How to solve the 122 question in the picture?
Answers
Answer:
{0°, 30°}
Step-by-step explanation:
2cos² β + sin β - 2 = 0
2cos²β + sin β - 2(sin²β + cos²β) = 0
sin β - 2sin²β = 0
(sin β)( 1 - 2sin β) = 0
If sin β = 0 , then β = 0°
If (1 - 2sin β) = 0 , then
2sin β = 1
sin β = 1/2 , then β = 30° = π/6
Answer:
GIven:
\sqrt{ \bigg(5^0 + \dfrac{2}{3} \bigg) } = (0.6)^2 - 3x
(5
0
+
3
2
)
=(0.6)
2
−3x
To FInd:
The value of x
Solution:
\sqrt{ \bigg(5^0 + \dfrac{2}{3} \bigg) } = (0.6)^2 - 3x
(5
0
+
3
2
)
=(0.6)
2
−3x
Rewriting 5⁰ = 1:
\sqrt{ \bigg(1 + \dfrac{2}{3} \bigg) } = (0.6)^2 - 3x
(1+
3
2
)
=(0.6)
2
−3x
\sqrt{ \dfrac{5}{3} }= (0.6)^2 - 3x
3
5
=(0.6)
2
−3x
Rationalise the LHS by multiplying √3/√3:
\dfrac{\sqrt{15} }{3} = (0.6)^2 - 3x
3
15
=(0.6)
2
−3x
Rewriting (0.6)² as a fraction:
\dfrac{\sqrt{15} }{3} = \bigg( \dfrac{6}{10} \bigg)^2 - 3x
3
15
=(
10
6
)
2
−3x
\dfrac{\sqrt{15} }{3} = \dfrac{9}{25} - 3x
3
15
=
25
9
−3x
Multiply both sides by 3:
\sqrt{15} = \dfrac{27}{25} - 9x
15
=
25
27
−9x
Find x:
9x = \dfrac{27}{25} - \sqrt{15}9x=
25
27
−
15
9x = \dfrac{27 - 25\sqrt{15} }{25}9x=
25
27−25
15
Dividing both sides by 9:
x = \dfrac{27 - 25\sqrt{15} }{225}x=
225
27−25
15