Hi there!
Begin by differentiating f(x) using the power rule:
dy/dx = nxⁿ⁻¹
Therefore:
f(x) = 3x² - 5x + 10
f'(x) = 6x - 5
Set this equation equal to 0 to find the x-intercept:
0 = 6x - 5
5 = 6x
x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.
Answer: 6π
<u>Step-by-step explanation:</u>
Area of a circle is π r².
Area of a section of a circle is π r² × the section of the circle.
Given: r = 6, Ф = 60°
Answer:
Construct MO, where O is the midpoint of CG. (As shown in the attached figure)
(1) LM = MG //given, CM is the median to the hypotenuse
(2) CO = OG // construction
(3) MO is a mid-segment //(1), (2) , Definition of a mid-segment
(4) MO // LC //triangle mid-segment theorem
(5) ∠MOG ≅ ∠LCO // corresponding angles in two parallel lines intersected by a transversal line (CG)
(6) m∠LCO=90° //given, ΔLCG is a right triangle
(7) m∠MOG=90° //(5), (6), definition of congruent angles
(8) m∠MOC=180° – 90° = 90° // linear pair
(9) ∠MOG ≅ ∠MOC //(7),(8), definition of congruent angles
(10) MO=MO //common side, reflexive property of equality
(11) ΔMCO ≅ ΔMGO //(2), (9), (10) Side-Angle-Side postulate
(12) MC = MG // Corresponding sides in congruent triangles (CPCTC)
(13) MG= ½LG // Given, CM is the median to the hypotenuse
(15) MC = ½LG //(12) , (13), substitution
