geno3141

"Three times the difference of x and 4"  beomes  "3(x - 4)"

   -8  ≤  3(x - 4)  ≤  10

The formula for the surface area of a sphere is:  Area  =  4·π·r²

Since the diameter is 40 mm, the radius is 20 mm.

The area is found by:      4·π·20²

Did you mean "-" or did you mean "="?

What do you want done with this function?

2.12 x 10^-18  =  (-2.18 x 10^-18) x [ 1/n² - 1/36 ]

Divide both sides by (-2.18 x 10^-18):

Since  [2.12 x 10^-18] ÷ [-2.18 x 10^-18]  =  -0.972       (The 10^-18's cancel.)

   -0.972  =  1/n² - 1/36

Add 1/36 to both sides:

   -0.945  =  1/n²

This has no real solutions, because you can't square a number and get a negative result.

If the problem is:  [2.39 x 10^-18] / [6.63 x 10^-34]

it can be separated into:  [2.39] / [6.63] x [10^-18 / 10^-34]

2.39 / 6.63 = 0.360

10^-18 / 10^-34  =  10^16               (subtract exponents)

Answer:  0.360 x 10^16

Depends: it might be:

13ln(11) / ( ln(17) - ln(11) )

or it might be:  13ln(11) / ln(17) - ln(11)

Use the distributive property:  2(4x) + 2(3x) + 2x

Simplify:                                   8x + 6x + 2x

                                                       16x

Draw a right triangle, with point A the top of the vertical pole, point C the bottom of the vertical pole, and point B the place where the wire reaches the ground.

Angle C is a right angle.  Angle B is 75°.

Side BC is the side adjacent to angle B and has a length of 10 ft.

Side AC is the height of the pole and is the side opposite angle B.

The tan function is defined to be the opposite side divided by the adjacent side.

tan(B) = AC / BC   --->   tan(75°)  =  AC / 10   --->  AC  =  10·tan(75°)  =  37.3 ft.

The length of the wire is side AB, the hypotenuse of the triangle.

The cos function is defined to be the adjacent side divide by the hypotenuse.

cos(B) = BC / AB   --->   cos(75°)  =  10 / AB   --->  AB  =  10 / cos(75°)  =  38.6 ft.

If you want a sequence to alternate:  -1, 1, -1, 1, -1, ...  use the expression (-1)^n

If you want a sequence to alternate:  1, -1, 1, -1, 1, ...  either use the expression (-1)^(n + 1) or the expression (-1)^(n - 1).

So:  [(-1)^(n + 1)]·6  will result in the sequence:  6, -6, 6, ...

To make typing easier, I'm going to replace 'f(x)' with 'y':

Problem:  if  y = (x + 4)³  then find the inverse:

First, exchange the variables 'x' and 'y':  x  =  (y + 4)³

Second:  solve for y:                               x^(1/3)  =  y + 4

                                                               y  =  x^(1/3) - 4

Finally, replace y with f-1(x)   --->        f-1(x)  =  x^(1/3) - 4