Answer:
Step-by-step explanation:
The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides.
19 + 34 = 53
34 - 19 = 15
from 16 cm to 52 cm
Answer:
3x 10^4 NOT NEGATIVE! POSITIVE
Answer:
![\bold{x =cos\theta}\\\bold{y=sin\theta}](https://tex.z-dn.net/?f=%5Cbold%7Bx%20%3Dcos%5Ctheta%7D%5C%5C%5Cbold%7By%3Dsin%5Ctheta%7D)
Step-by-step explanation:
The given system of linear equations is:
![(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0](https://tex.z-dn.net/?f=%28cos%5Ctheta%29x%2B%28sin%5Ctheta%29y%3D1%5C%5C%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29y%3D0)
We have to solve the equations for the values of
.
Let us use elimination method in which we eliminate one of the variables from the two variables.
For this, let us multiply the first equation by
and second equation by ![cos\theta](https://tex.z-dn.net/?f=cos%5Ctheta)
Now, the equations become:
![(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)](https://tex.z-dn.net/?f=%28cos%5Ctheta.sin%5Ctheta%29x%2B%28sin%5Ctheta.sin%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%28cos%5Ctheta.sin%5Ctheta%29x%2B%28sin%5E2%5Ctheta%29y%3Dsin%5Ctheta%20.......%20%281%29%5C%5C%5C%5C%28-sin%5Ctheta.cos%5Ctheta%29x%2B%28cos%5Ctheta.cos%5Ctheta%29y%3D0%5C%5C%5CRightarrow%20%28-sin%5Ctheta.cos%5Ctheta%29x%2B%28cos%5E2%5Ctheta%29y%3D0%20.....%20%282%29)
Now, let us add (1) and (2):
![(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta](https://tex.z-dn.net/?f=%28sin%5E2%5Ctheta%29y%2B%28cos%5E2%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%28sin%5E2%5Ctheta%2Bcos%5E2%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%281%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20y%20%3D%20sin%5Ctheta)
Using the equation:
![(-sin\theta)x+(cos\theta)y=0](https://tex.z-dn.net/?f=%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29y%3D0)
Putting value of
:
![\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta](https://tex.z-dn.net/?f=%5CRightarrow%20%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29sin%5Ctheta%3D0%5C%5C%5CRightarrow%20%28sin%5Ctheta%29x%3D%28cos%5Ctheta%29sin%5Ctheta%5C%5C%5CRightarrow%20x%20%3D%20cos%5Ctheta)
So, the answer to the system of linear equations is:
![\bold{x =cos\theta}\\\bold{y=sin\theta}](https://tex.z-dn.net/?f=%5Cbold%7Bx%20%3Dcos%5Ctheta%7D%5C%5C%5Cbold%7By%3Dsin%5Ctheta%7D)
Area is 96 inches because we needed to separate the triangles. After we got the big one we were missing the shortest side so to find that we use Pythagorean theorem. We get 16^2+x=20^2
400-256=144
Sq root of 144 is 12.
Now that we found all the missing sides. Let find area 1/2*b*h
16*12/2=96
Answer:
MP = RS 7,800
Step-by-step explanation:
Let
Marked price = MP
MP x (100 – 15) / 100 = Rs 6,630
MP × (85)/100 = Rs 6,630
MP = Rs 6,630 ÷ 85/100
MP = 6,630 × 100/85
MP = 663,000/85
MP = 7,800
MP = RS 7,800