630 sterling * 1 euro / 0.84 sterling
630 sterling divided by 0.84 sterling = 750 euros
Answer:
x + 2y = -8 = y = -4 - 1/2x
y= -1/2x + 4 = y = 4
y= -1/2x - 4 = y = -4
y=-2x - 4 = y = -4
y=1/2x-4 = y = -4
Step-by-step explanation:
(x + 2y = -8 = y = -4 - 1/2x)
![x+2y=-8\\2y=-8-x\\y=-4-\frac{1}{2}x\\](https://tex.z-dn.net/?f=x%2B2y%3D-8%5C%5C2y%3D-8-x%5C%5Cy%3D-4-%5Cfrac%7B1%7D%7B2%7Dx%5C%5C)
Answer:
![\frac{1}{49}(7x-1)e^{7x}+e^{-t}=C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B49%7D%287x-1%29e%5E%7B7x%7D%2Be%5E%7B-t%7D%3DC)
Step-by-step explanation:
We are given that
![\frac{dx}{dt}=\frac{1}{xe^{t+7x}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7Bxe%5E%7Bt%2B7x%7D%7D)
We have to find the implicit function
Using separation variable method
![\frac{dx}{dt}=\frac{1}{xe^t\cdot e^{7x}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7Bxe%5Et%5Ccdot%20e%5E%7B7x%7D%7D)
By using property ![x^a\cdot x^y=x^{a+y}](https://tex.z-dn.net/?f=x%5Ea%5Ccdot%20x%5Ey%3Dx%5E%7Ba%2By%7D)
![xe^{7x}dx=e^{-t}dt](https://tex.z-dn.net/?f=xe%5E%7B7x%7Ddx%3De%5E%7B-t%7Ddt)
By using property ![\frac{1}{x^a}=x^{-a}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%5Ea%7D%3Dx%5E%7B-a%7D)
Taking integration on both sides
![\int xe^{7x}dx=\int e^{-t}dt](https://tex.z-dn.net/?f=%5Cint%20xe%5E%7B7x%7Ddx%3D%5Cint%20e%5E%7B-t%7Ddt)
Parts integration method
![\int u\cdot v dx=u\int vdx-\int (\frac{du}{dx}\int vdx)dx](https://tex.z-dn.net/?f=%5Cint%20u%5Ccdot%20v%20dx%3Du%5Cint%20vdx-%5Cint%20%28%5Cfrac%7Bdu%7D%7Bdx%7D%5Cint%20vdx%29dx)
By parts integration method
![x\int e^{7x}dx-\int (\frac{dx}{dx}\int e^{7x}dx)dx=-e^{-t}+C](https://tex.z-dn.net/?f=x%5Cint%20e%5E%7B7x%7Ddx-%5Cint%20%28%5Cfrac%7Bdx%7D%7Bdx%7D%5Cint%20e%5E%7B7x%7Ddx%29dx%3D-e%5E%7B-t%7D%2BC)
Using formula ![\int e^{ax} dx=\frac{e^{ax}}{a}+C](https://tex.z-dn.net/?f=%5Cint%20e%5E%7Bax%7D%20dx%3D%5Cfrac%7Be%5E%7Bax%7D%7D%7Ba%7D%2BC)
![\frac{xe^{7x}}{7}-\frac{1}{7}\int e^{7x}dx=-e^{-t}+C](https://tex.z-dn.net/?f=%5Cfrac%7Bxe%5E%7B7x%7D%7D%7B7%7D-%5Cfrac%7B1%7D%7B7%7D%5Cint%20e%5E%7B7x%7Ddx%3D-e%5E%7B-t%7D%2BC)
![\frac{xe^{7x}}{7}-\frac{1}{49}e^{7x}+e^{-t}=C](https://tex.z-dn.net/?f=%5Cfrac%7Bxe%5E%7B7x%7D%7D%7B7%7D-%5Cfrac%7B1%7D%7B49%7De%5E%7B7x%7D%2Be%5E%7B-t%7D%3DC)
![\frac{1}{49}(7x-1)e^{7x}+e^{-t}=C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B49%7D%287x-1%29e%5E%7B7x%7D%2Be%5E%7B-t%7D%3DC)
We are given that
![F(x,t)=C](https://tex.z-dn.net/?f=F%28x%2Ct%29%3DC)
![F(x,t)=\frac{1}{49}(7x-1)e^{7x}+e^{-t}=C](https://tex.z-dn.net/?f=F%28x%2Ct%29%3D%5Cfrac%7B1%7D%7B49%7D%287x-1%29e%5E%7B7x%7D%2Be%5E%7B-t%7D%3DC)
Answer:
Step-by-step explanation:
We are given the following in the question:
Volume of cake = 351 cubic inches
Let x inches be the width of cake.
Width of cake, w =
![x\text{ inches}](https://tex.z-dn.net/?f=x%5Ctext%7B%20inches%7D)
Then, length of cake,l =
![(x + 4)\text{ inches}](https://tex.z-dn.net/?f=%28x%20%2B%204%29%5Ctext%7B%20inches%7D)
Height of cake,h =
![\dfrac{x}{3}\text{ inches}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B3%7D%5Ctext%7B%20inches%7D)
Volume of cake = Volume of cuboid
![V = lwh](https://tex.z-dn.net/?f=V%20%3D%20lwh)
Putting values, we get:
![351 = x(x+4)(\dfrac{x}{3})\\\\1053 = x^3 + 4x\\x^3+4x^2-1053= 0\\\\\text{For x = 9}\\(9)^3+4(9)^2-1053= 0](https://tex.z-dn.net/?f=351%20%3D%20x%28x%2B4%29%28%5Cdfrac%7Bx%7D%7B3%7D%29%5C%5C%5C%5C1053%20%3D%20x%5E3%20%2B%204x%5C%5Cx%5E3%2B4x%5E2-1053%3D%200%5C%5C%5C%5C%5Ctext%7BFor%20x%20%3D%209%7D%5C%5C%289%29%5E3%2B4%289%29%5E2-1053%3D%200)
Thus, dimensions of cake are:
![w = 9 \text{ inches}\\l = 13\text{ inches}\\h = 3\text{ inches}](https://tex.z-dn.net/?f=w%20%3D%209%20%5Ctext%7B%20inches%7D%5C%5Cl%20%3D%2013%5Ctext%7B%20inches%7D%5C%5Ch%20%3D%203%5Ctext%7B%20inches%7D)
Answer:
Step-by-step explanation: