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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]
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