Answer:
27/sqrt9, 4^2 are the rational numbers
Step-by-step explanation:
All the other ones do not terminate, so this leaves these as the answers.
hope this helps!
Answer:
a.![y+1=0](https://tex.z-dn.net/?f=y%2B1%3D0)
b.![2x+4y=1](https://tex.z-dn.net/?f=2x%2B4y%3D1)
Step-by-step explanation:
We are given that
![(x^2+y^2)^2=3x^2y-y^3](https://tex.z-dn.net/?f=%28x%5E2%2By%5E2%29%5E2%3D3x%5E2y-y%5E3)
a.(0,-1)
Differentiate w.r.t x
.....(1)
Substitute x=0 and y=-1 in equation (1)
![2(0+1)(-2y')=-3y'](https://tex.z-dn.net/?f=2%280%2B1%29%28-2y%27%29%3D-3y%27)
![-4y'+3y'=0](https://tex.z-dn.net/?f=-4y%27%2B3y%27%3D0)
![-y'=0](https://tex.z-dn.net/?f=-y%27%3D0)
![y'=0](https://tex.z-dn.net/?f=y%27%3D0)
![m=y'=0](https://tex.z-dn.net/?f=m%3Dy%27%3D0)
Point-slope form:
![y-y_0=m(x-x_0)](https://tex.z-dn.net/?f=y-y_0%3Dm%28x-x_0%29)
Using the formula
![y+1=0](https://tex.z-dn.net/?f=y%2B1%3D0)
This is required equation of tangent line to the given curve at point (0,-1).
b.(-1/2,1/2)
Substitute the value in equation (1)
![2(1/4+1/4)(-1+y')=6(-1/2)(1/2)+3(1/4)y'-3(1/4)y'](https://tex.z-dn.net/?f=2%281%2F4%2B1%2F4%29%28-1%2By%27%29%3D6%28-1%2F2%29%281%2F2%29%2B3%281%2F4%29y%27-3%281%2F4%29y%27)
![2(2/4)(-1+y')=-3/2+3/4y'-3/4y'](https://tex.z-dn.net/?f=2%282%2F4%29%28-1%2By%27%29%3D-3%2F2%2B3%2F4y%27-3%2F4y%27)
![-1+y'=-3/2](https://tex.z-dn.net/?f=-1%2By%27%3D-3%2F2)
![y'=-3/2+1=\frac{-3+2}{2}=-\frac{1}{2}](https://tex.z-dn.net/?f=y%27%3D-3%2F2%2B1%3D%5Cfrac%7B-3%2B2%7D%7B2%7D%3D-%5Cfrac%7B1%7D%7B2%7D)
![m=y'=-1/2](https://tex.z-dn.net/?f=m%3Dy%27%3D-1%2F2)
Again using point-slope formula
![y-1/2=-1/2(x+1/2)](https://tex.z-dn.net/?f=y-1%2F2%3D-1%2F2%28x%2B1%2F2%29)
![\frac{2y-1}{2}=-\frac{1}{4}(2x+1)](https://tex.z-dn.net/?f=%5Cfrac%7B2y-1%7D%7B2%7D%3D-%5Cfrac%7B1%7D%7B4%7D%282x%2B1%29)
![2y-1=-\frac{1}{2}(2x+1)](https://tex.z-dn.net/?f=2y-1%3D-%5Cfrac%7B1%7D%7B2%7D%282x%2B1%29)
![4y-2=-2x-1](https://tex.z-dn.net/?f=4y-2%3D-2x-1)
![2x+4y=2-1](https://tex.z-dn.net/?f=2x%2B4y%3D2-1)
![2x+4y=1](https://tex.z-dn.net/?f=2x%2B4y%3D1)
A is correct due to the smaller interquartile range
Answer:
9
Step-by-step explanation:
(a) put in t = 3 into the r(t) equation provided. Answer will be in gigameters
(b) Use the value of r(t) found in part (a) in the surface area of a sphere equation. S = 4(pi)r² Answer, S will be in units Gm²
(c) This is saying put the equation r(t) into the equation S(r) to make a new equation S(t) or h(t) as they put it.
h(t) = 4(pi)(1.36t + 0.002)²
(d) Put t = 3 into the new equation. Answer will agree with b