Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A 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 this question step-by-step:
1. Identify the Given Information:
- Dog's weight, [tex]\( w = 35 \)[/tex] pounds.
- The formula for the effective dosage, [tex]\( d \geq \frac{1}{5} w^2 \)[/tex].
2. Calculate the Effective Dosage:
Substitute [tex]\( w = 35 \)[/tex] into the formula:
[tex]\[ d \geq \frac{1}{5} \times (35)^2 \][/tex]
Calculate [tex]\( (35)^2 \)[/tex]:
[tex]\[ 35 \times 35 = 1225 \][/tex]
Now, calculate [tex]\( \frac{1}{5} \)[/tex] of 1225:
[tex]\[ \frac{1}{5} \times 1225 = \frac{1225}{5} = 245 \][/tex]
Therefore, the effective dosage is:
[tex]\[ d \geq 245 \text{ milligrams} \][/tex]
3. Evaluate Each Ordered Pair:
- Option A: [tex]\( (35, 260) \)[/tex]
Here, the dosage [tex]\( d = 260 \)[/tex].
Check if [tex]\( 260 \geq 245 \)[/tex]:
[tex]\[ 260 \geq 245 \quad \text{(True)} \][/tex]
This pair provides an effective dosage.
- Option B: [tex]\( (240, 35) \)[/tex]
Here, the dosage [tex]\( d = 240 \)[/tex].
Check if [tex]\( 240 \geq 245 \)[/tex]:
[tex]\[ 240 \geq 245 \quad \text{(False)} \][/tex]
This pair does not provide an effective dosage.
- Option C: [tex]\( (260, 35) \)[/tex]
Here, the dosage [tex]\( d = 260 \)[/tex].
Check if [tex]\( 260 \geq 245 \)[/tex]:
[tex]\[ 260 \geq 245 \quad \text{(True)} \][/tex]
This pair provides an effective dosage.
- Option D: [tex]\( (35, 240) \)[/tex]
Here, the dosage [tex]\( d = 240 \)[/tex].
Check if [tex]\( 240 \geq 245 \)[/tex]:
[tex]\[ 240 \geq 245 \quad \text{(False)} \][/tex]
This pair does not provide an effective dosage.
4. Conclusion:
Based on the calculations, the ordered pairs that give an effective dosage of antibiotics for a 35-pound dog are:
- Option A: [tex]\( (35, 260) \)[/tex]
- Option C: [tex]\( (260, 35) \)[/tex]
Therefore, the answer is:
- A) [tex]\( (35, 260) \)[/tex]
- C) [tex]\( (260, 35) \)[/tex]
1. Identify the Given Information:
- Dog's weight, [tex]\( w = 35 \)[/tex] pounds.
- The formula for the effective dosage, [tex]\( d \geq \frac{1}{5} w^2 \)[/tex].
2. Calculate the Effective Dosage:
Substitute [tex]\( w = 35 \)[/tex] into the formula:
[tex]\[ d \geq \frac{1}{5} \times (35)^2 \][/tex]
Calculate [tex]\( (35)^2 \)[/tex]:
[tex]\[ 35 \times 35 = 1225 \][/tex]
Now, calculate [tex]\( \frac{1}{5} \)[/tex] of 1225:
[tex]\[ \frac{1}{5} \times 1225 = \frac{1225}{5} = 245 \][/tex]
Therefore, the effective dosage is:
[tex]\[ d \geq 245 \text{ milligrams} \][/tex]
3. Evaluate Each Ordered Pair:
- Option A: [tex]\( (35, 260) \)[/tex]
Here, the dosage [tex]\( d = 260 \)[/tex].
Check if [tex]\( 260 \geq 245 \)[/tex]:
[tex]\[ 260 \geq 245 \quad \text{(True)} \][/tex]
This pair provides an effective dosage.
- Option B: [tex]\( (240, 35) \)[/tex]
Here, the dosage [tex]\( d = 240 \)[/tex].
Check if [tex]\( 240 \geq 245 \)[/tex]:
[tex]\[ 240 \geq 245 \quad \text{(False)} \][/tex]
This pair does not provide an effective dosage.
- Option C: [tex]\( (260, 35) \)[/tex]
Here, the dosage [tex]\( d = 260 \)[/tex].
Check if [tex]\( 260 \geq 245 \)[/tex]:
[tex]\[ 260 \geq 245 \quad \text{(True)} \][/tex]
This pair provides an effective dosage.
- Option D: [tex]\( (35, 240) \)[/tex]
Here, the dosage [tex]\( d = 240 \)[/tex].
Check if [tex]\( 240 \geq 245 \)[/tex]:
[tex]\[ 240 \geq 245 \quad \text{(False)} \][/tex]
This pair does not provide an effective dosage.
4. Conclusion:
Based on the calculations, the ordered pairs that give an effective dosage of antibiotics for a 35-pound dog are:
- Option A: [tex]\( (35, 260) \)[/tex]
- Option C: [tex]\( (260, 35) \)[/tex]
Therefore, the answer is:
- A) [tex]\( (35, 260) \)[/tex]
- C) [tex]\( (260, 35) \)[/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.