scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. the temperature…

scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. the temperature of the gaseous planet varies linearly with the height of the atmosphere. the delicate instruments on board completely fail at a height of 61.5 kilometers. what is the approximate temperature at this altitude? (78.11 km, 567.00 k) (18.40 km, 147.54 k) a. 200 k b. 250 k c. 300 k d. 400 k e. 450 k

scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. the temperature of the gaseous planet varies linearly with the height of the atmosphere. the delicate instruments on board completely fail at a height of 61.5 kilometers. what is the approximate temperature at this altitude? (78.11 km, 567.00 k) (18.40 km, 147.54 k) a. 200 k b. 250 k c. 300 k d. 400 k e. 450 k

Answer

Explanation:

Step1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(18.40,147.54)$ and $(x_2,y_2)=(78.11,567.00)$. So, $m=\frac{567.00 - 147.54}{78.11 - 18.40}=\frac{419.46}{59.71}\approx7.03$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$. We use the point $(18.40,147.54)$ and $x = 61.5$. Then $y-147.54=7.03\times(61.5 - 18.40)$. First, calculate $61.5 - 18.40 = 43.1$. Then $7.03\times43.1 = 7.03\times(43+0.1)=7.03\times43+7.03\times0.1=(7 + 0.03)\times43+0.703=(7\times43+0.03\times43)+0.703=(301+1.29)+0.703 = 302.29+0.703=302.993$. Then $y=302.993 + 147.54=450.533\approx450$ K.

Answer:

E. 450 K