Answer:
- 1 4/5
Step-by-step explanation:
-1 1/5 + - 3/5
Since the signs are the same, we add and take the sign
1 1/5 + 3/5
1 4/5
The sign is negative
- 1 4/5
On the number line start at - 1 1/5 and go to the left 3/5( since the sign is negative) you will end up at - 1 4/5
Answer:
The first listed equation is the correct equation to solve
The correct answer is: t = 5 seconds
Step-by-step explanation:
Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :
![y(t)=-16\,t^2+ 0 \,t +400](https://tex.z-dn.net/?f=y%28t%29%3D-16%5C%2Ct%5E2%2B%200%20%5C%2Ct%20%2B400)
and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:
![0=-16\,t^2+ 0 \,t +400\\16\,t^2+0\,t -400=0](https://tex.z-dn.net/?f=0%3D-16%5C%2Ct%5E2%2B%200%20%5C%2Ct%20%2B400%5C%5C16%5C%2Ct%5E2%2B0%5C%2Ct%20-400%3D0)
which solving for "t" becomes:
![16\,t^2-400 =0\\16\,t^2=400\\t^2=\frac{400}{16} \\t^2=25\\t= +/- 5\,\,sec](https://tex.z-dn.net/?f=16%5C%2Ct%5E2-400%20%3D0%5C%5C16%5C%2Ct%5E2%3D400%5C%5Ct%5E2%3D%5Cfrac%7B400%7D%7B16%7D%20%5C%5Ct%5E2%3D25%5C%5Ct%3D%20%2B%2F-%205%5C%2C%5C%2Csec)
So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.
That is: t = 5 seconds
Answer:
yesssss u are
Step-by-step explanation:
Answer:
a.P.I=![\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
b.G.S=![C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}](https://tex.z-dn.net/?f=C_1Cos%20%5Csqrt2%20x%2BC_2%20Sin%5Csqrt2%20x%2B%5Cfrac%7B1%7D%7B11%7De%5E%7B3x%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%7D)
Step-by-step explanation:
We are given that a linear differential equation
![y''+2y=e^{3x}+x^3](https://tex.z-dn.net/?f=y%27%27%2B2y%3De%5E%7B3x%7D%2Bx%5E3)
We have to find the particular solution
P.I=![\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7BD%5E2%2B2%7D%2B%5Cfrac%7Bx%5E3%7D%7BD%5E2%2B2%7D)
P.I=![\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B3%5E2%2B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%20x%5E3%281%2B%5Cfrac%7BD%5E2%7D%7B2%7D%29%5E%7B-2%7D)
P.I=![\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1-2%5Cfrac%7BD%5E2%7D%7B4%7D%2B3%5Cfrac%7BD%5E4%7D%7B16%7D%2B...%7D%7B2%7Dx%5E3)
P.I=
(higher order terms can be neglected
P.I=![\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B3x%7D%7D%7B11%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
b.Characteristics equation
![D^2+2=0](https://tex.z-dn.net/?f=D%5E2%2B2%3D0)
![D=\pm\sqrt2 i](https://tex.z-dn.net/?f=D%3D%5Cpm%5Csqrt2%20i)
C.F=![C_1cos \sqrt2x+C_2 sin\sqrt2 x](https://tex.z-dn.net/?f=C_1cos%20%5Csqrt2x%2BC_2%20sin%5Csqrt2%20x)
G.S=C.F+P.I
G.S=![C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)](https://tex.z-dn.net/?f=C_1Cos%20%5Csqrt2%20x%2BC_2%20Sin%5Csqrt2%20x%2B%5Cfrac%7B1%7D%7B11%7De%5E%7B3x%7D%2B%5Cfrac%7B1%7D%7B2%7D%28x%5E3-3x%29)
Answer:
-195 degrees
Step-by-step explanation:
we can subtract 360 from 165 to find the negative coterminal angle.
165-360=-195