Answer:
![(\frac{1}{2},\frac{-1}{2},\frac{1}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C%5Cfrac%7B-1%7D%7B2%7D%2C%5Cfrac%7B1%7D%7B2%7D%29)
Step-by-step explanation:
We have been given the intersection coordinates:
(7,1,-6) and perpendicular to the line x=-1+t ,y=-2+t and z=-1+t
From the condition of perpendicularity we know:
![(7,1,-6)(x,y,z)](https://tex.z-dn.net/?f=%287%2C1%2C-6%29%28x%2Cy%2Cz%29)
![\Rightarrow 7x+y-6z=0](https://tex.z-dn.net/?f=%5CRightarrow%207x%2By-6z%3D0)
Now, we have given x=-1+t , y=-2+t and z= -1+t
![7(-1+t)+(-2+t)-6(-1+t)=0](https://tex.z-dn.net/?f=7%28-1%2Bt%29%2B%28-2%2Bt%29-6%28-1%2Bt%29%3D0)
![-7+7t-2+t+6-6t=0](https://tex.z-dn.net/?f=-7%2B7t-2%2Bt%2B6-6t%3D0)
![\Rightarrow -3+2t=0](https://tex.z-dn.net/?f=%5CRightarrow%20-3%2B2t%3D0)
![2t=3](https://tex.z-dn.net/?f=2t%3D3)
![t=\frac{3}{2}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B3%7D%7B2%7D)
Now, substituting t in the given coordinates x,y and z we get:
![x=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
![y=-2+\frac{3}{2}=\frac{-1}{2}](https://tex.z-dn.net/?f=y%3D-2%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B-1%7D%7B2%7D)
And ![z=-1+\frac{3}{2}=\frac{1}{2}](https://tex.z-dn.net/?f=z%3D-1%2B%5Cfrac%7B3%7D%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D)
Answer:
a)
and ![c=\frac{-1-\sqrt{13}}{2}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B-1-%5Csqrt%7B13%7D%7D%7B2%7D)
Step-by-step explanation:
The idea for the solution of this equation is to find the value of c where both parts of the piecewise-defined function are the same. So we need to take the parts of the function and set them equal to each other, so we get:
![3-x^{2}=x](https://tex.z-dn.net/?f=3-x%5E%7B2%7D%3Dx)
and then solve for x. We move everything to one side of the equation so we get:
![x^{2}+x-3=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2Bx-3%3D0)
and we use the quadratic formula:
![x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
and we substitute:
![x=\frac{-1\pm \sqrt{(1)^2-4(1)(-3)}}{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B%281%29%5E2-4%281%29%28-3%29%7D%7D%7B2%281%29%7D)
and solve
![x=\frac{-1\pm \sqrt{1+12}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%2B12%7D%7D%7B2%7D)
![x=\frac{-1\pm \sqrt{13}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B13%7D%7D%7B2%7D)
so our two answers are:
a)
and ![c=\frac{-1-\sqrt{13}}{2}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B-1-%5Csqrt%7B13%7D%7D%7B2%7D)
Answer:
The angle has a measure of 135 degrees.
Step-by-step explanation:
90 / 2 = 45 degrees
90 + 45 = 135 degrees
<em><u>Hope I helped! Have a nice day! Plz mark as brainliest!!! :D</u></em>
<em><u>-XxDeathshotxX</u></em>
104 1/2ft cubed
To find the volume you would multiply
Length•width•height
So,
(6 1/3)(3)(5 1/2)=104 1/2
So it would be 104 and 1/2 or 104.5