Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>
Step-by-step explanation:
Given the function j(x) = 11.6
and k(x) = 
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) = are inverse functions.
She will need 5 fluid ounces to make purple paint hope that will hope you if not I'm sorry
Answer:
C. (18+4)
Step-by-step explanation:
The answer on ed
C is the answer because a number of children are unknown.
Answer:
He'll need 288 cups to make a waffle on his 24 foot diameter circular griddle.
Step-by-step explanation:
In order to find out how much batter Danny needs we first need to compute the area of the first pans, since it is a circular pan their area is given by A = 2*pi*r. So we have:
Area of the first pan = 2*pi*(6/2) = 18.84 square inches
Area of the second pan = 2*pi*(24/2) = 75.36 square foots
We now need to convert these values to be in the same unit, we'll convert from square foots to square inches:
Area of the second pan = 75.36 * (12)^2 = 10851.84 square inches
We can now use a proportion knowing that the batter and the thickness of the waffles are the same. If 0.5 cup of flour can make a waffle on 18.84 square inches then x cup of flour can make a waffle on 10851.85 square inches. Writing this in a mathematical form, we have:
0.5/x = 18.84/10851.84
18.84x = 0.5*10851.85
x = 10851.85*0.5/18.84 =288 cups
