Write 3 3/5 as a improper fraction
2 answers:
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Answer:
V = 1/6 cubic units
Step-by-step explanation:
Applying the concept of integrals for volume calculation:
(1)
V = volume of the solid bounded by x = a and x = b
S(x) = cross section area of the solid, perpendicular to the x axis
From the figure we have that S is the area of a triangle that has base Z and height Y
Area of the triangle = (2)
Calculation of y(x) and z(x)
We apply the equation of the point-slope line (plane xy):
Slope = (3)
Equation of the line = (4)
Replacing the points (1,0) and (0,1) in (3):
Replacing the point (1,0) and m = -1 in (4):
y(x) = -x + 1 (Line A-B) (5)
We apply the equation of the point-slope line (plane xz):
Slope = (6)
Equation of the line = (7)
Replacing the points (1,0) and (0,1) in (6):
Replacing the point (1,0) and m = -1 in (7):
z(x) = -x + 1 (Line A-C) (8)
Replacing (5) and (8) in (2)
(9)
Replacing (9) in (1) and knowing that a = 0 and b = 1:
evaluated from x=0 to x=1
Answer:
Area of trapezium = 4.4132 R²
Step-by-step explanation:
Given, MNPK is a trapezoid
MN = PK and ∠NMK = 65°
OT = R.
⇒ ∠PKM = 65° and also ∠MNP = ∠KPN = x (say).
Now, sum of interior angles in a quadrilateral of 4 sides = 360°.
⇒ x + x + 65° + 65° = 360°
⇒ x = 115°.
Here, NS is a tangent to the circle and ∠NSO = 90°
consider triangle NOS;
line joining O and N bisects the angle ∠MNP
⇒ ∠ONS = = 57.5°
Now, tan(57.5°) =
⇒ 1.5697 =
⇒ SN = 0.637 R
⇒ NP = 2×SN = 2× 0.637 R = 1.274 R
Now, draw a line parallel to ST from N to line MK
let the intersection point be Q.
⇒ NQ = 2R
Consider triangle NQM,
tan(∠NMQ) =
⇒ tan65° =
⇒ QM =
QM = 0.9326 R .
⇒ MT = MQ + QT
= 0.9326 R + 0.637 R (as QT = SN)
⇒ MT = 1.5696 R
⇒ MK = 2×MT = 2×1.5696 R = 3.1392 R
Now, area of trapezium is (sum of parallel sides/ 2)×(distance between them).
⇒ A = () × (ST)
= () × 2 R
= 4.4132 R²
⇒ Area of trapezium = 4.4132 R²