Answer:
x=pi*n/2+1/2arctan(7/5)
Step-by-step explanation:
5sin(2x)=7cos(2x)
5tan(2x)=7/5
2x=pi*n+arctan(7/5)
x=pi*n/2+1/2arctan(7/5) for n e Z
Answer:

Step-by-step explanation:
Please refer to the image attached with this answer. Assuming our triangle to be ΔABC and Line AD meeting BC at D.
As we are given that side b = side c
The angle subtended by them ∠B and ∠C must be equal . Let us assume them to be x each . hence
x + x + 52° +31° = 180°
2x + 73° = 180°
2x = 180°- 73°
2x = 107 °
x = 53.5°
Hence in ΔACD
x+ 31°+∠2= 180°
53.5°+31°+ ∠2 = 180°
∠2=180°-84.5°
∠2=95.5°
Also
∠1 + ∠2 = 180°
∠1 + 95.5° = 180°
∠1 = 180°-95.5°
∠1 =84.5°
Now applying Sine rule in ΔABD




Hence we have c as 15.14
as we are given that side c = side b , b=15.14
The properties of any triangle says that the sum of two sides of any triangle is always greater than the third side. Hence
a<b+c
12+2x-6<15.14+15.14
6+2x<30.28
2x<30.28-6
2x<24.28
x<12.14
also side a must be greater than 0
12+2x-6>0
6+2x>0
2x>-6
x>-3
Hence the range of x will be
-3 <x < 12.14
Answer:
Dude, we need an image to know what the figure is.
Answer:
Interest is a constant increase of a number over a fixed period of time.
EX: You put $10 into the bank with 3% interest on it in 10 years you would have $10.44
Step-by-step explanation:
Vector a = (2, 1, 2)
Vector b = (1, 2, 4)
Vector p = (k, k, k)
Vector a to vector b = vector b - vector a = (1, 2, 4) - (2, 1, 2) = (1 - 2, 2 - 1, 4 - 2) = (-1, 1, 2)
Vector a to vector p = vector p - vector a = (k, k, k) - (2, 1, 2) = (k - 2, k - 1, k - 2)
Vector a to b is perpendicular to vector a to p if the dot product of vector a to vector b and vector a to vector p is equal to zero.
i.e. (-1, 1, 2) . (k - 2, k - 1, k - 2) = 0
-1(k - 2) + (k - 1) + 2(k - 2) = 0
-k + 2 + k - 1 + 2k - 4 = 0
2k -3 = 0
2k = 3
k = 3/2