A = 8B
A + B = 180
8B + B = 180
9B = 180
B = 20
A = 8 * 20 = 160
Sin2(x) +cos(x)=1
from the relation: (sin2(x) +cos2(x) =1 )
so , sin2(x)=1-cos2(x)
by subs. in the main eqn.
1-cos2(x) + cos(x) =1
by simplify the eqn.
cos(x) -cos2(x)=0
take cos(x) as a common factor
cos(x)* (1-cos(x))=0
then cos(x)=0 && cos(x)=1
cos(x)=0 if x= pi/2
& cos(x) = 1 if x = 0 , 2*pi
so the solution is x= {0,pi/2 , 2*pi}
Answer:
12 possible outcomes
Step-by-step explanation:
Choosing 1 vehicle from 2 = 2C1 = 2
Choosing 1 color from 3 = 3C1 = 3
Choosing 1 type from 2 = 2C1 = 2
Number of possible outcomes :
2C1 * 3C1 * 2C1
2 * 3 * 2
= 12 different possible outcomes
Answer: The correct option is (B) 24 : 25.
Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.
We are to find the ratio of the area of R to the area of S.
Let 2x, 3x be the sides of rectangle R and y be the side of square S.
Then, according to the given information, we have

Therefore, the ratio of the area of R to the area of S is
![\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%5Ctimes3x%7D%7By%5Ctimes%20y%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B5x%5E2%7D%7By%5E2%7D%5C%5C%5C%5C%5C%5C%3D6%5Cleft%28%5Cdfrac%7Bx%7D%7By%7D%5Cright%29%5E2%5C%5C%5C%5C%5C%5C%3D6%5Ctimes%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%5Cright%29%5E2~~~~~~~~~~~%5B%5Ctextup%7BUsing%20equation%20%28i%29%7D%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B24%7D%7B25%7D%5C%5C%5C%5C%3D24%3A25.)
Thus, the required ratio of the area of R to the area of S is 24 : 25.
Option (B) is CORRECT.
Answer:
false
Step-by-step explanation: