Answer:
Nine hundred fourteen point two three eight
OR
Nine hundred one ten 4 one two tenths three hundredths and eight thousandths
Answer:
V = π (-2 (ln 2)² + 4 ln 2 − 1)
V ≈ 2.55
Step-by-step explanation:
V = π ∫₁² (1 − (ln x)²) dx
V/π = ∫₁² (1 − (ln x)²) dx
V/π = ∫₁² dx − ∫₁² (ln x)² dx
V/π = x |₁² − ∫₁² (ln x)² dx
V/π = 1 − ∫₁² (ln x)² dx
To evaluate the second integral, integrate by parts.
If u = (ln x)², then du = 2 (ln x) / x dx.
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= (ln x)² x − ∫ x (2 (ln x) / x) dx
= x (ln x)² − 2 ∫ ln x dx
Integrate by parts again.
If u = ln x, then du = 1/x dx.
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= x ln x − ∫ x (1/x dx)
= x ln x − ∫ dx
= x ln x − x
Substitute:
∫ (ln x)² dx = x (ln x)² − 2 ∫ ln x dx
∫ (ln x)² dx = x (ln x)² − 2 (x ln x − x)
∫ (ln x)² dx = x (ln x)² − 2x ln x + 2x
Substitute again:
V/π = 1 − ∫₁² (ln x)² dx
V/π = 1 − (x (ln x)² − 2x ln x + 2x) |₁²
V/π = 1 + (-x (ln x)² + 2x ln x − 2x) |₁²
V/π = 1 + (-2 (ln 2)² + 4 ln 2 − 4) − (-1 (ln 1)² + 2 ln 1 − 2)
V/π = 1 − 2 (ln 2)² + 4 ln 2 − 4 + 2
V/π = -2 (ln 2)² + 4 ln 2 − 1
V = π (-2 (ln 2)² + 4 ln 2 − 1)
V ≈ 2.55
Answer:
58/33 or 1.75
Step-by-step explanation:
The correct option is polygon E.
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given that, Which polygons have at least one pair of parallel sides but are not parallelograms,
Such polygons are called trapezoid.
A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.
Hence, the correct polygon is E.
Learn more about polygons, click;
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Answer:
Do you mean strandord or expanded form?
Step-by-step explanation:
The probability that you will choose a lemon-lime for your friend is the number of lemon-limes divided by the total number of drinks, 4/11.
The probability that you will subsequently choose one for yourself is the same ratio with different numbers (because a lemon-lime has already been selected), 3/10.
The probability of both of these events occurring is the product of their individual probabilities: (4/11)·(3/10) = 6/55