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23)
you need to first differentiate 0.1t^2 so you get 0.2t. Then simply sub in t=0.5 and get your first answer and then t=1.5 for your other answer.
Seeing as this is a circular stain, the area is (Pi r^2). And given r=x=0.1t^2, sub it in. so you ger A= pi(0.1t^2)^2. Then solve the bracket to give A=(pi t^4)/100. Then sub in the two values you got when you differentiated the radius expression into the area formula and you wll get your two ansters for the area at t=0.5 and t=1.5.
24)
The SA of a sphere is 4pi r^2. Sub x into the area formula. Th differentiate it and sub in t=3 into the SA foruula after differentiation. The Volume of a sphere is (4/3)pir^3. Sub in x, then differentiate and sub in t=3 also to get your Volume at t=3.
Graphically, they are asking you to find the tangent to the curve of the volume and SA of a sphere at t=3. To work out the tangent, you need to differentiate the equation for the cirve and then sub in the t value, as you are doing in this case.
Hope it was helpful.
Angs
you need to first differentiate 0.1t^2 so you get 0.2t. Then simply sub in t=0.5 and get your first answer and then t=1.5 for your other answer.
Seeing as this is a circular stain, the area is (Pi r^2). And given r=x=0.1t^2, sub it in. so you ger A= pi(0.1t^2)^2. Then solve the bracket to give A=(pi t^4)/100. Then sub in the two values you got when you differentiated the radius expression into the area formula and you wll get your two ansters for the area at t=0.5 and t=1.5.
24)
The SA of a sphere is 4pi r^2. Sub x into the area formula. Th differentiate it and sub in t=3 into the SA foruula after differentiation. The Volume of a sphere is (4/3)pir^3. Sub in x, then differentiate and sub in t=3 also to get your Volume at t=3.
Graphically, they are asking you to find the tangent to the curve of the volume and SA of a sphere at t=3. To work out the tangent, you need to differentiate the equation for the cirve and then sub in the t value, as you are doing in this case.
Hope it was helpful.
Angs
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