The modified area is (1/48) (2πr(4h+3r))
<u>Step-by-step explanation:</u>
Let the radius be 'r' and height be 'h'.
Area of cylinder= 2π r(h+r)
The radius is shrunk down to quarter of its original radius
r = r/4
The height is reduced to a third of its original height
h = h/3
New Area = 2π(r/4) [(h/3) +(r/4) ]
= (1/4)2πr[(4h+3r) /12]
= (1/48) (2πr(4h+3r))
Answer:
sin
(
x/
2
) = -
√
3
/2
Take the inverse sine of both sides of the equation to extract x
from inside the sine.
x/
2
=
arcsin
(
−
√
3/
2
)
The exact value of arcsin
(
−
√
3
/2
) is −
π
/3
.
/x
2
=
−
π
/3
Multiply both sides of the equation by 2
.
2
⋅
x
/2
=
2
⋅
(
−
π
/3
)
Simplify both sides of the equation.
x
=
−
2
π
/3
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2
π
, to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.
x
/2
=
2
π
+
π/
3
+
π
Simplify the expression to find the second solution.
x
=
2
π
/3
4
π
Add 4
π to every negative angle to get positive angles.
x
=
10
π
/3
The period of the sin
(
x
/2
) function is 4
π so values will repeat every 4
π radians in both directions.
x
=2
π
/3
+
4
π
n
,
10
π/
3
+
4
π
n
, for any integer n
Exclude the solutions that do not make sin
(
x
/2
)
=
−
√
3/
2 true.
x
=
10
π
/3
+
4
π
n
, for any integer n
Answer:
Step-by-step explanation:
The average value theorem sets:
if f (x) is continuous in [a, b] and derivable in (a, b) there is a c Є (a, b) such that
, where
f(a)=f(π/2)=-4*sin(π/2) = -4*1= -4
f(b)=(3π/2)=-4*sin(3π/2) = -4*-1 = 4
⇒
c≅130
So you could do $1725/3 (divided by) which would give you 575 then mulitply that by two and that will give you the months rent of, $1,150. I hope this helps!
-1400 + 800 - 350 = - 950 meters
