Answer:
Use Distributive Property.
Step-by-step explanation:
Multiply 3 times -4x to equal -12x
Multiply 3 times (+8) to equal 24
-12x + 24 =
Subtract 24 from each side
-12x + 24 -24 = -24
Divide both sides by -12
-12x/-12 = -24/-12
x = 2
Answer:
Cardiac output:![F=0.055 L\s](https://tex.z-dn.net/?f=F%3D0.055%20L%5Cs)
Step-by-step explanation:
Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.
To Find : Find the cardiac output.
Solution:
Formula of cardiac output:
---1
A = 3 mg
![\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5ET_0%20%7Bc%28t%29%7D%20%5C%2C%20dt%20%3D%5Cint%5Climits%5E%7B10%7D_0%20%7B20te%5E%7B-0.06t%7D%7D%20%5C%2C%20dt)
Do, integration by parts
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B20t%5Cint%7Be%5E%7B-0.6t%7D%20%5C%2Cdt%7D-%5Cint%5B%5Cfrac%7Bd%5B20t%5D%7D%7Bdt%7D%5Cint%20%7Be%5E%7B-0.6t%7D%20%5C%2C%20dt%5Ddt%5D%5E%7B10%7D_0)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B%5Cfrac%7B-20te%5E%7B-0.6t%7D%7D%7B0.6%7D%2B%5Cfrac%7B20%7D%7B0.6%7D%5Cint%20%7Be%5E%7B-0.6t%7D%20%5C%2Cdt%5D%5E%7B10%7D_0)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B%5Cfrac%7B-20te%5E%7B-0.6t%7D%7D%7B0.6%7D%2B%5Cfrac%7B20e%5E%7B-0.6t%7D%7D%7B%280.6%29%5E2%7D%5D%5E%7B10%7D_%7B0%7D)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5B%5Cfrac%7B-200e%5E%7B-6%7D%7D%7B0.6%7D%2B%5Cfrac%7B20e%5E%7B-6%7D%7D%7B%280.6%29%5E2%7D%5D%2B%5Cfrac%7B20%7D%7B%280.60%5E2%7D)
![[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%3D%5Cfrac%7B20%281-e%5E%7B-6%7D%7D%7B%280.6%29%5E2%7D-%5Cfrac%7B200e%5E%7B-6%7D%7D%7B0.6%7D)
![[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}](https://tex.z-dn.net/?f=%5B%5Cint%7B20te%5E%7B-0.6t%7D%7D%20%5C%2C%20dt%5D%5E%7B10%7D_0%5Csim%20%7B54.49%7D)
Substitute the value in 1
Cardiac output:![F=\frac{3}{54.49}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7B3%7D%7B54.49%7D)
Cardiac output:![F=0.055 L\s](https://tex.z-dn.net/?f=F%3D0.055%20L%5Cs)
Hence Cardiac output:![F=0.055 L\s](https://tex.z-dn.net/?f=F%3D0.055%20L%5Cs)
Answer:
![595.54](https://tex.z-dn.net/?f=595.54)
Step-by-step explanation:
The formula for a sector of a circle with angle
is
.
Substituting given values, we have:
![\frac{141}{360}\cdot 22^2\pi\approx \boxed{595.54}](https://tex.z-dn.net/?f=%5Cfrac%7B141%7D%7B360%7D%5Ccdot%2022%5E2%5Cpi%5Capprox%20%5Cboxed%7B595.54%7D)
3x - y = 2
y = 2x - 9
Substitute:
3x - 2x - 9 = 2
x - 9 = 2
x = 11
Substitute your answer into any equation:
y = 2x - 9
y = 2(11) - 9
y = 22 - 9
y = 13
Answer:
x = 11 ; y = 13
Answer:
A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen