Answer:
Patanahi bhhai sorry bro plz
For this case we define the following variables:
x: Number of party dresses
y: Number of suits
You have 30 hours per week to cut, that is, the first equation is given by:
![3x + 3y = 30\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C)
It is also known that 25 hours per week are available for sewing, that is:
![2x + 3y = 25\\](https://tex.z-dn.net/?f=2x%20%2B%203y%20%3D%2025%5C%5C)
It has a system of two equations with two unknowns, solving we have:
![3x + 3y = 30\\\\2x + 3y = 25\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C%5C%5C2x%20%2B%203y%20%3D%2025%5C%5C)
Multiplying the second equation by -1:
![3x + 3y = 30\\\\-2x-3y = -25\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C%5C%5C-2x-3y%20%3D%20-25%5C%5C)
Adding up:
![x + 0 = 5\\\\x = 5\\](https://tex.z-dn.net/?f=x%20%2B%200%20%3D%205%5C%5C%5C%5Cx%20%3D%205%5C%5C)
Substituting x in the first equation:
![3 * 5 + 3y = 30\\\\15 + 3y = 30\\](https://tex.z-dn.net/?f=3%20%2A%205%20%2B%203y%20%3D%2030%5C%5C%5C%5C15%20%2B%203y%20%3D%2030%5C%5C)
Clearing and:
![3y = 30-15\\\\3y = 15\\](https://tex.z-dn.net/?f=3y%20%3D%2030-15%5C%5C%5C%5C3y%20%3D%2015%5C%5C)
![y = \frac{15}{3}\\\\y = 5\\](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B15%7D%7B3%7D%5C%5C%5C%5Cy%20%3D%205%5C%5C)
Thus, per week, the designer can produce 5 party dresses and 5 suits working at her maximum capacity.
Answer:
5 Party dresses
5 Suits
Answer:
<u>Part 1:</u> Angle = 154.3°
<u>Part 2:</u> About 2.33 Rotations
Step-by-step explanation:
Part 1:
The arc length of a circle is given by the formula ![s=r\theta](https://tex.z-dn.net/?f=s%3Dr%5Ctheta)
Where
- s is the arc length
- r is the radius of the circle
is the angle
**The angle are in radians and we will use radian**
When smaller gear has made 1 complete rotations (
radians), the arc length traveled is ![s=r\theta\\s=(3)(2\pi)\\s=6\pi](https://tex.z-dn.net/?f=s%3Dr%5Ctheta%5C%5Cs%3D%283%29%282%5Cpi%29%5C%5Cs%3D6%5Cpi)
Now, what angle is swept by the larger circle when it travels
? Put in
and r is 7 to find
:
![s=r\theta\\6\pi=(7)\theta\\\theta= \frac{6\pi}{7}](https://tex.z-dn.net/?f=s%3Dr%5Ctheta%5C%5C6%5Cpi%3D%287%29%5Ctheta%5C%5C%5Ctheta%3D%20%5Cfrac%7B6%5Cpi%7D%7B7%7D)
** Since
radians is 180°, we plug in 180 into
and find the degree measure:
![\frac{6\pi}{7}=\frac{6*180}{7}=154.3](https://tex.z-dn.net/?f=%5Cfrac%7B6%5Cpi%7D%7B7%7D%3D%5Cfrac%7B6%2A180%7D%7B7%7D%3D154.3)
Angle = 154.3°
Part 2:
In one complete rotation of the larger gear, it travels a distance of:
![s=r\theta\\s=(7)(2\pi)\\s=14\pi](https://tex.z-dn.net/?f=s%3Dr%5Ctheta%5C%5Cs%3D%287%29%282%5Cpi%29%5C%5Cs%3D14%5Cpi)
We know that the smaller circle makes 1 rotation and travels
, so in
distance, it makes:
Rotations = ![\frac{14\pi}{6\pi}=\frac{14}{6}=2.33](https://tex.z-dn.net/?f=%5Cfrac%7B14%5Cpi%7D%7B6%5Cpi%7D%3D%5Cfrac%7B14%7D%7B6%7D%3D2.33)
About 2.33 Rotations
The correct answer would be D) or the Torah
Answer:
x=7
Step-by-step explanation:
This is a vertical line. Vertical lines are of the form x=
The x coordinate is 7
x=7