Study Guide
13. An anerd is heading toward Wercury at a rate of 154 x 31 ^ 6 * mc / h * c the attend is 65mn * T ^ 2 miles away from Mercury how many hours will it be before it hits Mercury? Write the answer in scentfic notation, expressed to the exact decimal place
To find the number of hours it will take before the anerd hits Mercury, we need to divide the distance to Mercury by the speed of the anerd.
Given:
Speed of the anerd = 154 x 31^6 * mc/h * c (in miles per hour)
Distance to Mercury = 65mn * T^2 miles
To express the answer in scientific notation, we need to calculate the division and then convert it to scientific notation.
Let's start by calculating the division:
Time = Distance to Mercury / Speed of the anerd
Time = (65mn * T^2) / (154 x 31^6 * mc / h * c)
To simplify the units and values, let's convert 154 x 31^6 to scientific notation.
154 x 31^6 = 154 x (3.1 x 10^1)^6
= 154 x 3.1^6 x 10^(1 x 6)
= 154 x 3.1^6 x 10^6
≈ 154 x 8.76 x 10^6 (rounded to two decimal places)
Substituting this value into the equation:
Time ≈ (65mn * T^2) / (154 x 8.76 x 10^6 * mc / h * c)
= (65mn * T^2) / (1349040mn * mc / h * c)
= (65mn)/(1349040mn) * (T^2)/(mc/h * c)
The units "mn" in the numerator and denominator cancel out, as well as the units "mc" in the denominator and "c" in the numerator. This simplifies the equation to:
Time ≈ (65)/(1349040) * (T^2)/(h)
To express this value in scientific notation, we calculate the division:
Time ≈ (65)/(1349040) * (T^2)/(h)
= 4.82 x 10^(-8) * (T^2)/(h)
Therefore, the expression for the number of hours before the anerd hits Mercury, in scientific notation, is approximately 4.82 x 10^(-8) * (T^2)/(h).
To calculate the time it will take for the anerd to hit Mercury, we need to divide the distance to Mercury by the speed of the anerd. Let's break down the given values:
Speed of the anerd = 154 x 31^6 * mc / h * c
Distance to Mercury = 65mn * T^2
Now, let's substitute the given values into the equation to calculate the time:
Time = Distance / Speed
Time = (65mn * T^2) / (154 x 31^6 * mc / h * c)
To express the answer in scientific notation, we'll simplify the equation:
Time = (6.5 x 10^1 x T^2) / (1.54 x 10^2 x 31^6 x mc / h x c)
Now, let's rearrange the equation and simplify further:
Time = (6.5 x 1.54 x 10^1 x T^2) / (31^6 x mc / h x c)
Time = (1.0011 x 10^2 x T^2) / (31^6 x mc / h x c)
Therefore, the time it will take for the anerd to hit Mercury can be expressed as 1.0011 x 10^2 x T^2 / (31^6 x mc / h x c) hours.
To find out how many hours it will take for the anerd to hit Mercury, we need to divide the distance to Mercury by the rate at which the anerd is heading towards it.
Given:
Rate = 154 x 31 ^ 6 * mc / h * c
Distance = 65mn * T ^ 2 miles
To convert the distance to scientific notation, we need to express it in the form of a number between 1 and 10 multiplied by 10 raised to a certain power.
65 million (mn) = 65,000,000 = 6.5 x 10^7 (converted to scientific notation)
T^2 = T * T
Combining the given values:
Distance = 6.5 x 10^7 * T^2 miles
Now, to calculate the time it will take for the anerd to hit Mercury, we divide the distance by the rate:
Time = Distance / Rate
Time = (6.5 x 10^7 * T^2) / (154 x 31 ^ 6 * mc / h * c)
Since the problem states to express the answer in scientific notation with the exact decimal place, we will simplify the equation and present the answer in that format:
Time = (6.5 x 10^7 * T^2) / (4.7745 x 10^24 * mc)
Dividing the exponents, we have:
Time = 1.36 x 10^(7 - 24) * T^2 / mc
Time = 1.36 x 10^-17 * T^2 / mc
Therefore, the time it will take for the anerd to hit Mercury can be expressed as 1.36 x 10^-17 * T^2 / mc hours (in scientific notation, expressed to the exact decimal place).