Answer:
El perímetro de la región impresa es 72 cm y su área es 288 cm².
Step-by-step explanation:
1. Tenemos el perímetro de la hoja de papel:
P₁ = 96 cm = 2l₁ + 2a₁ (1)
Como sabemos el margen superior, inferior, izquierdo y derecho podemos encontrar la relación entre el largo y ancho del rectángulo interno (región impresa) con el largo (l) y ancho (a) del rectángulo externo (hoja de papel):
(2)
(3)
El perímetro del rectángulo interno es:
(4)
Introduciendo la ecuación (2) y (3) en (4):
Por lo tanto el perímetro del rectángulo interno (región impresa) es 72 cm.
2. Ahora para encontrar el área rectángulo interno debemos encontrar el largo y ancho del mismo, sabiendo que:
(5)
Introduciendo (5) en (4):
![P_{2} = 2l_{2} + 2a_{2} = 2*2a_{2} + 2a_{2} = 6a_{2}](https://tex.z-dn.net/?f=%20P_%7B2%7D%20%3D%202l_%7B2%7D%20%2B%202a_%7B2%7D%20%3D%202%2A2a_%7B2%7D%20%2B%202a_%7B2%7D%20%3D%206a_%7B2%7D%20)
![a_{2} = \frac{P_{2}}{6} = \frac{72 cm}{6} = 12 cm](https://tex.z-dn.net/?f=%20a_%7B2%7D%20%3D%20%5Cfrac%7BP_%7B2%7D%7D%7B6%7D%20%3D%20%5Cfrac%7B72%20cm%7D%7B6%7D%20%3D%2012%20cm%20)
![l_{2} = 2a_{2} = 2*12 cm = 24 cm](https://tex.z-dn.net/?f=%20l_%7B2%7D%20%3D%202a_%7B2%7D%20%3D%202%2A12%20cm%20%3D%2024%20cm%20)
Entonces el área es:
![A_{2} = l_{2}*a_{2} = 12 cm*24 cm = 288 cm^{2}](https://tex.z-dn.net/?f=%20A_%7B2%7D%20%3D%20l_%7B2%7D%2Aa_%7B2%7D%20%3D%2012%20cm%2A24%20cm%20%3D%20288%20cm%5E%7B2%7D%20)
Por lo tanto el área del rectágulo interno (región impresa) es 288 cm².
Espero que te sea de utilidad!
Q1. The answer is To solve, you must divide both sides by 6
The equation is: 6d = 12
<span>Multiplication is the inverse operation: TRUE - 6d = 12 d = 12/6
Checking the solution involves multiplication: TRUE - 6 * 2 = 12
The equation represents the number that gives twelve when multiplied by 6: TRUE d is </span>the number that gives twelve when multiplied by 6<span>
To solve, you must divide both sides by 6: false
Q2. The answer is 18
</span><span>
x - the number of students
The students were divided equally among 3 chaperones: 3 chaperones per x
Each chaperone supervised 6 students: 1 chaperone per 6 students
3 : x = 1 : 6
x = 3 * 6 : 1
x = 18
Q3. The answer is </span><span>t is greater than or equal to five.
</span>
It will take Harlon at least five years to complete his college degree. The key word is at least. This means that it can include number 5 as well. He may need 5 years, 6 years, 7 years,... Hence, t is greater than or equal to five.
Q4. The answer is <span>1.2
</span>
<span>p over zero point three + 2 = 6
p/0.3 + 2 = 6
multiply both sides by 0.03
p + 2 * 0.3 = 6 * 0.3
p + 0.6 = 1.8
p = 1.8 - 0.6
p = 1.2
Q5. The answer is 2.
</span><span>16w = 32
Divide both sides by 16
16w/16 = 32/16
w = 2</span>
Answer:
![\bold{x =cos\theta}\\\bold{y=sin\theta}](https://tex.z-dn.net/?f=%5Cbold%7Bx%20%3Dcos%5Ctheta%7D%5C%5C%5Cbold%7By%3Dsin%5Ctheta%7D)
Step-by-step explanation:
The given system of linear equations is:
![(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0](https://tex.z-dn.net/?f=%28cos%5Ctheta%29x%2B%28sin%5Ctheta%29y%3D1%5C%5C%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29y%3D0)
We have to solve the equations for the values of
.
Let us use elimination method in which we eliminate one of the variables from the two variables.
For this, let us multiply the first equation by
and second equation by ![cos\theta](https://tex.z-dn.net/?f=cos%5Ctheta)
Now, the equations become:
![(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)](https://tex.z-dn.net/?f=%28cos%5Ctheta.sin%5Ctheta%29x%2B%28sin%5Ctheta.sin%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%28cos%5Ctheta.sin%5Ctheta%29x%2B%28sin%5E2%5Ctheta%29y%3Dsin%5Ctheta%20.......%20%281%29%5C%5C%5C%5C%28-sin%5Ctheta.cos%5Ctheta%29x%2B%28cos%5Ctheta.cos%5Ctheta%29y%3D0%5C%5C%5CRightarrow%20%28-sin%5Ctheta.cos%5Ctheta%29x%2B%28cos%5E2%5Ctheta%29y%3D0%20.....%20%282%29)
Now, let us add (1) and (2):
![(sin^2\theta)y+(cos^2\theta)y=sin\theta\\\Rightarrow (sin^2\theta+cos^2\theta)y=sin\theta\\\Rightarrow (1)y=sin\theta\\\Rightarrow y = sin\theta](https://tex.z-dn.net/?f=%28sin%5E2%5Ctheta%29y%2B%28cos%5E2%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%28sin%5E2%5Ctheta%2Bcos%5E2%5Ctheta%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20%281%29y%3Dsin%5Ctheta%5C%5C%5CRightarrow%20y%20%3D%20sin%5Ctheta)
Using the equation:
![(-sin\theta)x+(cos\theta)y=0](https://tex.z-dn.net/?f=%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29y%3D0)
Putting value of
:
![\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta](https://tex.z-dn.net/?f=%5CRightarrow%20%28-sin%5Ctheta%29x%2B%28cos%5Ctheta%29sin%5Ctheta%3D0%5C%5C%5CRightarrow%20%28sin%5Ctheta%29x%3D%28cos%5Ctheta%29sin%5Ctheta%5C%5C%5CRightarrow%20x%20%3D%20cos%5Ctheta)
So, the answer to the system of linear equations is:
![\bold{x =cos\theta}\\\bold{y=sin\theta}](https://tex.z-dn.net/?f=%5Cbold%7Bx%20%3Dcos%5Ctheta%7D%5C%5C%5Cbold%7By%3Dsin%5Ctheta%7D)
8x + 8 —————// hope it helps
Answer:
Time taken to walk 20km = 5 hours