4*10^6 = 4,000,000 1*10^4 = 10,000 4,000,000 x 10,000 = 40,000,000,000 ANSWER: 40,000,000,000
Answer:
Option D
Step-by-step explanation:
<h2>Distance between two points</h2>
The y-value of the two points is unchanged. So, the line is parralel to x-axis.
The distance will be the diffrence between the x-co ordinates.
![\sf Distance = 1 - (-2\dfrac{1}{2})](https://tex.z-dn.net/?f=%5Csf%20Distance%20%3D%201%20-%20%28-2%5Cdfrac%7B1%7D%7B2%7D%29)
![\sf =1+\dfrac{5}{2}\\\\= \dfrac{2}{2}+\dfrac{5}{2}\\\\=\dfrac{7}{2}\\\\=3\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Csf%20%3D1%2B%5Cdfrac%7B5%7D%7B2%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B2%7D%7B2%7D%2B%5Cdfrac%7B5%7D%7B2%7D%5C%5C%5C%5C%3D%5Cdfrac%7B7%7D%7B2%7D%5C%5C%5C%5C%3D3%5Cdfrac%7B1%7D%7B2%7D)
Answer:
C
Step-by-step explanation:
An approximation of an integral is given by:
![\displaystyle \int_a^bf(x)\, dx\approx \sum_{k=1}^nf(x_k)\Delta x\text{ where } \Delta x=\frac{b-a}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_a%5Ebf%28x%29%5C%2C%20dx%5Capprox%20%5Csum_%7Bk%3D1%7D%5Enf%28x_k%29%5CDelta%20x%5Ctext%7B%20where%20%7D%20%5CDelta%20x%3D%5Cfrac%7Bb-a%7D%7Bn%7D)
First, find Δx. Our a = 2 and b = 8:
![\displaystyle \Delta x=\frac{8-2}{n}=\frac{6}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5CDelta%20x%3D%5Cfrac%7B8-2%7D%7Bn%7D%3D%5Cfrac%7B6%7D%7Bn%7D)
The left endpoint is modeled with:
![x_k=a+\Delta x(k-1)](https://tex.z-dn.net/?f=x_k%3Da%2B%5CDelta%20x%28k-1%29)
And the right endpoint is modeled with:
![x_k=a+\Delta xk](https://tex.z-dn.net/?f=x_k%3Da%2B%5CDelta%20xk)
Since we are using a Left Riemann Sum, we will use the first equation.
Our function is:
![f(x)=\cos(x^2)](https://tex.z-dn.net/?f=f%28x%29%3D%5Ccos%28x%5E2%29)
Therefore:
![f(x_k)=\cos((a+\Delta x(k-1))^2)](https://tex.z-dn.net/?f=f%28x_k%29%3D%5Ccos%28%28a%2B%5CDelta%20x%28k-1%29%29%5E2%29)
By substitution:
![\displaystyle f(x_k)=\cos((2+\frac{6}{n}(k-1))^2)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x_k%29%3D%5Ccos%28%282%2B%5Cfrac%7B6%7D%7Bn%7D%28k-1%29%29%5E2%29)
Putting it all together:
![\displaystyle \int_2^8\cos(x^2)\, dx\approx \sum_{k=1}^{n}\Big(\cos((2+\frac{6}{n}(k-1))^2)\Big)\frac{6}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_2%5E8%5Ccos%28x%5E2%29%5C%2C%20dx%5Capprox%20%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%5CBig%28%5Ccos%28%282%2B%5Cfrac%7B6%7D%7Bn%7D%28k-1%29%29%5E2%29%5CBig%29%5Cfrac%7B6%7D%7Bn%7D)
Thus, our answer is C.
*Note: Not sure why they placed the exponent outside the cosine. Perhaps it was a typo. But C will most likely be the correct answer regardless.
Answer:
1. 83.6
2. 24
3. 95/2
4. 3
5. 30
6. 84.5
Step-by-step explanation: