Step-by-step explanation:
Reduce 24/96 to lowest terms
Find the GCD (or HCF) of numerator and denominator. GCD of 24 and 96 is 24.
24 ÷ 2496 ÷ 24.
Reduced fraction: 14. Therefore, 24/96 simplified to lowest terms is 1/4.
The right triangles are congruent, so
.. 2x -14 = 37 -x
.. 3x = 51 . . . . . . . add x+14
.. x = 17 . . . . . . . . divide by 3
x = 17
Calculation of relative maxima and minima of a function f (x) in a range [a, b]:
We find the first derivative and calculate its roots.
We make the second derivative, and calculate the sign taken in it by the roots of the first derivative, and if:
f '' (a) <0 is a relative maximum
f '' (a)> 0 is a relative minimum
Identify intervals on which the function is increasing, decreasing, or constant. G (x) = 1- (x-7) ^ 2
First derivative
G '(x) = - 2 (x-7)
-2 (x-7) = 0
x = 7
Second derivative
G '' (x) = - 2
G '' (7) = - 2 <0 is a relative maximum
answer:
the function is increasing at (-inf, 7)
the function is decreasing at [7, inf)
