Determine the $t$ -coordinate of $Q$ , giving your answer in the form $aln⁡5+bcln⁡5+d\frac{a \ln 5 + b}{c \ln 5 + d}$ where $a, b, c,$ and $d$ are integers to be found.

[4]

1.9.16 Implicit differentiation (A-level only) Questions

A Level
Maths
1.9.16 Implicit differentiation (A-level only)

A Level
Maths OCR (MEI)
Question bank

1.9.16 Implicit differentiation (A-level only)

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Question 28

The thermal profile of a synthetic crystal is modeled by the equation

5^t - 3tT + T^2 = 23, \quad T \ge 0

where $T$ is the temperature in degrees Celsius and $t$ is the time in hours. A specific observation point $P$ on the profile has $t = 1$ .

Find the temperature $T$ at point $P$ .

[2]

Find an expression for $dTdt\frac{dT}{dt}$ in terms of $T$ and $t$ .

[3]

The tangent to the profile at point $P$ intersects the horizontal $t$ -axis at point $Q$ .

Determine the $t$ -coordinate of $Q$ , giving your answer in the form $aln⁡5+bcln⁡5+d\frac{a \ln 5 + b}{c \ln 5 + d}$ where $a, b, c,$ and $d$ are integers to be found.

[4]

1.9.16 Implicit differentiation (A-level only) Questions

A Level
Maths
1.9.16 Implicit differentiation (A-level only)