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? a. 200 k b. 250 k c. 300 k d. 400 k e. 450 k

E. 450 K

Explanation:

It is given that the temperature of the gaseous planet is linearly related with height of the atmosphere. we can write this in the mathematical equation:

y = m x +c

where y is the temperature values, x is height, m is the slope and c is the y-intercept. we have been given two sets of value in the image, using which we can find the value of slope in y-intercept.

at x = 18.40 km, y = 147.54 K

⇒147.54 = 18.40 m + c      

⇒c = 147.54 - 18.40 m  ..(1)

at x =78.11 km, y = 567.00 K

⇒567.00 =78.11 m + c       ..(2)

Put equation 1 in 2 and solve:

⇒567.00 =78.11 m + 147.54 - 18.40 m

⇒419.46 = 59.71 m

⇒ m =419.46 ÷59.71 = 7.025 K/km

c = 147.54 - 18.40 × 7.025 = 18.28 K

At height, x = 61.5 km the approximate temperature is :

y = 7.025 K/km ×  61.5 km + 18.28 K = 450.3 K

Thus, the approximate temperature at altitude 61.5 km is 450 K.

force tends to be low and long diustance masses are high

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2