Answer:
∫ C ( y + e√x) dx + ( 2x + cosy² ) dy = 1/3
Step-by-step explanation: See Annex
Green Theorem establishes:
∫C ( Mdx + Ndy ) = ∫∫R ( δN/dx - δM/dy ) dA
Then
∫ C ( y + e√x) dx + ( 2x + cosy² ) dy
Here
M = 2x + cosy² δM/dy = 1
N = y + e√x δN/dx = 2
δN/dx - δM/dy = 2 - 1 = 1
∫∫(R) dxdy ∫∫ dxdy
Now integration limits ( see Annex)
dy is from x = y² then y = √x to y = x² and for dx
dx is from 0 to 1 then
∫ dy = y | √x ; x² ∫dy = x² - √x
And
∫₀¹ ( x² - √x ) dx = x³/3 - 2/3 √x |₀¹ = 1/3 - 0
∫ C ( y + e√x) dx + ( 2x + cosy² ) dy = 1/3
Answer:
- first mechanic: $105/hour
- second mechanic: $55/hour
Step-by-step explanation:
Let r represent the rate charged by the first mechanic. Then 160-r is the rate charged by the second mechanic. The total of charges is ...
20r +5(160-r) = 2375
15r +800 = 2375 . . . . . . eliminate parentheses
15r = 1575 . . . . . . . . . . . . subtract 800
r = 105 . . . . . . . . . . . . . . . divide by 15. First mechanic's rate.
160-r = 55 . . . . . Second mechanic's rate
The first mechanic charged $105 per hour; the second, $55 per hour.
Ax+by=c
a=1
b=1
slope= -a/b=-1
y=mx+b
y=-x+b
b=0
x+y=0
Answer:
2 and 10
Step-by-step explanation:
Let x be length of the small piece and y the length of the big one.
● y = 5x
Since the big piece is 5 times longer than the short one.
The total length is 12 ft
● y + x = 12
● 5x + x = 12
● 6x = 12
Divide both sides by 6
● 6x/6 = 12/6
● x = 2
So the length of the two pieces are 2 ft and 10 ft (5×2)
A linear function has 1 as the highest power of the variable.
A. f(x) = 2 - 7x
here, the highest power of the variable x is 1.
Hence it is a LINEAR function.
___________
B. f(x) = 2 + x + x^2
here, the highest power of the variable x is 2.
Hence it is NOT a linear function.
_______________
here, the highest power of the variable x is 1/2.
Hence it is NOT a linear function.
________________
