Answer:
Yes. Its the same shape. It doesnt need to be the same size to be similar
Step-by-step explanation:
Answer:
8y + 7
Step-by-step explanation:
add them: y + 5 + 3y + 5 + 4y - 3 = 8y + 7
Answer:
Angle 2, 4, 6 are exterior angles, see below
Step-by-step explanation:
Exterior Angles are what they sound like, they are angles on the outside of a traingle.
HOWEVER, the angles that are vertical to the ones in sides are not exterior angles. Angle 3 is not an exterior angle. All the other ones outside are.
Angle 2, 4, 6 are exterior angles
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:
2 3 1 3
Step-by-step explanation: