Answer:
-1/3
Step-by-step explanation:
I hope this helps!
Any irrational number when added to 0.4 produce an irrational sum.
Example: #0.4+pi# is irrational
Answer:
less than
Step-by-step explanation:
When light moves from one medium to another, it is refracted. If it moves from a medium with refractive index n1 to one with refractive index n2, with an incidence angle to the surface normal of θ1, the refraction angle θ2 can be calculated from Snell's law.
The Snell's law states that the ratio of the sines of the angles of incidence and refraction of a wave (in this case beam/light) are constant when it passes between two given media.
![n_1\sin\theta_1=n_2\sin\theta_2](https://tex.z-dn.net/?f=n_1%5Csin%5Ctheta_1%3Dn_2%5Csin%5Ctheta_2)
Given that a <span>laser travels from glass to water at an angle of 35° with the normal, </span>
![\theta_1](https://tex.z-dn.net/?f=%5Ctheta_1)
<span>. If water has an index of refraction of 1.33 and glass has an index of refraction of 1.52, then we have:
</span>
![1.52\sin35^o=1.33\sin\theta_2 \\ \\ \Rightarrow\sin\theta_2= \frac{1.52\sin35^o}{1.33} =0.6555\therefore\theta_2=\sin^{-1}0.6555\approx41^o](https://tex.z-dn.net/?f=1.52%5Csin35%5Eo%3D1.33%5Csin%5Ctheta_2%20%5C%5C%20%20%5C%5C%20%5CRightarrow%5Csin%5Ctheta_2%3D%20%5Cfrac%7B1.52%5Csin35%5Eo%7D%7B1.33%7D%20%3D0.6555%5Ctherefore%5Ctheta_2%3D%5Csin%5E%7B-1%7D0.6555%5Capprox41%5Eo)
<span>
</span>
Answer: The answer is ![\textup{The other root is }\dfrac{8}{3}~\textup{and}q=40.Step-by-step explanation: The given quadratic equation is[tex]3x^2+7x-q=0\\\\\Rightarrow x^2-\dfrac{7}{3}x-\dfrac{q}{3}=0.](https://tex.z-dn.net/?f=%5Ctextup%7BThe%20other%20root%20is%20%7D%5Cdfrac%7B8%7D%7B3%7D~%5Ctextup%7Band%7Dq%3D40.%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3EStep-by-step%20explanation%3A%20%20%3C%2Fstrong%3EThe%20given%20quadratic%20equation%20is%3C%2Fp%3E%3Cp%3E%5Btex%5D3x%5E2%2B7x-q%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E2-%5Cdfrac%7B7%7D%7B3%7Dx-%5Cdfrac%7Bq%7D%7B3%7D%3D0.)
Also given that -5 is one of the roots, we are to find the other root and the value of 'q'.
Let the other root of the equation be 'p'. So, we have
![p-5=-\dfrac{7}{3}\\\\\\\Rightarrow p=5-\dfrac{7}{3}\\\\\\\Rightarrow p=\dfrac{8}{3},](https://tex.z-dn.net/?f=p-5%3D-%5Cdfrac%7B7%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20p%3D5-%5Cdfrac%7B7%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20p%3D%5Cdfrac%7B8%7D%7B3%7D%2C)
and
![p\times(-5)=-\dfrac{q}{3}\\\\\\\Rightarrow \dfrac{8}{3}\times 5=\dfrac{q}{3}\\\\\\\Rightarrow q=40.](https://tex.z-dn.net/?f=p%5Ctimes%28-5%29%3D-%5Cdfrac%7Bq%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B8%7D%7B3%7D%5Ctimes%205%3D%5Cdfrac%7Bq%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20q%3D40.)
Thus, the other root is
and the value of 'q' is 40.