Answer:
The temperature is [tex]T_t = 65 ^oF[/tex]
Step-by-step explanation:
From the question we are told that
The elevation of the palm spring is [tex]E_1 = 500 \ ft[/tex]
The temperature is [tex]T = 100 ^oF[/tex]
The elevation of the mountain Mt. San Jacinto is [tex]E_2 = 10500 ft[/tex]
Gnerally the difference in elevation between the land of the palm spring CA and the mountain is mathematically evaluated as
[tex]\Delta E = E_2 - E_1[/tex]
=> [tex]\Delta E = 10500 - 500[/tex]
=> [tex]\Delta E = 10000 \ ft[/tex]
Gnerally the rate of decrease in temperature with increase in height is
[tex]R = \frac{3.5 \ ^oF }{ 1000\ ft }[/tex]
Gnerally the decreases in temperature for the evaluated difference in elevation is mathematically represented as
[tex]D = \Delta E * R[/tex]
=> [tex]D = 10000 * \frac{3.5}{1000}[/tex]
=> [tex]D = 35^oF[/tex]
Gnerally the temperature at the top of the mountain is
[tex]T_t = T - D[/tex]
=> [tex]T_t = 100 - 35[/tex]
=> [tex]T_t = 65 ^oF[/tex]