Answer:
17 cm
Step-by-step explanation:
1. Depth in fresh water
p(water) = hρg
d(max) = h = p/(ρg)
Convert atmospheres to pascals
0.056 atm × 101 325 Pa/1 atm = 5670 Pa
h = 5670 Pa/(1000 kg·m⁻³ × 9.806 m·s⁻²) × (1 kg·m⁻¹s⁻²/1 N) = 0.579 m
2. Depth in Dead Sea
d(max) = 5670/(1400 × 9.806) = 0.413 m
3. Difference
Difference = 0.579 – 0.413 = 0.17 m = 17 cm
The difference in d(max) is 17 cm.
<span>The solution to the problem is: x = (-2, -3)</span>
I assume you want to mathematically represent the above
Answer and explanation:
If Diego collected x kg of recycling and Lin collected 2/5 more than what Diego collected, then it would be represented mathematically thus:
Diego = x
Lin = x +2/5 of x= x+2/5x
if Lin biked x km and Diego biked 3/10km less than Lin, then we would represent this thus:
Lin=x
Diego= x-3/10 of x= x-3/10x
If Diego reads for x minutes and Lin reads 4/7 of what Diego read, then mathematically we represent this thus:
Diego=x
Lin =4/7 of x = 4/7x
Answer:
The graph of the function
is attached below.
Step-by-step explanation:
Considering the function
![f\left(x\right)=\:\log _{10}\:x-3](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D%5C%3A%5Clog%20_%7B10%7D%5C%3Ax-3)
![\mathrm{Domain\:of\:}\:\log _{10}\left(x\right)-3\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}](https://tex.z-dn.net/?f=%5Cmathrm%7BDomain%5C%3Aof%5C%3A%7D%5C%3A%5Clog%20_%7B10%7D%5Cleft%28x%5Cright%29-3%5C%3A%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3Ax%3E0%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%280%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
![\mathrm{Range\:of\:}\log _{10}\left(x\right)-3:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:](https://tex.z-dn.net/?f=%5Cmathrm%7BRange%5C%3Aof%5C%3A%7D%5Clog%20_%7B10%7D%5Cleft%28x%5Cright%29-3%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-%5Cinfty%20%5C%3A%3Cf%5Cleft%28x%5Cright%29%3C%5Cinfty%20%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-%5Cinfty%20%5C%3A%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
<u><em>Determining x-intercept:</em></u>
![\mathrm{x-intercept\:is\:a\:point\:on\:the\:graph\:where\:}y=0](https://tex.z-dn.net/?f=%5Cmathrm%7Bx-intercept%5C%3Ais%5C%3Aa%5C%3Apoint%5C%3Aon%5C%3Athe%5C%3Agraph%5C%3Awhere%5C%3A%7Dy%3D0)
![\log _{10}\left(x\right)-3=0](https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28x%5Cright%29-3%3D0)
![\log _{10}\left(x\right)=3](https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28x%5Cright%29%3D3)
Using the logarithmic definition
![\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c](https://tex.z-dn.net/?f=%5Cmathrm%7BIf%7D%5C%3A%5Clog%20_a%5Cleft%28b%5Cright%29%3Dc%5C%3A%5Cmathrm%7Bthen%7D%5C%3Ab%3Da%5Ec)
![\log _{10}\left(x\right)=3\quad \Rightarrow \quad \:x=10^3](https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28x%5Cright%29%3D3%5Cquad%20%5CRightarrow%20%5Cquad%20%5C%3Ax%3D10%5E3)
![x=1000](https://tex.z-dn.net/?f=x%3D1000)
so the x-intercept = (1000, 0)
<u><em /></u>
<u><em>Determining y-intercept:</em></u>
![y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0](https://tex.z-dn.net/?f=y%5Cmathrm%7B-intercept%5C%3Ais%5C%3Athe%5C%3Apoint%5C%3Aon%5C%3Athe%5C%3Agraph%5C%3Awhere%5C%3A%7Dx%3D0)
![\mathrm{Since}\:x=0\:\mathrm{is\:not\:in\:domain}](https://tex.z-dn.net/?f=%5Cmathrm%7BSince%7D%5C%3Ax%3D0%5C%3A%5Cmathrm%7Bis%5C%3Anot%5C%3Ain%5C%3Adomain%7D)
![\mathrm{No\:y-axis\:interception\:point}](https://tex.z-dn.net/?f=%5Cmathrm%7BNo%5C%3Ay-axis%5C%3Ainterception%5C%3Apoint%7D)
Therefore, the graph of the function
is attached below.
1. m=1/2 b=4 y=1/2x+4
2. m=-1/2 b=-3 y=-1/2x-3
3. m=-3/2 b=-1 y=-3/2x-1
4. m=1/2 b=-1 y=1/2x-1