 # College math questions and answers

Recent questions in Post Secondary Nathanial Levine 2022-10-03

### How many different phone numbers are possible in the area code 928? Note: Phone numbers cannot start with 0 or 1. Lisantiom 2022-10-03

### Find the critical points of $f\left(x,y\right)={x}^{2}y{e}^{-x-y}.$$x=0$ and $x=2$ both satisfy ${f}_{x}=0,{f}_{y}=0$, and when $x=2,y=1$. But when $x=0,y$,$x=0,y$ is arbritary. So how can I determine whether the critical point at $0$ is max/min/saddle? seguitzi2 2022-10-02

### Solve:${\int }_{0}^{\mathrm{\infty }}\left[x\right]{e}^{-x}dx$ spatularificw2 2022-10-02

### To determineA detailed explanation behind larger atomic size with larger Planck’s constant, h. Jensen Mclean 2022-10-02

### Why do I get different results when testing for increasing/decreasing intervals of a function here?I have the function $f\left(x\right)=6+\frac{6}{x}+\frac{6}{{x}^{2}}$ and I want to find the intervals where it increases or decreases. The problem is that when I find ${f}^{\prime }\left(x\right)=0$, which becomes $x=-2$. Once I put -2 on a number line, and find whether the numbers higher and lower than -2 produce positive or negative numbers when plugged into f′(x), I get both positives and negatives for different numbers when $x>-2$. For example, ${f}^{\prime }\left(-1\right)>0$ and ${f}^{\prime }\left(5\right)<0$.I am not sure if this is because the function has a vertical asymptote at $x=0$ and a horizontal attribute at $y=6$. If so, I'd like to know what I need to do to handle them.How I found the first derivative:$\frac{d}{dx}\frac{6}{x}=\frac{\left[0\right]-\left[6\cdot 1\right]}{{x}^{2}}=\frac{-6}{{x}^{2}}$$\frac{d}{dx}\frac{6}{{x}^{2}}=\frac{\left[0\right]-\left[6\cdot 2x\right]}{\left({x}^{2}{\right)}^{2}}=\frac{-12}{{x}^{3}}$${f}^{\prime }\left(x\right)=\frac{-6}{{x}^{2}}-\frac{-12}{{x}^{3}}$How I found the asymptotes:When you combine the fractions of f(x), $f\left(x\right)=\frac{6{x}^{2}+6x+6}{{x}^{2}}$. When set equal to zero, ${x}^{2}$ has an x-value of zero. Therefore, f(x) has a vertical asymptote at $x=0$.Once the fractions are combined, and when everything but the coefficients of the leading terms on the numerator and denominator are removed, $f\left(x\right)=\frac{6}{1}$. So f(x) has a horizontal asymptote at $y=6$.How I found the value of ${f}^{\prime }\left(x\right)=0$:$\frac{-6}{{x}^{2}}-\frac{12}{{x}^{3}}=0$Add $\frac{12}{{x}^{3}}$ to both sides$\frac{6}{{x}^{2}}=\frac{-12}{{x}^{3}}$Multiply both sides by ${x}^{3}$.$6x=-12$Divide both sides by 6.$x=\frac{-12}{6}=-2$ Aidyn Crosby 2022-10-02

### At a football game, a researcher randomly asks 100 people to name their favorite sport. Is this a biased sample? Aryan Lowery 2022-10-02

### Consider a proton with a 6.6 fm wavelength. What is the velocity of the proton in meters per second? Assume the proton is nonrelativistic. (1 femtometer $={10}^{-15}$ m) Janessa Benson 2022-10-02

### Suppose a neutrino is seen travelling so fast that its Lorentz gamma factor is 100,000. It races past an old, no longer active neutron star, narrowly missing it. As far as the neutrino is concerned, it is the neutron star that is moving at extreme speed, & its mass is 100,000 times larger than 2 solar masses. Therefore, from the speeding neutrino's perspective, the neutron star should appear to be a black hole definitely large enough to trap the neutrino. So how come the speeding neutrino continues its travel right past the old stellar remnant? Is there an agreed name for this question or paradox? mriteyl 2022-10-02

### The original functional was with . Solved for the Gateau derivative: . To use the Euler method, such that . However, I must have made a mistake that I can't see with that because it yields which doesn't tell me anything about what must be. Austin Rangel 2022-10-02

### How to compute ${\int }_{a}^{b}\left(b-x{\right)}^{\frac{n-1}{2}}\left(x-a{\right)}^{-1/2}dx$ odcinaknr 2022-10-02

### Test of confidence intervals?In one of my assignments I have to "test" if the confidence intervals for a set of parameters in a mixed effect model is accurate. I'm asked to simulate from fittet parameters and there after refit them using the same model many times, and lastly take 2.5% and 97.5% quantiles of them and compare with the original CIs. My question is, how does this procedure in anyway measure how accurate my original confidence intervals are? solvarmedw 2022-10-02

### Increasing and decreasing intervals of a function$f\left(x\right)={x}^{3}-4{x}^{2}+2$, which of the following statements are true:(1) Increasing in $\left(-\mathrm{\infty },0\right)$, decreasing in $\left(\frac{8}{3},+\mathrm{\infty }\right)$.(2) Increasing in both $\left(-\mathrm{\infty },0\right)$, decreasing in $\left(\frac{8}{3},+\mathrm{\infty }\right)$.(3) decreasing in both $\left(-\mathrm{\infty },0\right)$, and $\left(\frac{8}{3},+\mathrm{\infty }\right)$.(4) Decreasing in $\left(-\mathrm{\infty },0\right)$, Increasing in $\left(\frac{8}{3},+\mathrm{\infty }\right)$.(5) None of the above.${f}^{\prime }\left(x\right)=0=3{x}^{2}-8x=0⇒x=\frac{8}{3},x=0$ are the singular point/point of inflection.Could anyone tell me what next? tonan6e 2022-10-02

### Difference between first and second fundamental theorem of calculusIn first fundamental theorem of calculus,it states if $A\left(x\right)={\int }_{a}^{x}f\left(t\right)dt$ then ${A}^{\prime }\left(x\right)=f\left(x\right)$.But in second they say ${\int }_{a}^{b}f\left(t\right)dt=F\left(b\right)-F\left(a\right)$,But if we put x=b in the first one we get A(b).Then what is the difference between these two and how do we prove A(b)=F(b)−F(a)? garnirativ8 2022-10-02

### While including a data table for a lab report, the guidelines asked to include an uncertainty value for each raw data. In this particular lab where we used slotted masses the masses were already given (such as 50g, 200g, etc.). So while recording the masses into the data table, to how many significant figures should I record the uncertainty and for what reason? samuelaplc 2022-10-02

### Conclusion for confidence intervalIf I got, let's say, a 95 % confidence interval for the mean and a 95 % confidence interval for the variance.Would it then be wrong to conclude:The 95 % confidence interval for the mean contains with at least 95 % probability the true mean?andThe 95 % confidence interval for the variance contains with at least 95 % probability the true variance?What would be a more correct/precise way to express what the confidence intervals stand for? fofopausiomiava 2022-10-02

### Classify the following random variables as continuous or discrete: the height of a sky-scraper. Haiden Meyer 2022-10-02

### Let ${Z}_{1}$ and ${Z}_{2}$ be independent standard normal random variables and ${U}_{1}={Z}_{1}$ and ${U}_{2}={Z}_{1}+{Z}_{2}$. Are ${U}_{1}$ and ${U}_{2}$ independent? Why? miniliv4 2022-10-02

### Evaluate the series$1+\frac{1}{9}+\frac{1}{25}+\frac{1}{49}+\cdots$ Bridger Holden 2022-10-02 aurelegena 2022-10-02