Question

the temperature T, in degrees Celsius, is a function of d, the distance, in kilometres, below the earths surface. This relation can be modelled by the equation T(d)=10d+20


a) Determine T(5) AND explain what this value means in this context.


b) Determine d when T(d)=50 AND explain what this value means in this context.

Answer 1

Given :- T(d)=10d+20 .

To Find :-

• T(5) and d when T(d) is 50 .

Answer :-

→ T(d) = 10d + 20

→ T(1) = 10 * 1 + 20 = 10 + 20 = 30

→ T(2) = 10 * 2 + 20 = 20 + 20 = 40

so,

→ T(5) = 10 * 5 + 20 = 50 + 20 = 70 .

now,

→ T(d) = 50

then,

→ 50 = 10d + 20

→ 50 - 20 = 10d

→ 30 = 10d

→ d = 3 .

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Answer 2

SOLUTION

GIVEN

The temperature T, in degrees Celsius, is a function of d, the distance, in kilometres, below the earths surface. This relation can be modelled by the equation

T(d) = 10d + 20

TO DETERMINE

a) Determine T(5) and explain what this value means in this context.

b) Determine d when T(d)=50 and explain what this value means in this context.

EVALUATION

Here it is given that the temperature T, in degrees Celsius, is a function of d, the distance, in kilometres, below the earths surface.

Now this relation can be modelled by the equation

T(d) = 10d + 20 - - - - - (1)

a) We have to find T(5)

From Equation 1 we get by putting d = 5

$\sf{T(5) = (10 \times 5) + 20}$

$\sf{ \implies \: T(5) = 50 + 20}$

$\sf{ \implies \: T(5) =70}$

Hence T(5) = 70

The above value means that 5 km below the earth surface the temperature is 70°C

b) We have to find the distance d when T(d) = 50

Now T(d) = 50 gives

$\sf{ \implies \: 50 = 10d + 20}$

$\sf{ \implies \: 10d + 20 = 50}$

$\sf{ \implies \: 10d = 30}$

$\sf{ \implies \: d = 3}$

Hence the value of d = 3 when T(d) = 50

The above value means that 3 km below the earth surface the temperature is 50°C

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