#Homework

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junior vector
#

I translated this with gpt from german to english.. if you dont understand the translation i am happy to help with that

The so-called total ozone is a measure of the thickness of the ozone layer and is given in so-called Dobson Units (DU). The measurement data recorded by a weather balloon can be modeled by a quadratic function
𝑓
f. Here,
𝑓
f associates the total ozone density
𝑓
(
β„Ž
)
f(h) with the altitude
β„Ž
h (with
β„Ž
h in km, and
𝑓
(
β„Ž
)
f(h) in DU/km).

The highest value of
36
 
DU/km
36DU/km is measured at an altitude of
22
 
km
22km. At an altitude of
37
 
km
37km, the measured value is
1
 
DU/km
1DU/km.

Note:

𝑓
(
β„Ž
)
f(h) describes a quadratic function of the form
𝑓
(
β„Ž
)

π‘Ž
β‹…
β„Ž
2
+
𝑏
β‹…
β„Ž
+
𝑐
f(h)=aβ‹…h
2
+bβ‹…h+c.
The following conditions can be derived from the given information:

𝑓
(
37
)

1
f(37)=1
𝑓
(
22
)

36
f(22)=36
𝑓
β€²
(
22
)

0
f
β€²
(22)=0, since the highest value is measured at an altitude of
22
 
km
22km, which also represents the maximum point.
Form the first derivative of the function
𝑓
(
β„Ž
)
f(h). Then set up equations and solve the system of equations to find values for
π‘Ž
a,
𝑏
b, and
𝑐
c.

First, calculate
∫
7
37
𝑓
(
β„Ž
)
 
𝑑
β„Ž
∫
7
37
​
f(h)dh.
This can be done manually or with the help of GeoGebra:

Enter the function
𝑓
(
β„Ž
)
f(h) in the input field.
Choose Integral(<Function>,<Start Value>,<End Value>), where you set the function to
𝑓
(
β„Ž
)
f(h), the start value to
7
7, and the end value to
37
37.
Since
1
 
DU
1DU corresponds to a
0.01
 
mm
0.01mm-thick layer of pure ozone at the Earth's surface, the result of the integral must be multiplied by
0.01
0.01.

Determine
𝑓
(
β„Ž
)
f(h).

DU
1DU corresponds to a
0.01
 
mm
0.01mm-thick layer of pure ozone at the Earth's surface. The thickness of that layer of pure ozone at the Earth's surface, corresponding to the total ozone between altitudes of
7

Calculate the thickness
𝑀
w of this layer.

w=___mm

shy mauveBOT
#
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junior vector
#

Oh my god...

#

hahahah yes

#

i am lost

#

the format is crazy ima send a screen shot

#

from what ive got i need to first creat the function but i lowkey forgot how to do that

#

Do you have to find a,b,c?

#

yes

#

i need to give the function and 3 conditions are listed but i dont reamember how i can get the function out of it

#

use condition 1 substitute h=37

#

so a.37^2+37b+c=1

#

You can get 2 equations and eliminate c

#

i used to do it with my calculator but i cant figure out how i did it and i cant really do it by hand because i suck at that majorly

abstract pewter
#

there should be some tutorials on it

junior vector
#

oh i need to do more than just find it sadly

abstract pewter
junior vector
#

that it is 0

#

i have this rn and somehow i should be able to solve it but my programm aint doing it

image.png
abstract pewter
junior vector
#

idk i wanna give up

abstract pewter
chilly finchBOT
#

@junior vector

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