Answer:
D) 55/73
Step-by-step explanation:
The question is on trigonometry. Sine of an angle is obtained using the SOH of SOHCAHTOA formula of trigonometry. SOH is an acronym for sine, opposite and hypotenuse. Sine of an angle is obtained from the ratio of opposite and hypotenuse of a given triangle. Thus, SOH
is denoted as stated below.
![sine \: \beta = \frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=sine%20%5C%3A%20%20%5Cbeta%20%20%3D%20%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%20)
Hence, given the above triangle,
![sine \: of \: angle \: u = \frac{ |bc| }{ |ab| } = \frac{55}{73}](https://tex.z-dn.net/?f=sine%20%5C%3A%20of%20%5C%3A%20angle%20%5C%3A%20u%20%3D%20%20%5Cfrac%7B%20%7Cbc%7C%20%7D%7B%20%7Cab%7C%20%7D%20%20%3D%20%20%5Cfrac%7B55%7D%7B73%7D%20)
Therefore, the sine of angle u = 55/73 (D)
Answer:
4
Step-by-step explanation:
The x-intercept occurs when y=0, if you think about it graphically. Plug y=o into your equation:
10x - 5(0) = 40
10x = 40 (divide each side by 10)
x=4
X = 9
you multiply both sides by 3 because you have to get rid of it and what you do to one side you do to the other then you divide both sides by 2 to isolate the variable. i hope that makes sense.
Answer:
The correct answer is C.
Step-by-step explanation:
The given equation is;
![r=\frac{1}{1-\sin(\theta)}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B1-%5Csin%28%5Ctheta%29%7D)
This implies that;
![r(1-\sin(\theta)=1](https://tex.z-dn.net/?f=r%281-%5Csin%28%5Ctheta%29%3D1)
![r-r\sin(\theta)=1](https://tex.z-dn.net/?f=r-r%5Csin%28%5Ctheta%29%3D1)
Let us write in Cartesian coordinates by substituting;
![r=\sqrt{x^2+y^2} ,y=r\sin(\theta)](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D%20%2Cy%3Dr%5Csin%28%5Ctheta%29)
![\sqrt{x^2+y^2}-y=1](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2By%5E2%7D-y%3D1)
![\sqrt{x^2+y^2}=y+1](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2By%5E2%7D%3Dy%2B1)
Square both sides;
![(\sqrt{x^2+y^2})^2=(y+1)^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx%5E2%2By%5E2%7D%29%5E2%3D%28y%2B1%29%5E2)
This implies that;
![x^2+y^2=y^2+2y+1](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3Dy%5E2%2B2y%2B1)
![x^2=2y+1](https://tex.z-dn.net/?f=x%5E2%3D2y%2B1)
![y=\frac{1}{2}x^2-\frac{1}{2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%5E2-%5Cfrac%7B1%7D%7B2%7D)
This is an equation of a parabola that opens upwards with a y-intercept of
.
The correct choice is C