Mixing
Is it possible to switch from this interval to this one?
Clash Royale CLAN TAG#URR8PPP
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I have an interval $[0; 100]$ and would like to map it to this new interval: $[100;350]$.
I thought about multiplying it by $3.5$, but that would give the interval $[0;350]$. And adding to each of these elements $100$ would give: $[100;450]$. Hence my question: is it possible to do what I want?
Note that I can settle for the interval $[0;350]$ : in my program, it will be enough if I exclude the numbers present in the interval $[0;99]$.
interval-arithmetic
asked 39 mins ago
JarsOfJam-Scheduler
1278
add a comment |Â
up vote
1
down vote
favorite
I have an interval $[0; 100]$ and would like to map it to this new interval: $[100;350]$.
I thought about multiplying it by $3.5$, but that would give the interval $[0;350]$. And adding to each of these elements $100$ would give: $[100;450]$. Hence my question: is it possible to do what I want?
Note that I can settle for the interval $[0;350]$ : in my program, it will be enough if I exclude the numbers present in the interval $[0;99]$.
interval-arithmetic
asked 39 mins ago
JarsOfJam-Scheduler
1278
how about multiplying by 2.5 instead?
– Lord Shark the Unknown
34 mins ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have an interval $[0; 100]$ and would like to map it to this new interval: $[100;350]$.
I thought about multiplying it by $3.5$, but that would give the interval $[0;350]$. And adding to each of these elements $100$ would give: $[100;450]$. Hence my question: is it possible to do what I want?
Note that I can settle for the interval $[0;350]$ : in my program, it will be enough if I exclude the numbers present in the interval $[0;99]$.
interval-arithmetic
asked 39 mins ago
JarsOfJam-Scheduler
1278
I have an interval $[0; 100]$ and would like to map it to this new interval: $[100;350]$.
I thought about multiplying it by $3.5$, but that would give the interval $[0;350]$. And adding to each of these elements $100$ would give: $[100;450]$. Hence my question: is it possible to do what I want?
Note that I can settle for the interval $[0;350]$ : in my program, it will be enough if I exclude the numbers present in the interval $[0;99]$.
interval-arithmetic
interval-arithmetic
asked 39 mins ago
JarsOfJam-Scheduler
1278
asked 39 mins ago
JarsOfJam-Scheduler
1278
asked 39 mins ago
JarsOfJam-Scheduler
1278
asked 39 mins ago
JarsOfJam-Scheduler
1278
asked 39 mins ago
JarsOfJam-Scheduler
1278
1278
how about multiplying by 2.5 instead?
– Lord Shark the Unknown
34 mins ago
add a comment |Â
how about multiplying by 2.5 instead?
– Lord Shark the Unknown
34 mins ago
how about multiplying by 2.5 instead?
– Lord Shark the Unknown
34 mins ago
how about multiplying by 2.5 instead?
– Lord Shark the Unknown
34 mins ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
2
down vote
accepted
To map from $[a,b]$ to $[c, d]$,
Consider the straight line that connects $(a,c)$ to $(b,d)$.
We have the slope $m = fracd-cb-a,$ we are able to recover $m$.
$$y=mx+C$$
To recover $C$, just substitute one of the value say $(a,c)$ and solve for $C$. For our example, we have $a=0$ and $c=100$.
Hence your transformation can be of the form of $y=mx+100$. Can you compute the $m$ to find what you want?
answered 33 mins ago
Siong Thye Goh
86.1k1458107
add a comment |Â
up vote
2
down vote
The ratio of the lengths of the intervals is $2.5 :1,$ the position of the left extremity is schifted by $100.$ So take the mapping $$f(x)=2.5x+100.$$
answered 19 mins ago
user376343
1,392614
add a comment |Â
up vote
1
down vote
You can consider $xmapsto ax + bcolon [0,100]to [100,350]$ such that $0mapsto 100$ and $100mapsto 350$.
Thus, $$a cdot 0 + b = 100,\ acdot 100 + b = 350,$$ and solving it gives $a = frac 52$, $b = 100$.
In general, the same technique works for intervals $[x_1,x_2]$ and $[y_1,y_2]$:
$$ax_1 + b = y_1\
ax_2 + b = y_2.$$
Solving it gives $a = fracy_2 - y_1x_2 -x_1$ and $b = y_1 - ax_1$. All in all, it's a line $$y - y_1 = fracy_2-y_1x_2-x_1(x-x_1).$$ Looks familiar?
answered 10 mins ago
Ennar
13.3k32343
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
To map from $[a,b]$ to $[c, d]$,
Consider the straight line that connects $(a,c)$ to $(b,d)$.
We have the slope $m = fracd-cb-a,$ we are able to recover $m$.
$$y=mx+C$$
To recover $C$, just substitute one of the value say $(a,c)$ and solve for $C$. For our example, we have $a=0$ and $c=100$.
Hence your transformation can be of the form of $y=mx+100$. Can you compute the $m$ to find what you want?
answered 33 mins ago
Siong Thye Goh
86.1k1458107
add a comment |Â
up vote
2
down vote
accepted
To map from $[a,b]$ to $[c, d]$,
Consider the straight line that connects $(a,c)$ to $(b,d)$.
We have the slope $m = fracd-cb-a,$ we are able to recover $m$.
$$y=mx+C$$
To recover $C$, just substitute one of the value say $(a,c)$ and solve for $C$. For our example, we have $a=0$ and $c=100$.
Hence your transformation can be of the form of $y=mx+100$. Can you compute the $m$ to find what you want?
answered 33 mins ago
Siong Thye Goh
86.1k1458107
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
To map from $[a,b]$ to $[c, d]$,
Consider the straight line that connects $(a,c)$ to $(b,d)$.
We have the slope $m = fracd-cb-a,$ we are able to recover $m$.
$$y=mx+C$$
To recover $C$, just substitute one of the value say $(a,c)$ and solve for $C$. For our example, we have $a=0$ and $c=100$.
Hence your transformation can be of the form of $y=mx+100$. Can you compute the $m$ to find what you want?
answered 33 mins ago
Siong Thye Goh
86.1k1458107
To map from $[a,b]$ to $[c, d]$,
Consider the straight line that connects $(a,c)$ to $(b,d)$.
We have the slope $m = fracd-cb-a,$ we are able to recover $m$.
$$y=mx+C$$
To recover $C$, just substitute one of the value say $(a,c)$ and solve for $C$. For our example, we have $a=0$ and $c=100$.
Hence your transformation can be of the form of $y=mx+100$. Can you compute the $m$ to find what you want?
answered 33 mins ago
Siong Thye Goh
86.1k1458107
answered 33 mins ago
Siong Thye Goh
86.1k1458107
answered 33 mins ago
Siong Thye Goh
86.1k1458107
answered 33 mins ago
Siong Thye Goh
86.1k1458107
86.1k1458107
add a comment |Â
add a comment |Â
up vote
2
down vote
The ratio of the lengths of the intervals is $2.5 :1,$ the position of the left extremity is schifted by $100.$ So take the mapping $$f(x)=2.5x+100.$$
answered 19 mins ago
user376343
1,392614
add a comment |Â
up vote
2
down vote
The ratio of the lengths of the intervals is $2.5 :1,$ the position of the left extremity is schifted by $100.$ So take the mapping $$f(x)=2.5x+100.$$
answered 19 mins ago
user376343
1,392614
add a comment |Â
up vote
2
down vote
up vote
2
down vote
The ratio of the lengths of the intervals is $2.5 :1,$ the position of the left extremity is schifted by $100.$ So take the mapping $$f(x)=2.5x+100.$$
answered 19 mins ago
user376343
1,392614
The ratio of the lengths of the intervals is $2.5 :1,$ the position of the left extremity is schifted by $100.$ So take the mapping $$f(x)=2.5x+100.$$
answered 19 mins ago
user376343
1,392614
answered 19 mins ago
user376343
1,392614
answered 19 mins ago
user376343
1,392614
answered 19 mins ago
user376343
1,392614
1,392614
add a comment |Â
add a comment |Â
up vote
1
down vote
You can consider $xmapsto ax + bcolon [0,100]to [100,350]$ such that $0mapsto 100$ and $100mapsto 350$.
Thus, $$a cdot 0 + b = 100,\ acdot 100 + b = 350,$$ and solving it gives $a = frac 52$, $b = 100$.
In general, the same technique works for intervals $[x_1,x_2]$ and $[y_1,y_2]$:
$$ax_1 + b = y_1\
ax_2 + b = y_2.$$
Solving it gives $a = fracy_2 - y_1x_2 -x_1$ and $b = y_1 - ax_1$. All in all, it's a line $$y - y_1 = fracy_2-y_1x_2-x_1(x-x_1).$$ Looks familiar?
answered 10 mins ago
Ennar
13.3k32343
add a comment |Â
up vote
1
down vote
You can consider $xmapsto ax + bcolon [0,100]to [100,350]$ such that $0mapsto 100$ and $100mapsto 350$.
Thus, $$a cdot 0 + b = 100,\ acdot 100 + b = 350,$$ and solving it gives $a = frac 52$, $b = 100$.
In general, the same technique works for intervals $[x_1,x_2]$ and $[y_1,y_2]$:
$$ax_1 + b = y_1\
ax_2 + b = y_2.$$
Solving it gives $a = fracy_2 - y_1x_2 -x_1$ and $b = y_1 - ax_1$. All in all, it's a line $$y - y_1 = fracy_2-y_1x_2-x_1(x-x_1).$$ Looks familiar?
answered 10 mins ago
Ennar
13.3k32343
add a comment |Â
up vote
1
down vote
up vote
1
down vote
You can consider $xmapsto ax + bcolon [0,100]to [100,350]$ such that $0mapsto 100$ and $100mapsto 350$.
Thus, $$a cdot 0 + b = 100,\ acdot 100 + b = 350,$$ and solving it gives $a = frac 52$, $b = 100$.
In general, the same technique works for intervals $[x_1,x_2]$ and $[y_1,y_2]$:
$$ax_1 + b = y_1\
ax_2 + b = y_2.$$
Solving it gives $a = fracy_2 - y_1x_2 -x_1$ and $b = y_1 - ax_1$. All in all, it's a line $$y - y_1 = fracy_2-y_1x_2-x_1(x-x_1).$$ Looks familiar?
answered 10 mins ago
Ennar
13.3k32343
You can consider $xmapsto ax + bcolon [0,100]to [100,350]$ such that $0mapsto 100$ and $100mapsto 350$.
Thus, $$a cdot 0 + b = 100,\ acdot 100 + b = 350,$$ and solving it gives $a = frac 52$, $b = 100$.
In general, the same technique works for intervals $[x_1,x_2]$ and $[y_1,y_2]$:
$$ax_1 + b = y_1\
ax_2 + b = y_2.$$
Solving it gives $a = fracy_2 - y_1x_2 -x_1$ and $b = y_1 - ax_1$. All in all, it's a line $$y - y_1 = fracy_2-y_1x_2-x_1(x-x_1).$$ Looks familiar?
answered 10 mins ago
Ennar
13.3k32343
edited 7 secs ago
answered 10 mins ago
Ennar
13.3k32343
answered 10 mins ago
Ennar
13.3k32343
answered 10 mins ago
Ennar
13.3k32343
13.3k32343
add a comment |Â
add a comment |Â
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how about multiplying by 2.5 instead?
– Lord Shark the Unknown
34 mins ago