Question

lesson practice 7.3.07 name date period problems 6–7: the radius of earth is approximately 6,400 kilometers. the equator is the circle around earth that divides it into the northern and southern hemispheres. 6. is the circumference of a circle or the area of a circle more useful for finding the length of the equator? 7. what is the length of the equator? spiral review problems 8–10: this graph shows a proportional relationship between the number of hours a manufacturing factory is in operation and the number of kilowatt-hours (kwh) of electricity used. use the graph to determine whether each statement is true or false. 8. point f represents the number of kilowatt-hours of electricity used when the factory is in operation for 3 hours. 9. the factory uses 6 kilowatt-hours of electricity when it is in operation for 600 hours. 10. the factory uses 700 kilowatt-hours of electricity when it is in operation for 7 hours.

Explanation:

Step1: Answer Q6 (Identify relevant measure)

The equator is a circle's length, so circumference is useful.

Step2: Calculate equator length (Q7)

Use circumference formula $C=2\pi r$. Substitute $r=6400$ km:
$C=2\times\pi\times6400 = 12800\pi \approx 40212.39$ km

Step3: Analyze point F (Q8)

Point F is at $(3, 300)$: 3 hours = 300 kWh. Statement is true.

Step4: Check 600 hours usage (Q9)

From graph, rate is $\frac{300}{3}=100$ kWh/hour. For 600 hours: $600\times100=60000$ kWh. Statement is false.

Step5: Check 7 hours usage (Q10)

Use rate 100 kWh/hour: $7\times100=700$ kWh. Statement is true.

Answer:

1. The circumference of a circle
2. Approximately $40212.39$ kilometers (or $12800\pi$ kilometers)
3. True
4. False
5. True