Answer:
sec(4x) + C
Explanation:
original problem: ∫sec(4x)tan(x)dx
use integration by substitution (u-sub) by setting u = 4x
if u = 4x, then du/dx = 4 and du = 4dx (dx = du/4)
after substitution the integral is ∫sec(u)tan(u)(du/4)
move the 1/4 out of the integral by using the integral Constant rule to form 1/4∫sec(u)tan(u)du
the anti-derivative of sec(u)tan(u) is sec(u), memorize your trigonometric derivatives!!!!
after integration, we get sec(u)/4 + C , now plug u back into the equation
sec(4x) + C is the general solution
If a segment is separated by a midpoint, that means both sides are equal. therefore,
DE = EF
6x - 58 = 44
now just solve for x
6x = 102
x = 17
Answer:
One of many fieldwork positions in direct services is social workers.
Perimeter = 2(L + W) = 20 or L + W = 10
And Area = L x W = 24
So with have the SUM "S" of 2 numbers and te PRODUCT "P' of same numbers, then
we can apply te quadratic equation X² -SX + P
X² - 10X + 24 = 0, solve this equation and you'll find L = 6 in and W = 4in
or 4 in x 6 in
