Use the formula ω = θ/t to find the value of the missing variable.

θ = 2π/9 radian , ω = 5π/27 radian per min

Video transcript

Welcome back. I am so glad you're here. We are asked to solve for tea by using the formula. Omega equals theta divided by T. We are given that theta is equal to four pi divided by 11 radiant and Omega is equal to seven pi divided by 55 radians per minute. Our answer choices are answer choice. A 7/10 minutes. Answer choice B 20 pi divided by seven minutes. Answer choice, C seven divided by 20 minutes and answer choice D 20 divided by seven minutes. All right. So we know theta and we know Omega, we can fill those in on the left hand side. Omega is seven pi divided by 55 radians per minute. That's equal to in the numerator. Theta is four pi divided by 11 radiance and that is divided by T. So we want to get T by itself, we can multiply both sides of the equation by T. And on the right hand side, the TS cancel out and then we want to get rid of all of that, which is Omega on the left hand side. So we can multiply by the reciprocal of those fractions. So we can multiply by the reciprocal would have 55 divided by seven pi and then it will be minutes per radiance and then multiplying the other side by that as well, 55 divided by seven pi minutes per radiance. So on the left hand side, all that we've got left is T and that's equal to four pi divided by 11 radiance multiplied by 55 divided by seven pi minutes per radiance. Now, a few things are going to cancel out our radiance, cancel out and our pies cancel out. Now, we can just multiply straight across in the numerator. Four multiplied by 55 is 220. And then we still have minutes in the numerator and in the denominator 11 multiplied by seven is 77. And then there is no label left in the denominator. We can simplify this a little bit. Both 220 77 are divisible by 11. And that simplifies to be 20 divided by seven minutes. And that is our tea. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.