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Patient G was taking the drug every 8 hours and the total amount of DGMM present in his blood can be modelled by the trigonometric equation $g=-250\cos(\pi/4 × t) + 250$, where $g$ is measured in milligrams and $t$ is the time in hours since first taking the drug.
Patient H was taking a higher dosage of the drug but less often at 12 hourly intervals. The total amount of DGMM present in her blood peaked at 900 milligrams before returning to zero. It was noted by Dr George that it took half an hour from taking the drug before Patient H began to absorb any DGMM into the blood stream.
1.Find when the amount of DGMM in Patient G was first recorded at 400 milligrams.
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Find a mathematical model for the amount of DGMM in Patient H.
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Find when Patient G and Patient H both, at the same time, have at least 400 milligrams of DGMM in their blood if they begin taking their medicine together. Write everything in latex format. Give valid answer
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