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Can't read your LaTex !!

The totel surface of the cylinder:

Write this as tanθ - 2cosθtanθ = 0  or tanθ(1 - 2cosθ) = 0

So, either tanθ = 0  or  1 - 2cosθ = 0

Can you take it from here?

These might help:

YES THANK YOU SO MUCH

Use arctan (or atan on many calcuators).

The length of a rectangle is 9 centimeters less than the width. what are the dimensions of the rectangle if it’s area is 162 square centimeters

Here are parts 2 and 3:

so from what i got, dont blame me if im wrong but so the width is 9 and the length is 18, correct me if im wrong but yea that should be right

Solve the equation on the interval [0,2π). 8cos^2x+4cosx=0 Select ALL the correct solutions?

Here's Part 1)

Thank You!

First one:    2 pi  is one complete revolution

            6x = 2pi

              x = pi/3 = 3.1415/3 = ~1.047 sec

Second one:

   this is a cosine function with a multiplier in front of  -11   

          the cos function USUALLY ranges from -1 to 1....the  -11 makes it range from -11 to 11

              BUT the wave is also shifted  UP by 28 units    so it ranges from  17  to  39   

        the first minimum (17) occurs when?

           -11 cos (pix/48 - 5pi/12) + 28   = 17       subtract 28 from both sides and then divide by -11

                 cos(pix/48 - 5pi/12)  = 1                    arcos both sides

                    pix / 48 - 5pi/12 = 0

                       x = 20 minutes       8:00 + 20 mins = 8:20     

   You should be able to do similar for the first maximum....

Look at the answer to https://web2.0calc.com/questions/pre-calc-help_9 and try the same technique here.

As follows:

Let the foot of the perpendicular dropped from Q be H.

In triangle HQR, we have a Pythagorean triple: 15-20-25. (like 3-4-5 but you multiply each side by 5), so QH = 15.

Next, in triangle PQH, we have another Pythagorean triple, 8-15-17. So, we have PQ = 17.

The perimeter is PQ + QR + PR = 17 + 25 + 28 = 70.

sum of ingredients = final ingredients

x = 5 % amount  

(412-x) = 11% amount

.05 x       +  .11 ( 412-x)          =    .095 (412 )        solve for 5% amount, x....then 11% amount  =    412-x

x = nickels           value    = 5x

(81-x) = dimes     value =  10 (81-x)         summed, the values = 530

5x + 10(81-x) = 530     solve for 'x' ..the number of nickels   then dimes =   81-x

P1  V1  = P2 V2

P1 * 21   = 20.3  * 2.5      solve for P1 (in atm units)

Find the two values of x (one positive and one negative, which are closest to zero) for which tan(x) is undefined.

These two values determine the limits on the inverse function and, since tan(x) are undefined at these points, they cannot be contained in the domain of the inverse function.

(x+6      +   6x+2     +    2x+7  )/3 = 4x-7

(9x +15)/3   = 4x-7

(9x+15) = 3(4x-7)                    I think you should be able to take it from here !  

If  X  and  Y  are the two quantities, the relevant equation is:  Y  =  k/X.

To find the value of  k  for this problem, enter the given values of  X  and  Y   --->   18  =  k/15

                          multiply both sides by 15:                                                                  k  =  270

So, the final equation for this situation is:  Y  =  270/X

When  X  =  10   --->                                  Y  =  270/10     --->     Y  =  27

yes, that is what it shows in the assignment.

The largest area that 600 meters of fencing can enclose is a square with each side being 150 meters long.

To have this square enclose two identical playing fields, each field should have dimensions 75m by 150m.

Since I don't know what is contained in the figure, I don't know if there are any other restrictions upon the fields.

A square is the rectangular area that contains the most area for any given perimeter.

If you can create a circle, a circle would contain the most area for any given perimeter.

a^b = b^a.     b = 9a

a^(9a) = (9a)^a

a*log(a^9) = a*log(9a)

log(a^9) = log(9a)

a^9 = 9a

a^8 = 9

a = 9^(1/8)

m = 8, n = 9