Answer:
A. 8 gallons
B. Drive by car is $59.4 cheaper than travel by train
Step-by-step explanation:
According to the scenario, given data are as follows,
Total drive = 400 miles
Total drive per gallon = 50 miles
Fuel cost per gallon = $4.45
A. So, Total fuel required to drive 400 miles can be calculated as follows,
Total fuel required = Total drive ÷ Total drive per gallon
By putting value, we get,
Total fuel required = 400 ÷ 50
= 8 gallons
B. Total cost if drive by car = 8 gallons × $4.45 = $35.6
Cost if travel by train = $95
Hence it is clearly shows that drive by car is much cheaper than travel by train.
Cost saved by travel by car = $95 - $35.6 = $59.4
So, drive by car is $59.4 cheaper than travel by train.
Answer:
Step-by-step explanation:
g(-4) = 4 , x < -2
g(-2) = (x - 1)² ; -2≤x< 1
= (-2-1)²
= (-3)²
g(-2) = 9
g(0) = (x -1)² ; -2 ≤ x < 1
= (0 -1)²
= (-1)²
= 1
Hello,
y+1/2=3(x-2)
or y=3x-13/2
The Volume of the given solid using polar coordinate is:![\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B6%7D%20%5Cint%5Climits%5E%7B2%5Cpi%7D_%20%7B0%7D%20%5B%2860%29%20%5E%7B3%2F2%7D%20%5C%3B%20-%2864%29%20%5E%7B3%2F2%7D%20%5D%20d%5Ctheta)
V= ![\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B6%7D%20%5Cint%5Climits%5E%7B2%5Cpi%7D_%20%7B0%7D%20%5B%2860%29%20%5E%7B3%2F2%7D%20%5C%3B%20-%2864%29%20%5E%7B3%2F2%7D%20%5D%20d%5Ctheta)
<h3>
What is Volume of Solid in polar coordinates?</h3>
To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.
Consider the cylinder,
and the ellipsoid, 
In polar coordinates, we know that

So, the ellipsoid gives

4(
) +
= 64
= 64- 4(
)
z=± 
So, the volume of the solid is given by:
V= ![\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B2%5Cpi%7D_%200%20%5Cint%5Climits%5E1_0%7B%7D%20%5C%2C%20%5B%5Csqrt%7B64-4r%5E%7B2%7D%20%7D-%20%28-%5Csqrt%7B64-4r%5E%7B2%7D%20%7D%29%5D%20r%20dr%20d%5Ctheta)
= 
To solve the integral take,
= t
dt= -8rdr
rdr = 
So, the integral
become
=
= 
=
so on applying the limit, the volume becomes
V= 
=![\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B6%7D%20%5Cint%5Climits%5E%7B2%5Cpi%7D_%20%7B0%7D%20%5B%2864-4%281%29%5E%7B2%7D%29%20%5E%7B3%2F2%7D%20%5C%3B%20-%2864-4%282%29%5E%7B0%7D%29%20%5E%7B3%2F2%7D%20%5D%20d%5Ctheta)
V = ![\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B6%7D%20%5Cint%5Climits%5E%7B2%5Cpi%7D_%20%7B0%7D%20%5B%2860%29%20%5E%7B3%2F2%7D%20%5C%3B%20-%2864%29%20%5E%7B3%2F2%7D%20%5D%20d%5Ctheta)
Since, further the integral isn't having any term of
.
we will end here.
The Volume of the given solid using polar coordinate is:![\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B6%7D%20%5Cint%5Climits%5E%7B2%5Cpi%7D_%20%7B0%7D%20%5B%2860%29%20%5E%7B3%2F2%7D%20%5C%3B%20-%2864%29%20%5E%7B3%2F2%7D%20%5D%20d%5Ctheta)
Learn more about Volume in polar coordinate here:
brainly.com/question/25172004
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Answer:
less than
Step-by-step explanation: