Answer:
34 + 35 + 36 = 105
Step-by-step explanation:
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 105
3X + 3 = 105
3X + 3 - 3 = 105 - 3
3X = 102
3X/3 = 102/3
X = 34
Which means that the first number is 34, the second number is 34 + 1 and the third number is 34 + 2. Therefore, three consecutive integers that add up to 105 are 34, 35, and 36.
34 + 35 + 36 = 105
We know our answer is correct because 34 + 35 + 36 equals 105 as displayed above.
We have that
tan x=5
we know that
tan x =sin x/ cos x
sin x/ cos x=5------> squaring-----> sin² x/cos² x=25
remember that
sin² x+cos² x=1-----> cos² x=1-sin² x
substitute
sin² x/[1-sin² x]=25
sin² x=25-25*sin² x
26*sin² x=25
sin² x=25/26
sin x=5/√26
cos² x=1-(5/√26)²----> 1-(25/26)----> 1/26
cos x=1/√26
the answers are
sin x=5/√26
cos x=1/√26
Use the divergence theorem. Let
be the cylindrical region, then
(where
denotes the unit normal vector to
, but we don't need to worry about it now)
We have
For the solid
with boundary
, we can set up the following volume integral in cylindrical coordinates for ease:
One board is 31.5 inches long. all the boards together is 157.5 inches long
