Answer:
Step-by-step explanation:
If a number A is divisible by 7, then it satisfies the following condition
● A = 7k
k is an integer
Let A be the sum of consecutive integers raised to the power of n
● A = a^n + (a+1)^n + (a+2)^n + .....
For this sequence to be divisible by 7 it must satisfy the condition above
A = 7k where k is an integer
Answer:
8y + 8x + 0
Step-by-step explanation:
![4-x^2=x\\ x^2+x-4=0\\ \Delta=1^2-4\cdot1\cdot(-4)=1+16=17\\ x_1=\dfrac{-1-\sqrt{17}}{2}\\ x_2=\dfrac{-1+\sqrt{17}}{2}\\\\ \displaystyle V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(4-x^2-x)^2\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(16-4x^2-4x-4x^2+x^4+x^3-4x+x^3+x^2)\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(x^4+2x^3-7x^2-8x+16)\,dx\\ V=\pi \left[\dfrac{x^5}{5}+\dfrac{x^4}{2}-\dfrac{7x^3}{3}-4x^2+16x\right]_0^{\dfrac{-1+\sqrt{17}}{2}}\\ ](https://tex.z-dn.net/?f=4-x%5E2%3Dx%5C%5C%0Ax%5E2%2Bx-4%3D0%5C%5C%0A%5CDelta%3D1%5E2-4%5Ccdot1%5Ccdot%28-4%29%3D1%2B16%3D17%5C%5C%0Ax_1%3D%5Cdfrac%7B-1-%5Csqrt%7B17%7D%7D%7B2%7D%5C%5C%0Ax_2%3D%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%5C%5C%5C%5C%0A%5Cdisplaystyle%0AV%3D%5Cpi%5Cint%5Climits_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%284-x%5E2-x%29%5E2%5C%2Cdx%5C%5C%0AV%3D%5Cpi%5Cint%5Climits_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%2816-4x%5E2-4x-4x%5E2%2Bx%5E4%2Bx%5E3-4x%2Bx%5E3%2Bx%5E2%29%5C%2Cdx%5C%5C%0AV%3D%5Cpi%5Cint%5Climits_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%28x%5E4%2B2x%5E3-7x%5E2-8x%2B16%29%5C%2Cdx%5C%5C%0AV%3D%5Cpi%20%5Cleft%5B%5Cdfrac%7Bx%5E5%7D%7B5%7D%2B%5Cdfrac%7Bx%5E4%7D%7B2%7D-%5Cdfrac%7B7x%5E3%7D%7B3%7D-4x%5E2%2B16x%5Cright%5D_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%5C%5C%0A)
The rest of solution in the attachment.
There's a mistake in the picture
It shoud be
Well, we do not know how many fish Rita has, so lets represent that with y. Anyway, it says that catherine has twice as many fish as Rita. So that will be 2y. And Stella has twice as many as catherine, so that will be 2 x 2y. And that will be 4y. So Ruth has y, catherine has 2y and stella has 4y. And the total is 70. So that means that the number of fishes added together will be 70. That can be represented as;
y + 2y + 4y = 70
y is the same as 1y. And when you add y + 2y + 4y, you will get 7y. So
7y=70
Divide the both sides by 7. That will be;
y= 7 . So Rita has 7 fishes. Hope i helped.
