Question

The radius of Earth's moon is about (1 x 1,000) + (7 x 10) + (9 × 1) +(6 x T) miles. A moon for another planet has a different radius. That moon's radius is the same as Earth's moon except for the hundreds digit. The digit in the hundreds place for this planet’s moon’s radius is the same as the digit in the place that 1/10 the value of the hundred’s place in Earth’s moon radius. What is the radius of the other moon in standard form

Answer 1

The radius of the other moon is 1,709 miles when substituting the hundreds digit with 0, which is 1/10 of the hundreds digit of Earth's moon's radius.

Step-by-step explanation:

The radius of Earth's moon is given by the expression (1 x 1,000) + (7 x 10) + (9 × 1) + (6 x T) miles. In this expression, T represents an unspecified number. However, we know that the radius of Earth's moon is 1,737 miles, which means in this case, T would equal 1 (since 6 x 1 = 6). Now, we are asked to determine the radius of another moon where the hundreds digit is 1/10 of the hundreds digit of Earth's moon. Since the hundreds digit of Earth's moon is 3 (as in 1,737), this other moon's hundreds digit would be 0.1 x 3 = 0.

Therefore, the radius of the other moon in standard form, with the hundreds digit replaced by 0, would be (1 x 1,000) + (0 x 10) + (9 × 1) + (6 x 1) = 1,709 miles.

Answer 2

Given that the radius of the Earth's moon is

`(1*1000)+(7*10)+(9*1)+(6*(1)/(10))\text{ miles}`

This implies that the radius of the Earth's moon is

`\begin{gathered} (1000+70+9+0.6)miles \\ =1079.6\text{ miles} \end{gathered}`

If a moon for another planet has a different radius such that the moon's radius is same as the Earth's moon except for the hundreds digit.

Let x represent the hundreds digit of the moon's radius.

This implies that the radius of the planet's moon's radius is

`\begin{gathered} 1x79.6 \\ where \\ x\text{ is unknown} \end{gathered}`

If the digit in the hundreds place for the planet's moon's radius is same as the digit in the place that is 1/10 the value of the hundreds place in the Earth's moon's radius.

This implies that