Answer:
![y=2x^{2} -1](https://tex.z-dn.net/?f=y%3D2x%5E%7B2%7D%20-1)
Step-by-step explanation:
For a parabolic equation to NOT contain the point (0,0) it must have a numeric constant independent from both x and y variables, so the general form would be as follows:
![y=2x^{2} +c](https://tex.z-dn.net/?f=y%3D2x%5E%7B2%7D%20%2Bc)
Solving the equation for the point (1,1) would give the necessary value for the constant "c" to make the equation valid:
![y=2x^{2} +c\\1=2*(1)^{2} +c\\c = 1 -2 = -1](https://tex.z-dn.net/?f=y%3D2x%5E%7B2%7D%20%2Bc%5C%5C1%3D2%2A%281%29%5E%7B2%7D%20%2Bc%5C%5Cc%20%3D%201%20-2%20%3D%20-1)
Therefore, the equation that meets both of the required conditions is:
![y=2x^{2} -1](https://tex.z-dn.net/?f=y%3D2x%5E%7B2%7D%20-1)
Step-by-step explanation:
Initially, there's only 1 letter.
Tania sends the letter to 4 friends.
Each friend sends a letter to 4 more friends (4 × 4 = 16).
Each of those friends sends to 4 more friends (16 × 4 = 64).
The pattern is 1, 4, 16, 64, etc.
This is a geometric sequence. The first term is 1 and each term is 4 times the previous term.
a₁ = 1
aₙ = 4 aₙ₋₁
The explicit formula is:
aₙ = 1 (4)ⁿ⁻¹
Answer:
i believe the answer is 9.5
Step-by-step explanation:
cos60 = c / 19 = 9.5
Volume of a rectangular prism(the baseball card case) can be defined as follows: V = lwh
V = lwh
V = 12(6.5)(1.25)
V = 97.5 cm³
Answer:
![s = 21\ ft\\\\a = -6\ \frac{ft}{s^2}](https://tex.z-dn.net/?f=s%20%3D%2021%5C%20ft%5C%5C%5C%5Ca%20%3D%20-6%5C%20%5Cfrac%7Bft%7D%7Bs%5E2%7D)
Step-by-step explanation:
To find the changes in the slope of the function s(t) we find its derivative
![\frac{ds(t)}{dt} = 3t^2 - 18t +24\\](https://tex.z-dn.net/?f=%5Cfrac%7Bds%28t%29%7D%7Bdt%7D%20%3D%203t%5E2%20-%2018t%20%2B24%5C%5C)
Now we make ![\frac{ds(t)}{dt} = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bds%28t%29%7D%7Bdt%7D%20%3D%200)
![3t^2 - 18t +24 = 0](https://tex.z-dn.net/?f=3t%5E2%20-%2018t%20%2B24%20%3D%200)
![3t^2 - 18t +24\\\\3(t^2-6t + 8)\\\\3(t-4)(t-2)\\\\t_1 =4\\t_2=2\\](https://tex.z-dn.net/?f=3t%5E2%20-%2018t%20%2B24%5C%5C%5C%5C3%28t%5E2-6t%20%2B%208%29%5C%5C%5C%5C3%28t-4%29%28t-2%29%5C%5C%5C%5Ct_1%20%3D4%5C%5Ct_2%3D2%5C%5C)
The particle changes direction for the first time at t = 2 sec
The position at t = 2 sec is:
![s(t=2) = (2)^3 - 9(2)^2 + 24(2) + 1\\\\\s(2) = 21\ ft](https://tex.z-dn.net/?f=s%28t%3D2%29%20%3D%20%282%29%5E3%20-%209%282%29%5E2%20%2B%2024%282%29%20%2B%201%5C%5C%5C%5C%5Cs%282%29%20%3D%2021%5C%20ft)
The acceleration after t = 2 sec is the second derivative of s(t), evaluated at t = 2:
![\frac{d^2s(t)}{d^2t} = 6t -18\\\\\frac{d^2s(t)}{d^2t}(2) = 6(2) -18\\\\ a = 12-18\\\\a = -6\ \frac{ft}{s^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2s%28t%29%7D%7Bd%5E2t%7D%20%3D%206t%20-18%5C%5C%5C%5C%5Cfrac%7Bd%5E2s%28t%29%7D%7Bd%5E2t%7D%282%29%20%3D%206%282%29%20-18%5C%5C%5C%5C%20a%20%3D%2012-18%5C%5C%5C%5Ca%20%3D%20-6%5C%20%5Cfrac%7Bft%7D%7Bs%5E2%7D)