Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. 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 given equation step-by-step using the provided values [tex]\( a = 4 \)[/tex] and [tex]\( b = \frac{9}{2} \)[/tex].
The equation provided is:
[tex]$ \frac{\sqrt{b}}{a} = a^2 \times \sqrt[4]{b} $[/tex]
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[ a = 4, \quad b = \frac{9}{2} \][/tex]
2. Calculate the value on the left-hand side (LHS):
[tex]\[ \frac{\sqrt{b}}{a} \][/tex]
- Find [tex]\(\sqrt{b}\)[/tex]:
[tex]\[ b = \frac{9}{2} \implies \sqrt{b} = \sqrt{\frac{9}{2}} = \frac{\sqrt{9}}{\sqrt{2}} = \frac{3}{\sqrt{2}} = \frac{3\sqrt{2}}{2} \][/tex]
- Then, divide by [tex]\(a\)[/tex]:
[tex]\[ \frac{\frac{3\sqrt{2}}{2}}{4} = \frac{3\sqrt{2}}{2 \times 4} = \frac{3\sqrt{2}}{8} \][/tex]
~ The numerical result of [tex]\( \frac{3\sqrt{2}}{8} \approx 0.5303300858899106 \)[/tex]
3. Calculate the value on the right-hand side (RHS):
[tex]\[ a^2 \times \sqrt[4]{b} \][/tex]
- Find [tex]\(a^2\)[/tex]:
[tex]\[ a = 4 \implies a^2 = 4^2 = 16 \][/tex]
- Find [tex]\(\sqrt[4]{b}\)[/tex]:
[tex]\[ \sqrt[4]{b} = \sqrt[4]{\frac{9}{2}} = \left(\frac{9}{2}\right)^{1/4} \][/tex]
~ Using approximation, [tex]\( \left(\frac{9}{2}\right)^{1/4} \approx 1.456253 - Multiply \(a^2\)[/tex] by [tex]\(\sqrt[4]{b}\)[/tex]:
[tex]\[ 16 \times 1.456253 = 23.303605041951524 \][/tex]
Thus, after solving the equations with the given values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we have:
[tex]\[ \left( \frac{\sqrt{b}}{a}, a^2 \times \sqrt[4]{b} \right) = \left( 0.5303300858899106, 23.303605041951524 \right) \][/tex]
The equation provided is:
[tex]$ \frac{\sqrt{b}}{a} = a^2 \times \sqrt[4]{b} $[/tex]
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[ a = 4, \quad b = \frac{9}{2} \][/tex]
2. Calculate the value on the left-hand side (LHS):
[tex]\[ \frac{\sqrt{b}}{a} \][/tex]
- Find [tex]\(\sqrt{b}\)[/tex]:
[tex]\[ b = \frac{9}{2} \implies \sqrt{b} = \sqrt{\frac{9}{2}} = \frac{\sqrt{9}}{\sqrt{2}} = \frac{3}{\sqrt{2}} = \frac{3\sqrt{2}}{2} \][/tex]
- Then, divide by [tex]\(a\)[/tex]:
[tex]\[ \frac{\frac{3\sqrt{2}}{2}}{4} = \frac{3\sqrt{2}}{2 \times 4} = \frac{3\sqrt{2}}{8} \][/tex]
~ The numerical result of [tex]\( \frac{3\sqrt{2}}{8} \approx 0.5303300858899106 \)[/tex]
3. Calculate the value on the right-hand side (RHS):
[tex]\[ a^2 \times \sqrt[4]{b} \][/tex]
- Find [tex]\(a^2\)[/tex]:
[tex]\[ a = 4 \implies a^2 = 4^2 = 16 \][/tex]
- Find [tex]\(\sqrt[4]{b}\)[/tex]:
[tex]\[ \sqrt[4]{b} = \sqrt[4]{\frac{9}{2}} = \left(\frac{9}{2}\right)^{1/4} \][/tex]
~ Using approximation, [tex]\( \left(\frac{9}{2}\right)^{1/4} \approx 1.456253 - Multiply \(a^2\)[/tex] by [tex]\(\sqrt[4]{b}\)[/tex]:
[tex]\[ 16 \times 1.456253 = 23.303605041951524 \][/tex]
Thus, after solving the equations with the given values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we have:
[tex]\[ \left( \frac{\sqrt{b}}{a}, a^2 \times \sqrt[4]{b} \right) = \left( 0.5303300858899106, 23.303605041951524 \right) \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.