Answer:
D. 4z^3
Step-by-step explanation:
First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3
Hope this helps, if you want me to explain more, feel free to ask questions.
Have a good day! :)
If you spin the dial two times there three things that can happen:
1) Dial does not land in the region A
2) Dial lands once in the region A
3) Dial lands twice in the region A
The combined probability of these three events has to be 1.
Let's calculate probabilities of each event:
![1) P=P(1,1)=\frac{2}{3}\cdot\frac{2}{3}=\frac{4}{9}\\ 2)P=P(1,2)+P(2,1)=2\cdot \frac{2}{3}\cdot \frac{1}{3}=\frac{4}{9}\\ 3)P=P(3,3)=\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{9}](https://tex.z-dn.net/?f=1%29%20P%3DP%281%2C1%29%3D%5Cfrac%7B2%7D%7B3%7D%5Ccdot%5Cfrac%7B2%7D%7B3%7D%3D%5Cfrac%7B4%7D%7B9%7D%5C%5C%0A2%29P%3DP%281%2C2%29%2BP%282%2C1%29%3D2%5Ccdot%20%5Cfrac%7B2%7D%7B3%7D%5Ccdot%20%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B4%7D%7B9%7D%5C%5C%0A3%29P%3DP%283%2C3%29%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B1%7D%7B9%7D)
If we summ all those probabilities we get 1.
The answer would table C (lower left corner).
Using implicit differentiation, it is found that y is changing at a rate of 10 units per second.
---------------------
The equation is:
![y = x^3 + x^2 + 2](https://tex.z-dn.net/?f=y%20%3D%20x%5E3%20%2B%20x%5E2%20%2B%202)
Applying implicit differentiation in function of t, we have that:
![\frac{dy}{dt} = 3x^2\frac{dx}{dt} + 2x\frac{dx}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%203x%5E2%5Cfrac%7Bdx%7D%7Bdt%7D%20%2B%202x%5Cfrac%7Bdx%7D%7Bdt%7D)
- x-values changing at a rate of 2 units per second means that
![\frac{dx}{dt} = 2](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%202)
- Point Q(1,4) means that
.
We want to find
, thus:
![\frac{dy}{dt} = 3x^2\frac{dx}{dt} + 2x\frac{dx}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%203x%5E2%5Cfrac%7Bdx%7D%7Bdt%7D%20%2B%202x%5Cfrac%7Bdx%7D%7Bdt%7D)
![\frac{dy}{dt} = 3(1)^2(2) + 2(1)(2) = 6 + 4 = 10](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%203%281%29%5E2%282%29%20%2B%202%281%29%282%29%20%3D%206%20%2B%204%20%3D%2010)
y is changing at a rate of 10 units per second.
A similar problem is given at brainly.com/question/9543179
Rational between 5.2 and 5.5
5.2 × 10/10 = 52/10
5.5 × 10/10 = 55/10
rational no. b/w them is 53/10 = 5.3
rational because it is in p/q form where q is not zero and p and q are integers.
irrational.no. b/w 5.2 and 5.5
5.20102030405060708090.......
irrational.no because it is non terminating and non recurring