Answer:
1. (-4, 1)
2. I substituted (y = x + 5) into (3x + y = -11) first before substituting the value of x into (y = x + 5) to find the value of y.
Step-by-step explanation:
Substitute y = x + 5 into 3x + y = -11:
3x + y = -11
3x + x + 5 = -11
4x + 5 = -11
4x = -11 - 5
= -16
x = -16 ÷ 4
x = -4
Substitute x = 4 into y = x + 5:
y = x + 5
y = -4 + 5
y = 1
A coordinate point is written like this: (x, y)
Thus, the final answer is: (-4, 1)
Answer:
1) 20% change I think its an increase.
If needed I could try to answer the 2nd question but I am sure that I got the first one right.
Step-by-step explanation:
Since you didn't give an amount of time, we can't give an exact value. However, I can help you with the steps so you can get the correct answer.
First, you need to find the correct z-score. Then, use a standard normal distribution table to find the percent.
Let the time that you are looking for equal X.
The formula for your z-score is:
(x - 8.7) / 2.1 = z-score
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
