}x+ \boxed{\alpha *\beta} )](https://tex.z-dn.net/?f=P%28x%29%3D6%28x%5E2-%5Cboxed%7B%5Cdfrac%7B5%7D%7B6%7D%7Dx%2B%5Cboxed%7B%5Cdfrac%7Bk%7D%7B6%7D%7D%29%3D6%28x-%5Calpha%29%28x-%5Cbeta%29%3D6%28x%5E2-%5Cboxed%7B%28%5Calpha%20%2B%5Cbeta%29%7Dx%2B%20%5Cboxed%7B%5Calpha%20%2A%5Cbeta%7D%20%29)
And then we can identify the coefficients of the like terms to find the equations (1) and (2).
Now, we have <u>one more equation</u> which is:
![(3) \ \alpha -\beta =\dfrac{1}{6}](https://tex.z-dn.net/?f=%283%29%20%5C%20%5Calpha%20-%5Cbeta%20%3D%5Cdfrac%7B1%7D%7B6%7D)
(1)+(3) gives:
![\alpha + \beta +\alpha -\beta =\dfrac{5}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1 \\ \\ 2\alpha =1 \ \text{ divide by 2 } \\ \\ \alpha =\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Calpha%20%2B%20%5Cbeta%20%2B%5Calpha%20-%5Cbeta%20%3D%5Cdfrac%7B5%7D%7B6%7D%2B%5Cdfrac%7B1%7D%7B6%7D%3D%5Cdfrac%7B6%7D%7B6%7D%3D1%20%5C%5C%20%5C%5C%3C%3D%3E%202%5Calpha%20%3D1%20%5C%20%5Ctext%7B%20divide%20by%202%20%7D%20%5C%5C%20%5C%5C%20%3C%3D%3E%20%5Calpha%20%3D%5Cdfrac%7B1%7D%7B2%7D)
And we replace in (3) to get the value of the second zero.
![\beta = \dfrac{1}{2}-\dfrac{1}{6}=\dfrac{3-1}{6}=\dfrac{2}{6}=\dfrac{1}{3}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20%5Cdfrac%7B1%7D%7B2%7D-%5Cdfrac%7B1%7D%7B6%7D%3D%5Cdfrac%7B3-1%7D%7B6%7D%3D%5Cdfrac%7B2%7D%7B6%7D%3D%5Cdfrac%7B1%7D%7B3%7D)
And, finally, from (2), it comes:
![k=6*\alpha *\beta =6*\dfrac{1}{2}*\dfrac{1}{3}=\dfrac{6}{6}=1](https://tex.z-dn.net/?f=k%3D6%2A%5Calpha%20%2A%5Cbeta%20%3D6%2A%5Cdfrac%7B1%7D%7B2%7D%2A%5Cdfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B6%7D%7B6%7D%3D1)
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
B.
Step-by-step explanation: