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The mass, m grams, of a substance is increasing exponentially so that the mass at time t hours is m=250e^(0.021t). Find the time taken for the mass to double in value.

All exponential equations can be reduced to the form m=m 0 e kt , where m 0 is the initial mass. This means for our equation the initial mass is 250g. If the mass has doubled in size, then m now equals 2*250...
TJ
Answered by Tom J. • Maths tutor
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How can I determine the stationary points of a curve and their nature?

For example, y = 3x 3 + 9x 2 + 2. Determine the stationary points and their nature. Let's remind ourselves what a stationary point is, and what is meant by the nature of the points. A stationary point is a p...
TD
Answered by Tutor87017 D. • Maths tutor
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Find all the solutions of 2 cos 2x = 1 – 2 sinx in the interval 0 ≤ x ≤ 360°.

We know that having cos and sin functions in a question is going to cause us problems - we need a single function of x. So, step 1, we need to rewrite sin or cos in terms of the other. How do we choose which...
NH
Answered by Nicola H. • Maths tutor
24432 Views

Find the indefinite integral of sin(2x)(cos^2(x)) with respect to x.

We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)). Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x). We can now split the integral into...
PP
Answered by Patrick P. • Maths tutor
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A hollow sphere of radius r is being filled with water. The surface area of a hemisphere is 3pi*r^2. Question: When the water is at height r, and filling at a rate of 4cm^3s^-1, what is dS/dT?

By the chain rule ds/dt = ds/dr * dr/dv * dv/t. At a height of r, the water fills a hemisphere. So ds/dr = 6pi r. dr/dv = 1/(dv/dr), so we need to find dv/dr. Students should have the formula for the volume ...
HB
Answered by Henry B. • Maths tutor
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