CPhill

10^(10^100)

This number is so large, that it can't be physically written out.......if we made each zero the size of your garden-variety atom, there wouldn't be enough room on the Earth's surface to write it out......and we wouldn't live long enough to do so, anyway....

You have the correct set up....just make sure your calculator is in degree mode......your answer will reflect some angle......

2.528 X 10⁶

Remember, in scientific notation, we move the decimal one place to the right of the first non-zero digit. Then we count how many places we move it. Moving it to the left results in a positive exponent on "10" equal to the number of places we moved it. Moving it to the right results in a negative exponent on "10" equal to the places we moved it.

Your "set-up" is almost correct.....

But what does the tangent involve??   opposite and adjacent

And what are we looking for?? the hypoteneuse ....the length of the wire

What do we know??  an angle and the opposite side

And what function relates the opposite side and the hypoteneuse??

See if you can take it from here...

(I find it's helpful to draw a picture...also.....make sure you know your basic identities!!)

Good job, Anonymous....we could also express the answer as -15/8 if we wanted it in a "fractional" form....

Using the tangent, we have

tan(53°) = x/50   where x is the height of the tree

x = 50tan(53°) = about 66.35 ft. = 66ft.

We have

y = ab^x   ....   and we need to find a and b

So, using (0,5)  we have

5 = ab⁰

5 = a

And using (1, 15), we have

15 = 5b¹

15 = 5b     divide by 5 on both sides

b = 3        So our function is

y = (5)3^x

Since we know an angle and an adjacent side, we can use the cosine function to find the ladder length (the hypoteneuse), and we have......

cos(68°) = 12/x ............ where x is the ladder length

So......

x = 12/ cos(68°) = about 33.03 ft. = 33 ft.

Well...if the water level rose by 200 ml, each of the 4 golf b***s must have contributed to a 50ml rise.......thus, the volume of a single ball must be 50 ml.

This looks like some sort of "decay" function, so I'm going to assume you might mean.........

t(20)=16e^(-0.034x)

So, we're just putting "20" into the function to get an evaluation

So we have

$${\mathtt{16}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\mathtt{0.034}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)} = {\mathtt{8.105\: \!871\: \!877\: \!849\: \!435\: \!2}}$$