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The number of bacteria present in a culture at time t hours is modeled by the continuous variable N and the relationship N = 2000e^kt, where k is a constant. Given that when t = 3, N = 18 000, find (a) the value of k to 3 significant figures

putting in the conditions: 18000 = 2000e^3k .. ln(9) = 3k .. k=(1/3)ln(9)

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A speaker emits a sound wave through a metallic block, with a speed of 0.42 km/s, and a frequency of 16kHz. Calculate the wavelength to 3.s.f. Describe the characteristics of a longitudinal wave.

Firstly the values should be converted into more comfortable units. 0.42km/s = 420m/s, and 16kHz = 16,000Hz. Next, use the equation wavelength = speed/frequency This gives wavelength = 420m/s over 16,000/...

Answered by Joseph B. • Physics tutor

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A circle has the equation x^2 + y^2 - 4x + 10y - 115 = 0. Express the equation in the form (x - a)^2 + (y - b)^2 = k, and find the centre and radius of the circle.

Rearrange the equation so that the x terms and y terms bracketed together, like so: (x^2 - 4x) + (y^2 + 10y) - 115 = 0. Complete the square on both sets of brackets, giving (x - 2)^2 - 4 + (y + 5)^2 - 25 ...

Answered by Joseph B. • Maths tutor

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When do I use the preterite and when do I use the imperfect?

If you imagine a timeline (would draw out a line on the whiteboard here), the imperfect appears at some extended period over this. It is important to remember that the imperfect encompasses the ideas: som...

Answered by Paddy S. • Spanish tutor

1635 Views

How do I include quotations in essays?

There are several ways of including quotations in essays. I believe the best way is to use lots of quotations and ensure that they are embedded in your answer as to keep the argument smooth. Here is a goo...

Answered by Paddy S. • English Literature tutor

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