Answer:
a) 28,662 cm² max error
0,0111 relative error
b) 102,692 cm³ max error
0,004 relative error
Step-by-step explanation:
Length of cicumference is: 90 cm
L = 2*π*r
Applying differentiation on both sides f the equation
dL = 2*π* dr ⇒ dr = 0,5 / 2*π
dr = 1/4π
The equation for the volume of the sphere is
V(s) = 4/3*π*r³ and for the surface area is
S(s) = 4*π*r²
Differentiating
a) dS(s) = 4*2*π*r* dr ⇒ where 2*π*r = L = 90
Then
dS(s) = 4*90 (1/4*π)
dS(s) = 28.662 cm² ( Maximum error since dr = (1/4π) is maximum error
For relative error
DS´(s) = (90/π) / 4*π*r²
DS´(s) = 90 / 4*π*(L/2*π)² ⇒ DS(s) = 2 /180
DS´(s) = 0,0111 cm²
b) V(s) = 4/3*π*r³
Differentiating we get:
DV(s) = 4*π*r² dr
Maximum error
DV(s) = 4*π*r² ( 1/ 4*π*) ⇒ DV(s) = (90)² / 8*π²
DV(s) = 102,692 cm³ max error
Relative error
DV´(v) = (90)² / 8*π²/ 4/3*π*r³
DV´(v) = 1/240
DV´(v) = 0,004
Hello :
<span>16x²+20y² =4(4x²+5y²)</span>
Answer:
15.839 rounded to the nearest tenth is 15.8. This is because when we round it to the nearest hundredth it becomes 15.84 and then to the tenth it becomes 15.8, since 4 is less than 5.
X+9 = 6
-9 -9 (subtract 9 from both sides)
x =6-9
x =-3