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]
