Answer:
x= -2, y = -3
Step-by-step explanation:
1. substitute x = 4+2y in the first equation: 
simplify it : 
2. isolate y in 8 + 5y = -7 --> 5y = -7 - 8 -->
3. solve for y: 5y = -15 --> y = -15/5 --> y= -3
4. solve for x: x = 4 + 2y
x = 4 + 2(-3)
x = 4 + (-6)
x = -2
Step-by-step explanation:
To find the slope you use the slope formula which is y2-y2/x2-x1
And to find the y intercept you use y=mx +b. Yous substitute the slope as m and you substitute a point from the line to find b. Which is the y intercept
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
Answer: 0.185 gallons
Step-by-step explanation:
Divide 5/12 by 2 1/4
First convert the improper fraction to a proper fraction, 2 1/4 = 9/4
5/12 ÷ 9/4
= 5/12 × 4/9
= 5/27 = 0.185
Answer:
250 mins
Step-by-step explanation:
since number of taps times time is constant
