Write an equivalent first-order differential equation and initial condition for y

y=−1+∫x1(t−y(t))dt

Anyangwa Emmanuel Atekwana
2022-10-16

Write an equivalent first-order differential equation and initial condition for y

y=−1+∫x1(t−y(t))dt

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asked 2022-05-09

Identify each of the following statements as true or false in relation to confidence intervals (CIs). **Note: 0.5 marks will be taken away for each incorrect answer. The minimum score is 0.**

True | False | |
---|---|---|

A 95% CI is a numerical interval within which we are 95% confident that the true mean μ$\mu $ lies. | ||

A 95% CI is a numerical interval within which we are 95% confident that the sample mean x¯¯¯$\overline{x}$ lies. | ||

The true mean μ$\mu $ is always inside the corresponding confidence interval. | ||

For a sample size n=29$n=29$, the number of degrees of freedom is n=30$n=30$. | ||

If we repeat an experiment 100 times (with 100 different samples) and construct a 95% CI each time, then approximately 5 of those 100 CIs would not$not$ contain the true mean 𝜇. |

asked 2022-09-04

Show that if $\xi $ is a random variable in ${L}^{2}(F)$ and G is a $\sigma $ -field contained in F, then $E(\xi |G)$ is the orthogonal projection of $\xi $ onto the subspace ${L}^{2}(G)$ in ${L}^{2}(F)$ consisting of G-measurable random variables.

asked 2021-02-15

Let Z be a cycle of generalized eigenvectors of a linear operator T on V that corresponds to the eingenvalue lambda.Prove that span(Z) is a T-invariant subspace of V.

asked 2020-11-16

Advanced Math

A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of$2{m}^{2}$ . At nominal operation, the current density for a single cell of the electrolyzer stack is 0.40 $\frac{A}{c}{m}^{2}$ . The nominal operating temperature of the water electrolyzer stack is $70}^{\circ$ C and pressure 1 bar. The voltage over a single electrolytic cell is 1.96 V at nominal load and 1.78 V at 50% of nominal load. The Faraday efficiency of the water electrolyzer stack is 95% at nominal current density, but at 50% of nominal load, the Faraday efficiency decreases to 80%.

(Give your answer to at least three significant digits.)

Calculate the nominal stack voltage:

Answer in V

Calculate the nominal stack current:

Answer in A

Calculate the nominal power on the water electrolyzer stack:

Answer in kW

A bipolar alkaline water electrolyzer stack module comprises 160 electrolytic cells that have an effective cell area of

(Give your answer to at least three significant digits.)

Calculate the nominal stack voltage:

Answer in V

Calculate the nominal stack current:

Answer in A

Calculate the nominal power on the water electrolyzer stack:

Answer in kW

asked 2021-08-15

asked 2022-09-04

Quasi-concavity of a function of two variables such as $z=({x}^{a}+{y}^{b}{)}^{2}$ with a and b both greater than one... is it enough to show that it is not quasiconcave by showing that the second derivatives are not negative?

asked 2022-02-09

*implicit differentiation*1.if y^2=×

2.if ×^2+3×y+2y^2=3,find dy/dx at point (-1,2)