3x - 2y = -16
Slope intercept form is y = mx + b, so solve it for 'y'
First subtract 3x to both sides:
-2y = -3x - 16
Now divide -2 to both sides:
y = 3/2x + 8
Answer:
Area= base×height
7×18? 126
Step-by-step explanation:
The area of Ted’s patio is 126 ft.
Answer:
A
Hope this helps
Step-by-step explanation:
Answer:
<em>The correct option is C.</em>
Step-by-step explanation:
<u>Root Of Complex Numbers</u>
If a complex number is expressed in polar form as
Then the cubic roots of Z are
![\displaystyle Z_1=\left(\sqrt[3]{r},\frac{\theta}{3}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_1%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%5Cright%29)
![\displaystyle Z_2=\left(\sqrt[3]{r},\frac{\theta}{3}+120^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_2%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%2B120%5Eo%5Cright%29)
![\displaystyle Z_3=\left(\sqrt[3]{r},\frac{\theta}{3}+240^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_3%3D%5Cleft%28%5Csqrt%5B3%5D%7Br%7D%2C%5Cfrac%7B%5Ctheta%7D%7B3%7D%2B240%5Eo%5Cright%29)
We are given the complex number in rectangular components
Converting to polar form
It's located in the second quadrant, so
The number if polar form is
Its cubic roots are
![\displaystyle Z_1=\left(\sqrt[3]{2},\frac{120^o}{3}\right)=\left(\sqrt[3]{2},40^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_1%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C%5Cfrac%7B120%5Eo%7D%7B3%7D%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%5Cright%29)
![\displaystyle Z_2=\left(\sqrt[3]{2},40^o+120^o\right)=\left(\sqrt[3]{2},160^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_2%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%2B120%5Eo%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C160%5Eo%5Cright%29)
![\displaystyle Z_3=\left(\sqrt[3]{2},40^o+240^o\right)=\left(\sqrt[3]{2},280^o\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Z_3%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C40%5Eo%2B240%5Eo%5Cright%29%3D%5Cleft%28%5Csqrt%5B3%5D%7B2%7D%2C280%5Eo%5Cright%29)
Converting the first solution to rectangular coordinates
![z_1=\sqrt[3]{2}(\ cos40^o+i\ sin40^o)](https://tex.z-dn.net/?f=z_1%3D%5Csqrt%5B3%5D%7B2%7D%28%5C%20cos40%5Eo%2Bi%5C%20sin40%5Eo%29)
The correct option is C.
This is a question of resolving the forces in question into horizontal and vertical and then finding the action of the resultant force.
The first force acts at an angle less than 90° and thus its resolved forces are positive. The second force acts at angle larger than 90° and is incident and thus its horizontal value is positive while its vertical value is negative.
Therefore;
For force of 300 N at 30°;
Horizontal value = 300*Cos 30 = 259.81 N
Vertical value = 300*Sin 30 = 150 N
For 150 N at 135°;
Horizontal value = 150*Cos (180-135) = 106.07 N
Vertical value = -150*Sin (180-135) = -106.07 N
Then,
Resultant horizontal value = 259.81+106.07 = 365.88 N
Resultant vertical value = 150-106.07 = 43.93 N
Therefore,
Resultant force, v = Sqrt (365.88^2+43.93^2) = 368.51 N
Angle of action measured from horizontal = tan ^-1(43.93/365.88) 6.85°
Then,
v = 368.51 N at 6.85° from horizontal
