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Find x when: (2^x)(e^(3x+1))=10. Give your answer in the form (a + ln(b)) / (c + ln(d)) , where a,b,c,d are integers.

First notice x is currently written as a power of 2 and 3x + 1 is written as a power of e, so we are going to need to use some sort of log to start getting x on its own. You can take a clue from the question...
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Answered by Thomas S. • Maths tutor
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The function f is defined for all real values of x as f(x) = c + 8x - x^2, where c is a constant. Given that the range of f is f(x) <= 19, find the value of c. Given instead that ff(2) = 8, find the possible values of c.

We know -x^2 has a maximum point of 0 at x=0, and -x^2 dominates the behaviour of f. We complete the square on this eqn, so we have f(x) = -(x - 4)^2 + 16 + c. We note that g(x) = -(x - 4)^2 has a maximum of...
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Answered by Sanmay K. • Maths tutor
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State the 3 different types of plate boundaries, and describe their movement.

Convergent - Where two plates collide together, and the crust is destroyed.2) Divergent - Where two plates move away from each other, and new crust is formed.3) Transform - Where the two plates slide past ea...
Answered by • Geology tutor
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Compare and contrast the structure and functions of DNA and RNA.

DNA and RNA are both essential components of cells, and thus life. The structure of DNA is similar to that of RNA in that these are both made of nucleotides, which in turn are made of the same basic units: a...
Answered by • Biology tutor
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Describe the processes involved in the absorption of the products of starch digestion

glucose moves in with sodium into epithelial cellvia carrier/channel protein sodium removed from epithelial cell by active transport/sodium-potassium pump into blood therefore maintaining low conc of sodium ...
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Answered by Mo B. • Biology tutor
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