Help Fast PLEASE!!
check for corrections on my problems
1.Rewrte the following in simplified radical form, Assume all variables represents positive real numbers: square root 48y^10= 4y^5 square root 3
2.Rationalize the denomintor and simplify: square root33/square root 21= square root77/7
3.Solve for y: 6/(y+1)(y+6)=4+3/y+6=y=-7,-3/4
PLEASE CHECK MY QUESTIONS SOON! I'M ON A DEADLINE, AND I TRULY NEED YOUR HELP!!
Thanks
1. correct
2. correct
3. if your equation is 6/(y+1)(y+6)=4+3/(y+6)
then you are correct
Thanks Reiny, You have been a blessing for me checking my answers.
10^1,64
Sure, I'd be happy to help you with these problems. Let's go through each of them step by step:
1. To rewrite √(48y^10), you can break it down into smaller factors where you have perfect squares. In this case, you can rewrite it as √(16y^10) * √(3). Breaking down the square root of 48 into 16 * 3. Further simplification gives you 4y^5 * √(3).
2. Rationalizing the denominator in √33/√21, you need to multiply both the numerator and the denominator by the conjugate of the denominator. In this case, since the denominator is √21, the conjugate is √21 as well. Therefore, you multiply the numerator and denominator by √21. This gives you (√33 * √21) / (√21 * √21) = √(33*21) / 21 = √(693) / 21. Further simplification is not possible as the square root of 693 cannot be simplified into nice whole numbers.
3. To solve for y in the equation 6 / (y+1)(y+6) = 4 + 3/y + 6, you can start by simplifying the equation. Multiply both sides of the equation by (y+1)(y+6) to get rid of the denominator on the left side. This gives you 6 = 4(y+1)(y+6) + 3(y+6). Expanding and simplifying further, you have 6 = 4(y^2 + 7y + 6) + 3y + 18. Distributing the 4 on the right side gives you 6 = 4y^2 + 28y + 24 + 3y + 18. Combining like terms gives you 6 = 4y^2 + 31y + 42. Rearranging the equation to have everything on one side, you have 4y^2 + 31y + 42 - 6 = 0. Simplifying further, you get 4y^2 + 31y + 36 = 0. To solve this quadratic equation, you can either factor it or use the quadratic formula. Factoring the equation gives you (4y + 9)(y + 4) = 0. Setting each factor equal to zero gives you two possibilities: 4y + 9 = 0 or y + 4 = 0. Solving for y in each equation gives you y = -9/4 or y = -4.
I hope this helps! Let me know if you have any further questions.