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Solve the following, giving your answers in terms of ln a: 7 sechx - tanhx =5

7sechx - tanhx = 5 7/coshx - sinhx/coshx = 5 7 - sinhx = 5 cosh x 7 - 0.5(e x - e -x ) = 2.5(e x + e -x ) 7 -0.5e x + 0.5e -x = 2.5e x + 2.5e -x 0 = 3e x - 7 + 2e -x 0 = 3e 2x - 7e x + 2 0 = (3e x - 1)(e x -...
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Differentiate the following: 3/2 x^(3/4) + 1/3 x^(-1/4)

In simple differentiation, we can use the fact that if y= x^n, dy/dx is equal to nx^(n-1). In other words, multiply the x term by the power, then decrease the power by 1. Here we have 2 terms so approach the...
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Answered by Alex W. • Maths tutor
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Find the Lowest common multiple of 96 and 132

First, split into prime factors- 96= 2^5 * 3 and 132= 2^2 * 3 * 11 Whilst very similar to highest common factor, lowest common multiple is found by comparing the two sets of prime factors, and for each prime...
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Answered by Alex W. • Maths tutor
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What is the ontological argument and its features?

The Ontological Argument (OA) is related to the nature and essence of an object and this argument attempts to prove that God must exist by his very nature. Many philosophers formulate theories to support thi...
SF
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There are n sweets in a bag, 6 of which are orange. If the probablility of eating 2 orange sweets from the bag, one after the other, is 1/3, show that n^2 - n - 90 = 0. State any assumptions made.

We are assuming that the sweets are selected at random. The question says that the sweets are eaten, so we are also assuming that they aren't put back into the bag. The total probability of selecting the two...
JB
Answered by James B. • Maths tutor
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