Answer:
The required answer is
Therefore the number in green box should be 7.
Step-by-step explanation:
Given:
AB = 7√2
AD = a , BD = b , DC = c , AC = d
∠B = 45°, ∠C = 30°
To Find:
c = ?
Solution:
In Right Angle Triangle ABD Sine identity we have

Substituting the values we get


Now in Triangle ADC Tangent identity we have

Substituting the values we get

The required answer is
Please use " ^ " to denote exponentiation:
<span>f(x) = –(x + 8)^2 – 1
Find the first derivative: f '(x) = -2(x+8)(1)
Set this = to 0: -2(x+8) = 0
solve for x: x = -8
Divide the number line into subintervals based upon x=-8:
(-inf, -8) and (-8, inf)
Choose a test value for x from each interval, e. g., -10 from the first interval and 20 from the second.
Subst. this test value into the derivative, shown above.
If the result is + the function is incr on that interval; if - the fn. is decr.
Questions welcome!</span>