Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. R is the region between the graph of f and the x-axis.
1 answer:
Answer:
0.089
Step-by-step explanation:
f(x) = -ln(x) and g(x) = x²
Start by graphing the region. The two curves intersect at about (0.653, 0.426), with g(x) on the left and f(x) on the right. The region is the triangular area between the curves and above the x-axis.
If we were to cut the region horizontally (perpendicular to the y-axis), the resulting line is the width of the square cross section. The thickness of this square is dy. So the volume of the square is:
dV = A dy
dV = s² dy
dV = (x₂ − x₁)² dy
dV = (e⁻ʸ − √y)² dy
The total volume is the sum of all the squares from y=0 to y=0.426.
V = ∫ dV
V = ∫₀⁰'⁴²⁶ (e⁻ʸ − √y)² dy
Evaluate with a calculator:
V ≈ 0.089
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Question: Given that BE bisects ∠CEA, which statements must be true? Select THREE options.
(See attachment below for the figure)
m∠CEA = 90°
m∠CEF = m∠CEA + m∠BEF
m∠CEB = 2(m∠CEA)
∠CEF is a straight angle.
∠AEF is a right angle.
Answer:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
Step-by-step explanation:
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Angle on a straight line = 180°. Therefore, m<CEA + m<AEF = m<CEF. Each right angle measures 90°.
Thus, the three statements that must be TRUE are:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
