Answer:
y = -6x + 5
Step-by-step explanation:
The first thing you should know about a perpendicular line is that the slope is the opposite reciprocal. So, this is your current equation: y= -6x + b. Plug in your coordinate to the equation to get this: 23 = -6(-3) + b. Multiply -6 by -3 to get 18. This is what is should look like: 23 = 18 + b. Subtract 18 from both sides to get your y-intercept of 5. Go back to your original equation and plug in 5 to b. This is your final equation: y = -6x + 5. Hope this helped!
In quadrant IV, cosine is positive and sine is negative. This means that
![\cos^2(x)+\sin^2(x)=1 \iff \sin^2(x)=1-\cos^2(x) \implies \sin(x)=-\sqrt{1-\cos^2(x)](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%2B%5Csin%5E2%28x%29%3D1%20%5Ciff%20%5Csin%5E2%28x%29%3D1-%5Ccos%5E2%28x%29%20%5Cimplies%20%5Csin%28x%29%3D-%5Csqrt%7B1-%5Ccos%5E2%28x%29)
The cotangent is defined as the ratio between the cosine and sine:
![\cot(x)=\dfrac{\cos(x)}{\sin(x)}=\dfrac{\cos(x)}{-\sqrt{1-\cos^2(x)}}=-\dfrac{2}{7}\iff \dfrac{\cos(x)}{\sqrt{1-\cos^2(x)}}=\dfrac{2}{7}](https://tex.z-dn.net/?f=%5Ccot%28x%29%3D%5Cdfrac%7B%5Ccos%28x%29%7D%7B%5Csin%28x%29%7D%3D%5Cdfrac%7B%5Ccos%28x%29%7D%7B-%5Csqrt%7B1-%5Ccos%5E2%28x%29%7D%7D%3D-%5Cdfrac%7B2%7D%7B7%7D%5Ciff%20%20%5Cdfrac%7B%5Ccos%28x%29%7D%7B%5Csqrt%7B1-%5Ccos%5E2%28x%29%7D%7D%3D%5Cdfrac%7B2%7D%7B7%7D)
So, we have the following equation:
![2\sqrt{1-\cos^2(x)}=7\cos(x)](https://tex.z-dn.net/?f=2%5Csqrt%7B1-%5Ccos%5E2%28x%29%7D%3D7%5Ccos%28x%29)
Squaring both sides yields
![4(1-\cos^2(x))=49\cos^2(x) \iff 4-4\cos^2(x)=49\cos^2(x)\iff 53\cos^2(x)=4](https://tex.z-dn.net/?f=4%281-%5Ccos%5E2%28x%29%29%3D49%5Ccos%5E2%28x%29%20%5Ciff%204-4%5Ccos%5E2%28x%29%3D49%5Ccos%5E2%28x%29%5Ciff%2053%5Ccos%5E2%28x%29%3D4)
The solution to this equation would be
![\cos^2(x)=\dfrac{4}{53}\iff \cos^2(x)=\pm\dfrac{2}{\sqrt{53}}](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%3D%5Cdfrac%7B4%7D%7B53%7D%5Ciff%20%5Ccos%5E2%28x%29%3D%5Cpm%5Cdfrac%7B2%7D%7B%5Csqrt%7B53%7D%7D)
But we know that the cosine has to be positive, so we have
![\cos(x)=\dfrac{2}{\sqrt{53}}](https://tex.z-dn.net/?f=%5Ccos%28x%29%3D%5Cdfrac%7B2%7D%7B%5Csqrt%7B53%7D%7D)
And
![\sin(x)=-\sqrt{1-\dfrac{4}{53}}=-\sqrt{\dfrac{49}{53}}=-\dfrac{7}{\sqrt{53}}](https://tex.z-dn.net/?f=%5Csin%28x%29%3D-%5Csqrt%7B1-%5Cdfrac%7B4%7D%7B53%7D%7D%3D-%5Csqrt%7B%5Cdfrac%7B49%7D%7B53%7D%7D%3D-%5Cdfrac%7B7%7D%7B%5Csqrt%7B53%7D%7D)
Finally, the secant is the inverse of the cosine, so it's
![\sec(x)=\dfrac{1}{\cos(x)}=\dfrac{\sqrt{53}}{2}](https://tex.z-dn.net/?f=%5Csec%28x%29%3D%5Cdfrac%7B1%7D%7B%5Ccos%28x%29%7D%3D%5Cdfrac%7B%5Csqrt%7B53%7D%7D%7B2%7D)
Answer:
true
Step-by-step explanation:
Answer:slope=3
intercept=2
Step-by-step explanation:
y=mx-b m is slope amd b is intercept
Answer:
48 m^2
Step-by-step explanation:
Since this is a parallelogram, you can think of it as taking the triangle off of the left side and reattaching it on the right side to make a rectangle. After you visualize it as a rectangle, you just have to multiply 8 by 6 to get 48 meters squared.