Elise’s number is 24
-56 divided by -7 is 8
8 + 16 is 24
basically you just do everything in reverse
Answer: 20 hr
Step-by-step explanation:
Given
The depth of accumulated snow is ![d=10\ in.](https://tex.z-dn.net/?f=d%3D10%5C%20in.)
Snow is melting at the rate of ![r=0.5\ \text{in. per hour}](https://tex.z-dn.net/?f=r%3D0.5%5C%20%5Ctext%7Bin.%20per%20hour%7D)
Time taken for complete melting of snow is
![\Rightarrow t=\frac{d}{r}\\\\\Rightarrow t=\frac{10}{0.5}=20\ hr](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cfrac%7Bd%7D%7Br%7D%5C%5C%5C%5C%5CRightarrow%20t%3D%5Cfrac%7B10%7D%7B0.5%7D%3D20%5C%20hr)
Answer:
Step-by-step explanation:
SAS Similarity postulate
Answer: For this one, I'll use y=mx+b because that equation make the most sense in this scenario.
A) X is the number of hours, and 15, or b is the tip
B) y= 30x + 15.
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
Answer:
(a) First order linear separable differential equation
(b)
![y(x)=2+C_1e^{x-x^2} \\\\I=(-\infty,\infty)](https://tex.z-dn.net/?f=y%28x%29%3D2%2BC_1e%5E%7Bx-x%5E2%7D%20%5C%5C%5C%5CI%3D%28-%5Cinfty%2C%5Cinfty%29)
(c)
(d)
![y(x)=2-e^{x-x^2}](https://tex.z-dn.net/?f=y%28x%29%3D2-e%5E%7Bx-x%5E2%7D)
Step-by-step explanation:
(b) Solve for ![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D)
![\frac{dy}{dx}=4x+y-2xy-2\\ \\Simplify\\\\\frac{dy}{dx}=(2x-1)(2-y)\\\\Divide\hspace{3}both\hspace{3}sides\hspace{3}by\hspace{3}2-y\hspace{3}and\hspace{3}multiply\hspace{3}both\hspace{3}sides\hspace{3}by\hspace{3}dx\\\\\frac{dy}{2-y}=(2x-1) dx\\\\Integrate\hspace{3}both\hspace{3}sides\\\\\int\frac{dy}{2-y} \, =\int\ (2x-1) dx\\\\Evaluate\hspace{3}the\hspace{3}integrals\\\\-log(2-y)=x^2-x+C_1\\\\Solving\hspace{3}for\hspace{3}y\\\\y=2+C_1e^{x-x^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D4x%2By-2xy-2%5C%5C%20%5C%5CSimplify%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%282x-1%29%282-y%29%5C%5C%5C%5CDivide%5Chspace%7B3%7Dboth%5Chspace%7B3%7Dsides%5Chspace%7B3%7Dby%5Chspace%7B3%7D2-y%5Chspace%7B3%7Dand%5Chspace%7B3%7Dmultiply%5Chspace%7B3%7Dboth%5Chspace%7B3%7Dsides%5Chspace%7B3%7Dby%5Chspace%7B3%7Ddx%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7B2-y%7D%3D%282x-1%29%20dx%5C%5C%5C%5CIntegrate%5Chspace%7B3%7Dboth%5Chspace%7B3%7Dsides%5C%5C%5C%5C%5Cint%5Cfrac%7Bdy%7D%7B2-y%7D%20%5C%2C%20%3D%5Cint%5C%20%282x-1%29%20dx%5C%5C%5C%5CEvaluate%5Chspace%7B3%7Dthe%5Chspace%7B3%7Dintegrals%5C%5C%5C%5C-log%282-y%29%3Dx%5E2-x%2BC_1%5C%5C%5C%5CSolving%5Chspace%7B3%7Dfor%5Chspace%7B3%7Dy%5C%5C%5C%5Cy%3D2%2BC_1e%5E%7Bx-x%5E2%7D)
The domain of y is: ![x\in R\hspace{3}or\hspace{3}(-\infty,\infty)](https://tex.z-dn.net/?f=x%5Cin%20R%5Chspace%7B3%7Dor%5Chspace%7B3%7D%28-%5Cinfty%2C%5Cinfty%29)
So the lasrgest interval I on which the solution is defined is:
![I=(-\infty,\infty)](https://tex.z-dn.net/?f=I%3D%28-%5Cinfty%2C%5Cinfty%29)
(c)
Differentiate y:
![\frac{dy}{dx}=C_1(1-2x)e^{x-x^2} =C_1e^{x-x^2}-2xC_1e^{x-x^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3DC_1%281-2x%29e%5E%7Bx-x%5E2%7D%20%20%3DC_1e%5E%7Bx-x%5E2%7D-2xC_1e%5E%7Bx-x%5E2%7D)
Evaluate this result into the differential equation:
![\frac{dy}{dx}=4x+y-2xy-2\\\\C_1e^{x-x^2} -2xC_1e^{x-x^2} =4x+2+C_1e^{x-x^2}-4x-2xC_1e^{x-x^2}-2\\\\C_1e^{x-x^2} -2xC_1e^{x-x^2} =C_1e^{x-x^2} -2xC_1e^{x-x^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D4x%2By-2xy-2%5C%5C%5C%5CC_1e%5E%7Bx-x%5E2%7D%20-2xC_1e%5E%7Bx-x%5E2%7D%20%3D4x%2B2%2BC_1e%5E%7Bx-x%5E2%7D-4x-2xC_1e%5E%7Bx-x%5E2%7D-2%5C%5C%5C%5CC_1e%5E%7Bx-x%5E2%7D%20-2xC_1e%5E%7Bx-x%5E2%7D%20%3DC_1e%5E%7Bx-x%5E2%7D%20-2xC_1e%5E%7Bx-x%5E2%7D)
Therefore, the solution is correct.
(d)
Simply evaluate the function y for x=0 and solve for C1:
![y(0)=2+C_1e^{0-0^2} =1\\\\2+C_1e^0=1\\\\2+C_1*1=1\\\\2+C_1=1\\\\C_1=-1](https://tex.z-dn.net/?f=y%280%29%3D2%2BC_1e%5E%7B0-0%5E2%7D%20%3D1%5C%5C%5C%5C2%2BC_1e%5E0%3D1%5C%5C%5C%5C2%2BC_1%2A1%3D1%5C%5C%5C%5C2%2BC_1%3D1%5C%5C%5C%5CC_1%3D-1)
Finally substitute into y:
![y(x)=2-e^{x-x^2}](https://tex.z-dn.net/?f=y%28x%29%3D2-e%5E%7Bx-x%5E2%7D)