Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inv
1 answer:
The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
![y= \sqrt[5]{Bx+C}](https://tex.z-dn.net/?f=y%3D%20%5Csqrt%5B5%5D%7BBx%2BC%7D%20)
</span>
To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
You might be interested in
Answer:
3 cups
Step-by-step explanation:
We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches
We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)
Therefore, she needs 3 cups of chocolate chips to make 30 servings.
Answer:
A 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].
Step-by-step explanation:
We are given the weights, in the ounces, of a sample of 12 boxes below;
Weights (X): 21.88, 21.76, 22.14, 21.63, 21.81, 22.12, 21.97, 21.57, 21.75, 21.96, 22.20, 21.80.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean weight =
= 21.88 ounces
s = sample standard deviation = = 0.201 ounces
n = sample of boxes = 12
= population mean weight
<em>Here for constructing a 90% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.</em>
<u>So, 90% confidence interval for the population mean, </u><u> is ;</u>
P(-1.796 < < 1.796) = 0.90 {As the critical value of t at 11 degrees of
freedom are -1.796 & 1.796 with P = 5%}
P(-1.796 < < 1.796) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [21.78, 21.98]
Therefore, a 90% confidence interval for the mean weight is [21.78 ounces, 21.98 ounces].