Answer:
241
Step-by-step explanation:
Answer:
35.9 grams
Step-by-step explanation:
We use the formula:
![q=m*C_p*\Delta T](https://tex.z-dn.net/?f=q%3Dm%2AC_p%2A%5CDelta%20T)
Where
q is heat released
m is mass
C_p is the constant 2.44
ΔT is change in temperature
We put the info in the formula and solve for m (mass):
![q=m*C_p*\Delta T\\-3.12 = m*2.44(12.3-47.9)\\-3.12*10^3=m*(-86.864)\\m=35.9](https://tex.z-dn.net/?f=q%3Dm%2AC_p%2A%5CDelta%20T%5C%5C-3.12%20%3D%20%20m%2A2.44%2812.3-47.9%29%5C%5C-3.12%2A10%5E3%3Dm%2A%28-86.864%29%5C%5Cm%3D35.9)
The mass of ethanol is 35.9 grams
Step-by-step explanation:
A ball is launched straight up in the air from a height of 6 feet. The velocity as a function of time t is given by :
f(t) = -32 t+285
Height of the ball is :
![h(t)=\int\limits{f(t){\cdot} dt}\\\\h(t)=\int\limits{(-32t+285){\cdot} dt}\\\\h(t)=-16t^2+285t+C](https://tex.z-dn.net/?f=h%28t%29%3D%5Cint%5Climits%7Bf%28t%29%7B%5Ccdot%7D%20dt%7D%5C%5C%5C%5Ch%28t%29%3D%5Cint%5Climits%7B%28-32t%2B285%29%7B%5Ccdot%7D%20dt%7D%5C%5C%5C%5Ch%28t%29%3D-16t%5E2%2B285t%2BC)
C is constant. Here the ball is launched from a height of 6 feet. So,
![h(t)=-16t^2+285t+6](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%2B285t%2B6)
At t = 2 s, ![h(t)=-16(2)^2+285(2)+6=512\ m](https://tex.z-dn.net/?f=h%28t%29%3D-16%282%29%5E2%2B285%282%29%2B6%3D512%5C%20m)
At t = 9 s, ![h(t)=-16(9)^2+285(9)+6=1275\ m](https://tex.z-dn.net/?f=h%28t%29%3D-16%289%29%5E2%2B285%289%29%2B6%3D1275%5C%20m)
Between 2 s and 9 s, the ball's height changed is : 1275 - 512 = 763 m.
Answer:
y=4/3x-5
Step-by-step explanation:
4x-3y=15
-4x -4x
______________
-3y=-4x+15
---- --- ---- (divide all by -3)
-3 -3 -3
y=4/3x-5
solve for y
2x−4y=10
-2x -2x subtract -2x from both sides
-4y = -2x +10
-4 -4 Divide both sides by -4 (coefficient on y)
y = -2/-4x + 10/-4
y = 1/2x - 5/2
the slope is the number on the x (coefficient)
and its 1/2