Answer:
missing side: 133 cm
Explanation:
Provided <u>2 length sides</u> and <u>one angle</u> also need to find <u>one missing side</u>.
So, use cosine rule:
⇒ a² = b² + c² - 2bc cos(A)
<u>Insert values</u>
⇒ g² = 166² + 147² - 2(166)(147) cos(50)
⇒ g² = 17794.3935
⇒ g = √17794.3935
⇒ g = 133.3956
⇒ g = 133 (rounded to nearest whole number)
Step-by-step explanation:
so first convert it into an algebraic equation
4 - ⅛w = 16
⅛w = 16-4
⅛w = 12
w=12÷ 
w=12×8=96
check: 4 - ⅛(96)=4-12=-8
-8<16 (-8 less than 16)
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The coefficient of x in this case is 1. (x*x = x^2)
Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.
We then multiply everything together to simplify:
sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes
3x^2 * sin(x^3)/(cos(x^3))^2
and multiplying the constant 7 from the beginning:
7 * 3x^2 = 21x^2, so...
our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2

By the fundamental theorem of calculus,

Now the arc length over an arbitrary interval

is

But before we compute the integral, first we need to make sure the integrand exists over it.

is undefined if

, so we assume

and for convenience that

. Then