Answer:
![\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D-%5Csqrt%5B3%5D%7B%5Cfrac%7By%7D%7Bx%7D%20%7D)
Step-by-step explanation:
Recall that using the chain rule we can state:
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
And similarly:
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
now notice that we can find ![cos(t) = \sqrt[3]{y}](https://tex.z-dn.net/?f=cos%28t%29%20%3D%20%5Csqrt%5B3%5D%7By%7D)
from the expression for y,
and ![sin(t) = \sqrt[3]{x}](https://tex.z-dn.net/?f=sin%28t%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
![\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D-%5Cfrac%7Bcos%28t%29%7D%7Bsin%28t%29%7D%3D-%5Csqrt%5B3%5D%7B%5Cfrac%7By%7D%7Bx%7D%20%7D)
In 44 liquid quarts, there are 88 liquid pints. 2 pints per 1 quart. Hope this helps ;)
Answer:
16% probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night
Step-by-step explanation:
The Empirical Rule(Standard Deviation) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 7.5
Standard deviation = 1.2
Using the Standard Deviation Rule, what is the probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night?
8.7 = 7.5 + 1.2
So 8.7 is one standard deviation above the mean.
By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than one standard deviation from the mean. Since the normal probability distribution is symmetric, 16% are more than one standard deviation below the mean and 16% are more than one standard deviation above the mean(above 8.7 hours)
So, 16% probability that a randomly chosen U.S. adult sleeps more than 8.7 hours per night
Answer: “6b”
Step-by-step explanation:
Answer:
Step-by-step explanation:
We multiply 4/5 times 3/1 to find how many miles the penguins swam in one hour.
4 x 3/5 x 1
12/5
The penguins swam 12/5, or 2 and 2/5 miles in one hour.
Table:
Miles 4/5 12/5
Hours 1/3 1
