Answer:
If P = (x,y) then formulas for each trigonometric functions are:
sin x = y/r
cos x = x/r
tan x = y/x
cot x = x/y
sec x = r/x
cosec x = r/y
where r = √(x²+y²).
First find r:
r = √(13²+84²)=√(169+7056)=√7225=85.
Then just substitute:
sin x = 84/85
cos x = 13/85
tan x = 84/13
cot x = 13/84
sec x = 85/13
cosec x = 85/84
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
Answer:
Step-by-step explanation:
According the Triangle sum theorem:
m<T + m<U + m<V =180
x + 2x + x + 80 = 180
solve: x=25
Therefore m<T = 25, m<U = 50, and m<V = 105
Answer:
x = 6
Step-by-step explanation:
7 x = 56-14
7 x = 42
7 x/7 to remain with x only = 42
then x = 6
Answer:
The number of feet she will travel back is 1 or 7 feet
Step-by-step explanation:
Here, we need to solve the quadratic equation
That will be as follows;
0 = x^2 -8x + 7
x^2-x-7x+ 7 = 0
x(x-1)-7(x-1) = 0
(x-1)(x-7) = 0
x = 1 or 7
The number of feet she will travel before coming back to the surface of the water is 1 or 7 feet
