Answer:
Your answer is absolutely correct
Step-by-step explanation:
The work would be as follows:
![\int _0^{\sqrt{\pi }}4x^3\cos \left(x^2\right)dx,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> 4\cdot \int _0^{\sqrt{\pi }}x^3\cos \left(x^2\right)dx\\\\\mathrm{Apply\:u-substitution:}\:u=x^2\\=> 4\cdot \int _0^{\pi }\frac{u\cos \left(u\right)}{2}du\\\\\mathrm{Apply\:Integration\:By\:Parts:}\:u=u,\:v'=\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\int \sin \left(u\right)du\right]^{\pi }_0\\\\](https://tex.z-dn.net/?f=%5Cint%20_0%5E%7B%5Csqrt%7B%5Cpi%20%7D%7D4x%5E3%5Ccos%20%5Cleft%28x%5E2%5Cright%29dx%2C%5C%5C%5C%5C%5Cmathrm%7BTake%5C%3Athe%5C%3Aconstant%5C%3Aout%7D%3A%5Cquad%20%5Cint%20a%5Ccdot%20f%5Cleft%28x%5Cright%29dx%3Da%5Ccdot%20%5Cint%20f%5Cleft%28x%5Cright%29dx%5C%5C%3D%3E%204%5Ccdot%20%5Cint%20_0%5E%7B%5Csqrt%7B%5Cpi%20%7D%7Dx%5E3%5Ccos%20%5Cleft%28x%5E2%5Cright%29dx%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Au-substitution%3A%7D%5C%3Au%3Dx%5E2%5C%5C%3D%3E%204%5Ccdot%20%5Cint%20_0%5E%7B%5Cpi%20%7D%5Cfrac%7Bu%5Ccos%20%5Cleft%28u%5Cright%29%7D%7B2%7Ddu%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3AIntegration%5C%3ABy%5C%3AParts%3A%7D%5C%3Au%3Du%2C%5C%3Av%27%3D%5Ccos%20%5Cleft%28u%5Cright%29%5C%5C%3D%3E%204%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29-%5Cint%20%5Csin%20%5Cleft%28u%5Cright%29du%5Cright%5D%5E%7B%5Cpi%20%7D_0%5C%5C%5C%5C)
![\int \sin \left(u\right)du=-\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0\\\\\mathrm{Simplify\:}4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0:\quad 2\left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0\\\\\mathrm{Compute\:the\:boundaries}:\quad \left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0=-2\\=> 2(-2) = - 4](https://tex.z-dn.net/?f=%5Cint%20%5Csin%20%5Cleft%28u%5Cright%29du%3D-%5Ccos%20%5Cleft%28u%5Cright%29%5C%5C%3D%3E%204%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29-%5Cleft%28-%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%5C%5C%5C%5C%5Cmathrm%7BSimplify%5C%3A%7D4%5Ccdot%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29-%5Cleft%28-%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%3A%5Cquad%202%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29%2B%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%5C%5C%5C%5C%5Cmathrm%7BCompute%5C%3Athe%5C%3Aboundaries%7D%3A%5Cquad%20%5Cleft%5Bu%5Csin%20%5Cleft%28u%5Cright%29%2B%5Ccos%20%5Cleft%28u%5Cright%29%5Cright%5D%5E%7B%5Cpi%20%7D_0%3D-2%5C%5C%3D%3E%202%28-2%29%20%3D%20-%204)
Hence proved that your solution is accurate.
Answer: The answer is, A 7.1 units
Step-by-step explanation:
Answer:
Step-by-step explanation:
46-32 x 5/9 = 7.8
82-32x 5/9 = 27.8
Answer:
The initial number of bacteria in the culture was 1949
Step-by-step explanation:
The relative growth rate for a certain type of bacteria population is 78% per hour.
As we know the growth of bacteria is exponential function.

where,
P is population of bacteria after n hours.
P₀ is initial population.
r is rate of growth per hour
n is number of hours
A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture.
P = 34820 , n = 5 , r = 0.78



Hence, The initial number of bacteria in the culture was 1949
Answer:
We know that 30/25 is 1.2 or 1 1/5. SO if we divide 20 by that then we'll get 16.6667. So I won't give you the answer because its best that you learn to do this yourself because its more beneficial than telling you. What you have left is 16.6667=4x-4. Combine like terms and you'll get your answer. But if your still stuck then you can just let me know and I'll help you as much as I can.