Answer:
4600
Step-by-step explanation:
STEP 1: Determine type of progression
![d1 = - 2 - ( - 6) \\ d1 = 4 \\ \\ d2 = 2 - ( - 2) \\ d2 = 4](https://tex.z-dn.net/?f=d1%20%3D%20%20-%202%20-%20%28%20-%206%29%20%5C%5C%20d1%20%3D%204%20%5C%5C%20%20%5C%5C%20d2%20%3D%202%20-%20%28%20-%202%29%20%5C%5C%20d2%20%3D%204)
Since d1 = d2, it is Arithmetic progression, with a common difference of 4
STEP 2: Evaluate the sum
![s = \frac{n}{2} (2a + (n - 1)d) \\ s = \frac{50}{2} (2( - 6) + (50 - 1)4) \\ s = 4600](https://tex.z-dn.net/?f=s%20%3D%20%20%5Cfrac%7Bn%7D%7B2%7D%20%282a%20%2B%20%28n%20-%201%29d%29%20%5C%5C%20s%20%3D%20%20%5Cfrac%7B50%7D%7B2%7D%20%282%28%20-%206%29%20%2B%20%2850%20-%201%294%29%20%5C%5C%20s%20%3D%204600)
Hi,
The total amount is $1,350.
<em /><span><em>So, firstly we'll start off with the easiest one. We know that they bought a cake for </em><em>$250</em><em>. We also know that there were </em><em>50 people </em><em>invited. Appetizers per person cost $2. So we multiply $2 by 50 people. That's $100. They also charge $20 per person for the main course. Now we multiply $20 by 50 people and get $1,000. Now we add $1,000, $250, and $100 to get our total!</em></span>
Answer:
Option 4: x^2+y^2 = 52
Step-by-step explanation:
Given
Centre at origin
Point on circle = (-4, -6)
The distance between origin and point on circle will be the radius of the circle
So,
![r = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}\\r= \sqrt{(-4-0)^2+(-6-0)^2} \\r = \sqrt{(-4)^2+(-6)^2}\\r = \sqrt{16+36} \\r = \sqrt{52}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E%7B2%7D%2B%28y_2-y_1%29%5E%7B2%7D%7D%5C%5Cr%3D%20%5Csqrt%7B%28-4-0%29%5E2%2B%28-6-0%29%5E2%7D%20%5C%5Cr%20%3D%20%5Csqrt%7B%28-4%29%5E2%2B%28-6%29%5E2%7D%5C%5Cr%20%3D%20%5Csqrt%7B16%2B36%7D%20%5C%5Cr%20%3D%20%5Csqrt%7B52%7D)
As the center is at origin the standard equation will be:
![x^2+y^2 = r^2\\](https://tex.z-dn.net/?f=x%5E2%2By%5E2%20%3D%20r%5E2%5C%5C)
Putting the value of r
![x^2+y^2 = (\sqrt{52})^2\\x^2+y^2 = 52](https://tex.z-dn.net/?f=x%5E2%2By%5E2%20%3D%20%28%5Csqrt%7B52%7D%29%5E2%5C%5Cx%5E2%2By%5E2%20%3D%2052)
Hence, last option i.e. Option 4 is correct ..