Q: Assume that y varies inversely with x and that y is 2 when x is 4 what is the equation of inverse variation?

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If we assume a constant inverse relationship then we can start with the equation y = c/x where c is the constant of proportionality. Plugging in the known values of x = 7 and y = 5 we determine that c = 35. We now have the equation of y = 35/x. Plugging in 4 for x we see that y = 35/4 = 8.75.

Yes, that's how it is done. Assuming the contrary should eventually lead you to some contradiction.

Log 200=a can be converted to an exponential equation if we know the base of the log. Let's assume it is 10 and you can change the answer accordingly if it is something else. 10^a=200 would be the exponential equation. For a base b, we would have b^a=200

I assume there are a missing + and =, that is the equation is either:3x + 5y = 53x = 5y + 5(though the first is the most likely).They are both the equation of a straight line.

No. Variance and standard deviation are dependent on, but calculated irrespective of the data. You do, of course, have to have some variation, otherwise, the variance and standard deviation will be zero.

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If we assume a constant inverse relationship then we can start with the equation y = c/x where c is the constant of proportionality. Plugging in the known values of x = 7 and y = 5 we determine that c = 35. We now have the equation of y = 35/x. Plugging in 4 for x we see that y = 35/4 = 8.75.

I assume you mean the opposite of a synonym. The opposite of a synonym is an antonym.

I assume you mean the additive inverse. The sum of any number and its additive inverse is zero. For example, 7 + (-7) = 0.

assume its not. make two cases show that the two cases are equal

Answer this question… Which term best describes a proof in which you assume the opposite of what you want to prove?

Assume that f:S->T is invertible with inverse g:T->S, then by definition of invertible mappings f*g=i(S) and g*f=i(T), which defines f as the inverse of g. So g is invertible.

Reactance of capacitor is inversely proportional to frequency. I should not need to write the exact equation here, its in your textbook. All you need is that its inversely proportional to frequency for proof.We will now assume an ideal capacitor to keep the analysis simple.at DC the frequency is zero, the inverse of this is infinite reactance: open circuitat low frequency AC frequency is low, the inverse of this is high reactanceat midrange frequency AC frequency is midrange, the inverse of this is midrange reactanceat high frequency AC frequency is high, the inverse of this is low reactanceat infinite frequency AC frequency is infinite, the inverse of this is zero reactance: short circuitThis disproves your original statement as written, except for the special cases of DC and infinite frequency AC (which does not occur), for ideal capacitors.As all real capacitors are nonideal, they have leakage resistance. This means that even for the special case of DC the capacitor is not a true open circuit, just a very high resistance resistor. Which also disproves it for the remaining case of DC in real capacitors.

No, not at all!I'll assume you mean the additive inverse, although the following examples can be adapted to the multiplicative inverse as well.The additive inverse of 5 is -5, and 5 is indeed greater than -5.However, the additive inverse of -5 is 5, and -5 is SMALLER than 5.

I assume you mean, in an equation. Such a number is called a "solution" or a "root" of the equation.

It depends on what the equation is for: area, perimeter, diagonal or something else. You cannot assume that someone else knows what equation you mean.

I believe it was estimated to be around 8.14 for most of it's lengths, but I have to assume that there is wide variation