Answer:
9
Step-by-step explanation:
y=x
y=kx
substitute k for 0.75 and x for 12 in the above equation
y=0.75×12
y=9
Answer:
24.23
Step-by-step explanation:
The tan(x) would equal to the opposite side over the adjacent one
So 9/20. To get the degree we need to get the arctan of it, so arctan(9/20) = 24.23
So basically you want to isolate only one of the variable on one side so
y=-9+x^2
add 9 to both sides
y+9=x^2
square root both sides
x=
12) 2.3
13) 4/13
14) 8 7/11
7) .3434...
8) 3.166...
15) (2700-600)/2700 = 2100/2700 = 21/27 = 7/9
1) .4666666667
2) .4444...
3) -0.6666666667
4) -0.8571428571
5) 3.3409090909...
6) -2.227272727273
**bar notation is when you put a bar over the repeating part of a decimal because you can't right it all since it goes on forever
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
