Answer:
The company must sell 60 or 70 items to obtain a weekly profit of 200.
Step-by-step explanation:
The profit is the difference between the revenue and the cost of a given task, therefore:
![\text{profit} = R - C\\\text{profit} = 66*x - 0.2*x^2 - (40*x + 640)\\\text{profit} = 66*x - 0.2*x^2 - 40*x - 640\\\text{profit} = - 0.2*x^2 + 26*x - 640](https://tex.z-dn.net/?f=%5Ctext%7Bprofit%7D%20%3D%20R%20-%20C%5C%5C%5Ctext%7Bprofit%7D%20%3D%2066%2Ax%20-%200.2%2Ax%5E2%20-%20%2840%2Ax%20%2B%20640%29%5C%5C%5Ctext%7Bprofit%7D%20%3D%2066%2Ax%20-%200.2%2Ax%5E2%20-%2040%2Ax%20-%20640%5C%5C%5Ctext%7Bprofit%7D%20%3D%20-%200.2%2Ax%5E2%20%2B%2026%2Ax%20-%20640)
To have a profit of 200, we need to sell:
![-0.2*x^2 + 26*x - 640 = 200\\-0.2*x^2 + 26*x -840 = 0\text{ } *\frac{-1}{0.2}\\x^2 -130 + -4200 = 0\\x_{1,2} = \frac{-(-130) \pm \sqrt{(-130)^2 - 4*1*(-4200)}}{2*1}\\x_{1,2} = \frac{130 \pm \sqrt{16900 + 16800}}{2}\\x_{1,2} = \frac{130 \pm \sqrt{100}}{2}\\x_{1,2} = \frac{130 \pm 10}{2}\\x_{1} = \frac{130 + 10}{2} = \frac{140}{2} = 70\\ x_{2} = \frac{130 - 10}{2} = \frac{120}{2} = 60](https://tex.z-dn.net/?f=-0.2%2Ax%5E2%20%2B%2026%2Ax%20-%20640%20%3D%20200%5C%5C-0.2%2Ax%5E2%20%2B%2026%2Ax%20-840%20%3D%200%5Ctext%7B%20%7D%20%2A%5Cfrac%7B-1%7D%7B0.2%7D%5C%5Cx%5E2%20-130%20%2B%20-4200%20%3D%200%5C%5Cx_%7B1%2C2%7D%20%3D%20%5Cfrac%7B-%28-130%29%20%5Cpm%20%5Csqrt%7B%28-130%29%5E2%20-%204%2A1%2A%28-4200%29%7D%7D%7B2%2A1%7D%5C%5Cx_%7B1%2C2%7D%20%3D%20%5Cfrac%7B130%20%5Cpm%20%5Csqrt%7B16900%20%2B%2016800%7D%7D%7B2%7D%5C%5Cx_%7B1%2C2%7D%20%3D%20%5Cfrac%7B130%20%5Cpm%20%5Csqrt%7B100%7D%7D%7B2%7D%5C%5Cx_%7B1%2C2%7D%20%3D%20%5Cfrac%7B130%20%5Cpm%2010%7D%7B2%7D%5C%5Cx_%7B1%7D%20%3D%20%5Cfrac%7B130%20%2B%2010%7D%7B2%7D%20%3D%20%5Cfrac%7B140%7D%7B2%7D%20%3D%2070%5C%5C%20x_%7B2%7D%20%3D%20%5Cfrac%7B130%20-%2010%7D%7B2%7D%20%3D%20%5Cfrac%7B120%7D%7B2%7D%20%20%3D%2060)
The company must sell 60 or 70 items to obtain a weekly profit of 200.
Answer:
CotR = -√3
Step-by-step explanation:
In the 4th quadrant, sin is negative;
Since Cos R = √3/2,
Adjacent = √3
Hypotenuse = 2
Get the opposite;
opp^2 = 2^2 -(√3)^2
opp^2 = 4 - 3
opp^2 = 1
Opp = 1
Get sinR
Sin R = opp/hyp
SinR= -1/2
CotR = cosR/sinR
CostR = (√3/2)/(-1/2)
CotR = √3/2* -2/1
CotR = -√3
Volume = l x w x h
180 = l (5 x 4)
180 = 20 l
6 = l
That means that the couch will fit, because the length of the van is 6 ft, which is also the length of the couch.
The domain is (-inf,+inf) and the range is (-inf,8]
Answer:
A
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given (h, k) = (0, - 7) and r = 11, then
(x - 0)² + (y - (- 7))² = 11², that is
x² + (y + 7)² = 121 → A