Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
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
Answer:
21 N
Step-by-step explanation:
let mass be m and weight be w
Given w varies directly with m then the equation relating them is
w = km ← k is the constant of variation
To find k use the condition m = 7 , w = 49 , then
49 = 7k ( divide both sides by 7 )
7 = k
w = 7m ← equation of variation
When m = 3 , then
w = 7 × 3 = 21 N
We are asked in the problem to evaluate the integral of <span>(cosec^2 x-2005)÷cos^2005 x dx. The function is an example of a complex function with a degree that is greater than one and that uses special rules to integrate the function via the trigonometric functions. For example, we integrate
2005/cos^2005x dx which is equal to 2005 sec^2005 x since sec is the inverse of cos. The integral of this function when n >3 is equal to I=</span><span>∫<span>sec(n−2)</span>xdx+∫tanx<span>sec(n−3)</span>x(secxtanx)dx
Then,
</span><span>∫tanx<span>sec(<span>n−3)</span></span>x(secxtanx)dx=<span><span>tanx<span>sec(<span>n−2)</span></span>x/(</span><span>n−2)</span></span>−<span>1/(<span>n−2)I
we can then integrate the function by substituting n by 3.
On the first term csc^2 2005x / cos^2005 x we can use the trigonometric identity csc^2 x = 1 + cot^2 x to simplify the terms</span></span></span>
