Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To solve this problem, we need to follow these steps systematically:
1. Understand the given relationship:
We know that [tex]\(\sqrt{q}\)[/tex] is inversely proportional to [tex]\(r\)[/tex]. This tells us that [tex]\(\sqrt{q} = \frac{k}{r}\)[/tex], where [tex]\(k\)[/tex] is a constant of proportionality.
2. Use the initial given values to find [tex]\(k\)[/tex]:
We are told that [tex]\(\sqrt{q} = 9\)[/tex] when [tex]\(r = 4\)[/tex]. Substituting these values into the equation, we get:
[tex]\[ 9 = \frac{k}{4} \][/tex]
To solve for [tex]\(k\)[/tex], we multiply both sides of the equation by 4:
[tex]\[ k = 9 \times 4 = 36 \][/tex]
3. Determine [tex]\(r\)[/tex] when [tex]\(q=4\)[/tex]:
First, find [tex]\(\sqrt{q}\)[/tex] for the new value of [tex]\(q\)[/tex]:
[tex]\[ \sqrt{q} = \sqrt{4} = 2 \][/tex]
4. Use the constant [tex]\(k\)[/tex] to find the new [tex]\(r\)[/tex]:
We now use the relationship [tex]\(\sqrt{q} = \frac{k}{r}\)[/tex]. Plugging in the value of [tex]\(\sqrt{q} = 2\)[/tex] and [tex]\(k = 36\)[/tex], we get:
[tex]\[ 2 = \frac{36}{r} \][/tex]
Solving for [tex]\(r\)[/tex], we multiply both sides of the equation by [tex]\(r\)[/tex]:
[tex]\[ 2r = 36 \][/tex]
Dividing both sides by 2, we get:
[tex]\[ r = \frac{36}{2} = 18 \][/tex]
Therefore, the value of [tex]\(r\)[/tex] when [tex]\(q = 4\)[/tex] is [tex]\(18\)[/tex].
1. Understand the given relationship:
We know that [tex]\(\sqrt{q}\)[/tex] is inversely proportional to [tex]\(r\)[/tex]. This tells us that [tex]\(\sqrt{q} = \frac{k}{r}\)[/tex], where [tex]\(k\)[/tex] is a constant of proportionality.
2. Use the initial given values to find [tex]\(k\)[/tex]:
We are told that [tex]\(\sqrt{q} = 9\)[/tex] when [tex]\(r = 4\)[/tex]. Substituting these values into the equation, we get:
[tex]\[ 9 = \frac{k}{4} \][/tex]
To solve for [tex]\(k\)[/tex], we multiply both sides of the equation by 4:
[tex]\[ k = 9 \times 4 = 36 \][/tex]
3. Determine [tex]\(r\)[/tex] when [tex]\(q=4\)[/tex]:
First, find [tex]\(\sqrt{q}\)[/tex] for the new value of [tex]\(q\)[/tex]:
[tex]\[ \sqrt{q} = \sqrt{4} = 2 \][/tex]
4. Use the constant [tex]\(k\)[/tex] to find the new [tex]\(r\)[/tex]:
We now use the relationship [tex]\(\sqrt{q} = \frac{k}{r}\)[/tex]. Plugging in the value of [tex]\(\sqrt{q} = 2\)[/tex] and [tex]\(k = 36\)[/tex], we get:
[tex]\[ 2 = \frac{36}{r} \][/tex]
Solving for [tex]\(r\)[/tex], we multiply both sides of the equation by [tex]\(r\)[/tex]:
[tex]\[ 2r = 36 \][/tex]
Dividing both sides by 2, we get:
[tex]\[ r = \frac{36}{2} = 18 \][/tex]
Therefore, the value of [tex]\(r\)[/tex] when [tex]\(q = 4\)[/tex] is [tex]\(18\)[/tex].
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.