Answer:
the sum is -4
Step-by-step explanation:
The value of a is between 0 and 1.
For question 9 - It is stating that AE is equal to 38. So the length of the entire line is 38. We then need to look at which figures are actually useful to us, which in this case is AC which is 10. Therefore the answer is as simple as 38-10, which gives us an answer of 28 for the other half of the line, notated as CE.
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
