.23 times 5 is 1.15
the answer would be she used 1.15 feet of ribbon
Answer:
1 ) sin 165°
2 ) cos 330°
3 ) Tan 157.5°
4 ) ![sin^2 157.5](https://tex.z-dn.net/?f=sin%5E2%20157.5)
Step-by-step explanation:
1 )
Given expression is ![\sqrt{\frac{1-cos330}{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B1-cos330%7D%7B2%7D%20%7D)
We know that ![cos2x=1-2sinx^{2}](https://tex.z-dn.net/?f=cos2x%3D1-2sinx%5E%7B2%7D)
![sinx^{2}=\frac{1-cos2x}{2}](https://tex.z-dn.net/?f=sinx%5E%7B2%7D%3D%5Cfrac%7B1-cos2x%7D%7B2%7D)
![(sinx/2)^2=\frac{1-cosx}{2}](https://tex.z-dn.net/?f=%28sinx%2F2%29%5E2%3D%5Cfrac%7B1-cosx%7D%7B2%7D)
So the first expression is sin (330/2)° =sin 165°
2 )
GIven expression is ![1-2sin^2165](https://tex.z-dn.net/?f=1-2sin%5E2165)
We know that ![cos2x=1-2sinx^{2}](https://tex.z-dn.net/?f=cos2x%3D1-2sinx%5E%7B2%7D)
So the result is cos 330°
3 )
Given expression is ![\frac{1-cos 315}{sin315}](https://tex.z-dn.net/?f=%5Cfrac%7B1-cos%20315%7D%7Bsin315%7D)
We know that ![cos2x=1-2sinx^{2}](https://tex.z-dn.net/?f=cos2x%3D1-2sinx%5E%7B2%7D)
Also we know that sin2x = 2sinxcosx
So The numerator becomes
. and the denominator becomes as ![2sinx/2cosx/2](https://tex.z-dn.net/?f=2sinx%2F2cosx%2F2)
![\frac{2sin^2x/2}{2sinx/2cosx/2}=tanx/2](https://tex.z-dn.net/?f=%5Cfrac%7B2sin%5E2x%2F2%7D%7B2sinx%2F2cosx%2F2%7D%3Dtanx%2F2)
So the result is Tan 157.5°
4 )
Given expression is ![\frac{1-cos 315}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1-cos%20315%7D%7B2%7D)
We know that ![cos2x=1-2sinx^{2}](https://tex.z-dn.net/?f=cos2x%3D1-2sinx%5E%7B2%7D)
![(sinx/2)^2=\frac{1-cosx}{2}](https://tex.z-dn.net/?f=%28sinx%2F2%29%5E2%3D%5Cfrac%7B1-cosx%7D%7B2%7D)
So the result is ![sin^2 157.5](https://tex.z-dn.net/?f=sin%5E2%20157.5)
Answer:
1 positive solution (and 1 negative)
the greatest solution is about 2.87
Step-by-step explanation:
so, it is
x² + 2x + 7 = 21
x² + 2x - 14 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -14
x = (-2 ± sqrt(2² - 4×1×-14))/(2×1) =
= (-2 ± sqrt(4 + 56))/2 = (-2 ± sqrt(60))/2 =
= (-2 ± sqrt(4×15))/2 = (-2 ± 2×sqrt(15))/2 =
= -1 ± sqrt(15)
x1 = -1 + sqrt(15) = 2.872983346... ≈ 2.87
x2 = -1 - sqrt(15) = -4.872983346...