Integrate both sides twice to recover the general form of
:
![f''(x)=5+\cos x\implies f'(x)=5x+\sin x+C_1\implies f(x)=\dfrac52x^2-\cos x+C_1x+C_2](https://tex.z-dn.net/?f=f%27%27%28x%29%3D5%2B%5Ccos%20x%5Cimplies%20f%27%28x%29%3D5x%2B%5Csin%20x%2BC_1%5Cimplies%20f%28x%29%3D%5Cdfrac52x%5E2-%5Ccos%20x%2BC_1x%2BC_2)
With the given boundary conditions, we have
![\begin{cases}-1+C_2=-1\\\\\dfrac52\left(\dfrac{3\pi}2\right)^2+\dfrac{3\pi}2C_1+C_2=0\end{cases}\implies C_1=-\dfrac{15\pi}4,C_2=0](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D-1%2BC_2%3D-1%5C%5C%5C%5C%5Cdfrac52%5Cleft%28%5Cdfrac%7B3%5Cpi%7D2%5Cright%29%5E2%2B%5Cdfrac%7B3%5Cpi%7D2C_1%2BC_2%3D0%5Cend%7Bcases%7D%5Cimplies%20C_1%3D-%5Cdfrac%7B15%5Cpi%7D4%2CC_2%3D0)
So,
![f(x)=\dfrac52x^2-\cos x-\dfrac{15\pi}4x](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac52x%5E2-%5Ccos%20x-%5Cdfrac%7B15%5Cpi%7D4x)
Answer:
The answer is D. 55%
40% cashews in 15 ounces = 40/100 × 15 = 600/100 = 6 ounces of cashew
60% cashew in 45 ounces = 60/100 × 45 = 2700/100 = 27 ounce of cashew
total weight of the mixed nuts = 15 + 45 = 60 ounces
total weight of cashew = 27 + 6 = 33 ounces
% of cashew in the 60 ounce bag = 33/60 × 100 = 3300/60 = 55%
Use the law of Sines
Angle C = 18 degrees
c/Sin 18 = 10/Sin 12
Cross multiply
(10Sin18)/Sin12 = c
c = 14.9 cm
Answer:
<em />
<em />
<em />
Step-by-step explanation:
Given
![Yellow = 5\ seconds](https://tex.z-dn.net/?f=Yellow%20%3D%205%5C%20seconds)
![Green = 50\ seconds](https://tex.z-dn.net/?f=Green%20%3D%2050%5C%20seconds)
![Red = 50\ seconds](https://tex.z-dn.net/?f=Red%20%3D%2050%5C%20seconds)
Required
Determine the probability of Green or Yellow
First, we need to determine the total time
![Total = 50 + 50 + 5](https://tex.z-dn.net/?f=Total%20%3D%2050%20%2B%2050%20%2B%205)
![Total = 105\ seconds](https://tex.z-dn.net/?f=Total%20%3D%20105%5C%20seconds)
Next, is to determine the required probability
<em>This is calculated as follows:</em>
![P(Yellow\ or\ Green) = P(Yellow) + P(Green)](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20P%28Yellow%29%20%2B%20P%28Green%29)
![P(Yellow\ or\ Green) = \frac{n(Yellow)}{Total} + \frac{n(Green)}{Total}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7Bn%28Yellow%29%7D%7BTotal%7D%20%2B%20%5Cfrac%7Bn%28Green%29%7D%7BTotal%7D)
![P(Yellow\ or\ Green) = \frac{5}{105} + \frac{50}{105}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7B5%7D%7B105%7D%20%2B%20%5Cfrac%7B50%7D%7B105%7D)
![P(Yellow\ or\ Green) = \frac{5 + 50}{105}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7B5%20%2B%2050%7D%7B105%7D)
![P(Yellow\ or\ Green) = \frac{55}{105}](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%20%5Cfrac%7B55%7D%7B105%7D)
![P(Yellow\ or\ Green) = 0.52380952381](https://tex.z-dn.net/?f=P%28Yellow%5C%20or%5C%20Green%29%20%3D%200.52380952381)
<em />
<em> -- Approximated</em>
Answer:
4
Step-by-step explanation:
(3-4)+5
-1+5
4