Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Sure, let's solve the equation [tex]\( V = \sqrt[3]{\frac{a x^2 h}{b - h}} \)[/tex] for [tex]\( h \)[/tex]. Follow these steps:
1. Given the equation:
[tex]\[ V = \sqrt[3]{\frac{a x^2 h}{b - h}} \][/tex]
2. To eliminate the cube root, cube both sides of the equation:
[tex]\[ V^3 = \left( \sqrt[3]{\frac{a x^2 h}{b - h}} \right)^3 \][/tex]
[tex]\[ V^3 = \frac{a x^2 h}{b - h} \][/tex]
3. Now, to isolate [tex]\( h \)[/tex] on one side, multiply both sides of the equation by [tex]\( b - h \)[/tex]:
[tex]\[ V^3 (b - h) = a x^2 h \][/tex]
4. Distribute [tex]\( V^3 \)[/tex] on the left-hand side:
[tex]\[ V^3 b - V^3 h = a x^2 h \][/tex]
5. Gather all terms involving [tex]\( h \)[/tex] on one side of the equation:
[tex]\[ V^3 b = a x^2 h + V^3 h \][/tex]
6. Factor out [tex]\( h \)[/tex] from the terms on the right-hand side:
[tex]\[ V^3 b = h (a x^2 + V^3) \][/tex]
7. Finally, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( a x^2 + V^3 \)[/tex]:
[tex]\[ h = \frac{V^3 b}{a x^2 + V^3} \][/tex]
Hence, the value of [tex]\( h \)[/tex] expressed in terms of [tex]\( V \)[/tex], [tex]\( a \)[/tex], [tex]\( x \)[/tex], and [tex]\( b \)[/tex] is:
[tex]\[ h = \frac{V^3 b}{a x^2 + V^3} \][/tex]
1. Given the equation:
[tex]\[ V = \sqrt[3]{\frac{a x^2 h}{b - h}} \][/tex]
2. To eliminate the cube root, cube both sides of the equation:
[tex]\[ V^3 = \left( \sqrt[3]{\frac{a x^2 h}{b - h}} \right)^3 \][/tex]
[tex]\[ V^3 = \frac{a x^2 h}{b - h} \][/tex]
3. Now, to isolate [tex]\( h \)[/tex] on one side, multiply both sides of the equation by [tex]\( b - h \)[/tex]:
[tex]\[ V^3 (b - h) = a x^2 h \][/tex]
4. Distribute [tex]\( V^3 \)[/tex] on the left-hand side:
[tex]\[ V^3 b - V^3 h = a x^2 h \][/tex]
5. Gather all terms involving [tex]\( h \)[/tex] on one side of the equation:
[tex]\[ V^3 b = a x^2 h + V^3 h \][/tex]
6. Factor out [tex]\( h \)[/tex] from the terms on the right-hand side:
[tex]\[ V^3 b = h (a x^2 + V^3) \][/tex]
7. Finally, solve for [tex]\( h \)[/tex] by dividing both sides by [tex]\( a x^2 + V^3 \)[/tex]:
[tex]\[ h = \frac{V^3 b}{a x^2 + V^3} \][/tex]
Hence, the value of [tex]\( h \)[/tex] expressed in terms of [tex]\( V \)[/tex], [tex]\( a \)[/tex], [tex]\( x \)[/tex], and [tex]\( b \)[/tex] is:
[tex]\[ h = \frac{V^3 b}{a x^2 + V^3} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.