Answer:
y = 2w - 1 + aw
Step-by-step explanation:
Given
y - aw = 2w - 1 ( isolate y by adding aw to both sides )
y = aw - 1 + aw
Answer:
skewed to the left
Step-by-step explanation:
when you look at the graph, you look for where the peaks are. if the peak is not centered, it is skewed. in this case, it leans towards the left. hope this helps :)
Perimeter: x + (4x + 9) + (x + 11)
The value x is for the bottom of the triangle.
Simplified, it would be 6x + 20
Answer:
Explanation:
The number of emails is multiplied by <em>4</em> every <em>9.1 weeks.</em>
Thus, since <em>Tobias initially sent the chain letter to 37 friends</em>, the number of letters will grow as per this geometric series:
Start: 37 letters
- In 2 × 9.1 weeks: 37 × (4)²
- In 3 × 9.1 weeks: 37 × (4)³
As you see, the exponent is the number of weeks divided by 9.1
Thus, if your variable is the number of weeks, t, then the exponent is t/9.1
And the exponential function, P(t) will be:
![P(t)=37\times (4)^{(t/9.1)}](https://tex.z-dn.net/?f=P%28t%29%3D37%5Ctimes%20%284%29%5E%7B%28t%2F9.1%29%7D)
Answer:
a) ![\left(x,y\right)=\left(4.95,-4.95\right)](https://tex.z-dn.net/?f=%5Cleft%28x%2Cy%5Cright%29%3D%5Cleft%284.95%2C-4.95%5Cright%29)
b) ![r\angle\theta = 7\angle0.5236\,\text{radians}](https://tex.z-dn.net/?f=r%5Cangle%5Ctheta%20%3D%207%5Cangle0.5236%5C%2C%5Ctext%7Bradians%7D)
Step-by-step explanation:
Polar coordinates are represented as:
, where 'r' is the length (or magnitude) of the line, and '
' is the angle measured from the positive x-axis.
in our case:
![7\angle\dfrac{3\pi}{4}](https://tex.z-dn.net/?f=7%5Cangle%5Cdfrac%7B3%5Cpi%7D%7B4%7D)
to covert the polar to cartesian:
![x = r\cos{\theta}](https://tex.z-dn.net/?f=x%20%3D%20r%5Ccos%7B%5Ctheta%7D)
![y = r\sin{\theta}](https://tex.z-dn.net/?f=y%20%3D%20r%5Csin%7B%5Ctheta%7D)
we can plug in our values:
![x = 7\cos{\dfrac{3\pi}{4}} = -7\dfrac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=x%20%3D%207%5Ccos%7B%5Cdfrac%7B3%5Cpi%7D%7B4%7D%7D%20%3D%20-7%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
![y = 7\sin{\dfrac{3\pi}{4}} = 7\dfrac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=y%20%3D%207%5Csin%7B%5Cdfrac%7B3%5Cpi%7D%7B4%7D%7D%20%3D%207%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
the Cartesian coordinates are:
![\left(x,y\right)=\left(-7\dfrac{\sqrt{2}}{2},7\dfrac{\sqrt{2}}{2}\right)](https://tex.z-dn.net/?f=%5Cleft%28x%2Cy%5Cright%29%3D%5Cleft%28-7%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C7%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Cright%29)
![\left(x,y\right)=\left(4.95,-4.95\right)](https://tex.z-dn.net/?f=%5Cleft%28x%2Cy%5Cright%29%3D%5Cleft%284.95%2C-4.95%5Cright%29)
(b) to convert (x,y) = (6.06,-3.5)
we'll use the pythagoras theorem to find 'r'
![r^2 = x^2+y^2](https://tex.z-dn.net/?f=r%5E2%20%3D%20x%5E2%2By%5E2)
![r^2 = (6.06)^2+(-3.5)^2](https://tex.z-dn.net/?f=r%5E2%20%3D%20%286.06%29%5E2%2B%28-3.5%29%5E2)
![r = \sqrt{48.97} \approx 7](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B48.97%7D%20%5Capprox%207)
the angle can be found by:
![\tan{\theta} = \dfrac{y}{x}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cdfrac%7By%7D%7Bx%7D)
![\tan{\theta} = \dfrac{3.5}{6.06}](https://tex.z-dn.net/?f=%5Ctan%7B%5Ctheta%7D%20%3D%20%5Cdfrac%7B3.5%7D%7B6.06%7D)
![\theta = \arctan{left(\dfrac{3.5}{6.06}\right)}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20%5Carctan%7Bleft%28%5Cdfrac%7B3.5%7D%7B6.06%7D%5Cright%29%7D)
![\theta = 0.5236 \text{radians}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%200.5236%20%5Ctext%7Bradians%7D)
to convert radians to degrees:
![\theta = 0.5236 \times \dfrac{180}{\pi} \approx 30^\circ](https://tex.z-dn.net/?f=%5Ctheta%20%3D%200.5236%20%5Ctimes%20%5Cdfrac%7B180%7D%7B%5Cpi%7D%20%5Capprox%2030%5E%5Ccirc)
writing in polar coordinates:
![r\angle\theta = 7\angle30^\circ\,\,\text{OR}\,\,7\angle0.5236\,\text{radians}](https://tex.z-dn.net/?f=r%5Cangle%5Ctheta%20%3D%207%5Cangle30%5E%5Ccirc%5C%2C%5C%2C%5Ctext%7BOR%7D%5C%2C%5C%2C7%5Cangle0.5236%5C%2C%5Ctext%7Bradians%7D)