Answer/Step-by-step explanation:
Recall: SOH CAH TOA
✔️Find <A:
Reference angle (θ) = A
Opposite side = 14 cm
Hypotenuse = 20 cm
Apply SOH:
Sin θ = Opp/Hyp
Substitute
Sin A = 14/20
A = 
m<A = 44° (nearest whole number)
✔️Find <C:
Reference angle (θ) = C
Adjacent side = 14 cm
Hypotenuse = 20 cm
Apply CAH:
Cos θ = Adj/Hyp
Substitute
Cos C = 14/20
C = 
m<C = 46° (nearest whole number)
✔️Find AB:
Reference angle (θ) = C = 46°
Opposite side = AB
Hypotenuse = 20 cm
Apply SOH:
Sin θ = Opp/Hyp
Sin 46° = AB/20
20*Sin 46° = AB
AB = 14.4 cm (one decimal place)
Answer:
volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a (
x + b )² dx
Step-by-step explanation:
Given the data in the question and as illustrated in the image below;
R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)
from the image;
the equation of AB will be;
y-b / b-0 = x-0 / 0-a
(y-b)(0-a) = (b-0)(x-0)
0 - ay -0 + ba = bx - 0 - 0 + 0
-ay + ba = bx
ay = -bx + ba
divide through by a
y =
x + ba/a
y =
x + b
so R is bounded by y =
x + b and y =0, 0 ≤ x ≤ a
The volume of the solid revolving R about x axis is;
dv = Area × thickness
= π( Radius)² dx
= π (
x + b )² dx
V = π ₀∫^a (
x + b )² dx
Therefore, volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a (
x + b )² dx
<span>The area of an n-sided regular polygon approaches the area of a circle as n gets very large. ... If an N-gon (polygon with N sides) has perimeter P, then each of the N ... and we can use one of them to derive theequation sin(theta/2) ... 2*pi/N radians), R is the length of the lines to the center (the radius of the ...</span><span>
</span>
Answer:
ans: ii) 87° and iii) 60°
Step-by-step explanation:
ii)
y° = 180° - ( 56° + 37°)
missing angle on triangle is alternate angle of y° so are equal and sum of angles of triangle is 180°
iii)
x° + 2x° = 180°
sum of co interior angles is 180°