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Exercises $45-48$ refer to the function $g d(y)=\tan ^{-1}(\sinh y),$ called the Gudermannian. In a map of the earth constructed by Mercator projection, points located y radial units from the equator correspond to points on the globe of latitude $g d(y) .$
Let $t(y)=\sinh ^{-1}(\tan y)$ Show that $t(y)$ is the inverse of $g d(y)$ for $0 \leq y < \pi / 2$

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So in the given question, we have three terms two times 10 of 75 by 64 times 10 of nine by by four and eight times 10 of five by 3, 10 of 10 by by three. And we are told to find what are these symptoms uh, farming are they're forming an A P a G p, an a G P or N H P. So what we can do first is to find the values of these terms. So we can write ton of seven by by six as ton of five plus by by six, Which is actually going to turn off by by six itself, which gives us the value of 2, 10 of 7, 5 x six as two divided by Route three. Since then, by way six is equal to one by Route three. Similarly, when we take four times 10 of nine by by four, we can write it as to buy blessed by by four rights and gives us four times turned off by by four ton of by by four is equal to one. So four times standby before is equal to four. Next we can take eight times three by plus by my three. We're just equal eight times turn off. Victory is equal to eight times square root of three Since stand off by by three NZ golden square root of three. So now when we it starts to by three four and 803 We can see that when we multiply two by rule three With two times through three we get four. And when we multiply four with two times through three we get eight through three. Right? So to route three actually asked us a combination of study storms which means The terms to buy route three four And 8-3 r. a. At this uh pregnant required answer. I hope you understand the government. Mhm.

In this problem, age I have four years of full, so I'm just writing the reaction here. Just look at it carefully. I fear so four plus Bs er, two will react to form B A and so forth and at fiesta food plus any edge. We will react to form f e o it 0.2. This is of white PPT. This is of white PPD. So according to the option option B it correct answer for this problem.

We have a number 18 inch figure is given and various options option from eight and is given. And we need to find the correct option against that. The a term given So we have been provided with we have been given toe. Ask the Tangent Tangent line named Attendant Line from this figure. So tenant line is that line which intersects the circle or touches the circle at one and only one point. So there is only there is Onley Point C on which it is intercepting. That is CF line segment cf is intercepting Onley at point C so CFL with attendant so option C often d g Sorry, g option is the correct option as it it indicates the line c f so Jill the correct answer. Thank