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Q: What is the derivative of f plus g of 3 and f times g of 3 given that f of 3 equals 5 d dx f of 3 equals 1.1 g of 3 equals -4 d dx g of 3 equals 7 Also please explain QUICK THANK YOU?

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80 x 6 = 480 take away 1 x 6 leaves 474. There's always a quick way!

not sure exaclty what you asking, but if ur asking for an example of what logarithms are used for in real life, then there are a heaps of examples. briefly, some examples are banks use logarithmic functions to calculate the accumilation of interest in bank accounts over the years (eg. Interest = xyz^0.01k), engineers use it to determine how quick things dry/cool down, etc. if u want a proper algebratic example, here is newtons law of cooling which is: y=yi x e^-kt where: y - different between temprature of body and the constant temp of room yi - initial temprature difference of body and room e - eulers number (2.718...) t - time in mins k - constant for that particular body (usually what u are trying to find out in class tasks) using logarithms, newtons law can predict how how a body (such as cup of coffee) will be after any given period of time. This was the most practicle example i could think of ;) Nick

YES! Simply by taking a quick glance at a graph, you can see several characteristics of the function: local minimums/maximums, points of inflection, end behavior, asymptotes, etc etc... If you wanted to find these without the graph, you would have to do some math which might end up being very time consuming for very complicated functions. Even worse: what if the function is not elementary, and you can't express it in terms of finite arithmetic operations?

When a number "goes evenly" into another number, we just say that number divides another number. Example: 2 divides 102. This is denoted with a vertical bar, "|", e.g. 2|102The number is even, so 2 divides 102.Quick lesson on digital roots. Digital roots are summing the digits of a number, until you are left with a single digit.Example: Find the digital root of 9939 + 9 + 3 = 21 (not a single digit, repeat the process)2 + 1 = 3Therefore, the digital root of 993 is 3.Now this is where digital roots come in handy:If the digital root of a number is equal to 3, 6, or 9 then 3 divides that number.If the digital root of a number is equal to 3, 6, or 9 AND is even then 6 divides that number.If the digital root of a number is equal to 9, then 9 divides it.The digital root of 102 is 1+0+2=3 and 102 is even.So 3|102 and 6|102102/2 = 51, therefore 51|102102/3 = 34, therefore 34|102102/6 = 17, therefore 17|102Numbers that evenly go into 102 are:2, 3, 6, 17, 34, and 51 (1 and 102 can also be included)

Your question is fairly vague, but I'm interpreting it as:What is the range of y=12cos(x)?Shortform:-1212(pi)/6-->6sqrt(3)~10.392(pi)/4-->6sqrt(2)~8.485(pi)/3-->6(pi)/2-->02(pi)/3-->-63(pi)/4-->-6sqrt(2)~-8.4855(pi)/6-->-6sqrt(3)~-10.392(pi)-->-12If you continue this, you'll notice that the values keep switching back and forth from 12 to -12 then back to 12, passing through all the values in between. This is to be expected, because if you look at the graph of cosine (as well as sine), it oscillates back and forth between two values, giving it a wave-like appearance. From this you can easily surmise that the maximum value that 12cos(x) will ever reach is 12 and the minimum it will ever reach is -12, giving you the range [-12,12].Conceptually, if you examine just the function cos(x), you realize that it oscillates back and forth between -1 and 1. So the function 12cos(x) will just take whatever results from cos(x) and multiply it by 12. Since the range of cos(x) is [-1,1], the range of 12cos(x) will just be 12 times the range of cos(x), [-12,12]. This works for any numerical amplitude modification of a sine or cosine function (putting a number in front of the function). The range of 5cos(x) would be [-5,5], the range of (pi)cos(x) would be [-(pi),(pi)], and so on for any real number.

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