Recent questions in Secondary

Arc of a Circle
Answered

Databasex3
2022-08-12

I kwo how to deal with the integrals over the horizontal segment of the sector and over the arc of the circle. My problem is the "diagonal segment". When I parametrize it, I do not get something easy to integrate. How could I approach this?

(The path of integration was suggested in my book, so I do not think that is the problem).

Electromagnets
Answered

garkochenvz
2022-08-12

Geometric Probability
Answered

Flambergru
2022-08-12

Consider rolling n fair dice. Let p(n) be the probability that the product of the faces is prime when you roll n dice. For example, when $$ = $\frac{1}{2}$

When $$

When $$ $\frac{1}{24}$. Find the infinite sum of p(n) (when n starts at 0) (Hint: Consider differentiating both sides of the infinite geometric series: infinite sum of $$ when $$)

I can differentiate the two sides of the geometric series but I'm lost regarding what to do after that. I don't fully understand the question.

Logarithms
Answered

targetepd
2022-08-12

I was given a log equation:

$D=10\mathrm{log}(I/{I}_{0})$

$I$ is the unknown in this case, ${I}_{0}={10}^{-12}$ and $D=89.3$

I did the following steps:

$\begin{array}{rl}\text{}89.3& =10\mathrm{log}\left(\frac{I}{{10}^{-12}}\right)\\ \text{}\frac{89.3}{10}& =\mathrm{log}\left(\frac{I}{{10}^{-12}}\right)\\ \text{}8.93& =\mathrm{log}\left(\frac{I}{{10}^{-12}}\right)\end{array}$

I'm not quite sure how to isolate I after step 3, and I'm also unsure if dividing $89.3/10$ is correct as well. So how can I find the unknown ($I$)?

Mutually Exclusive Events
Answered

rivasguss9
2022-08-12

Fractions
Answered

Katelyn Reyes
2022-08-12

What is the percentage form of 0.75?

Electromagnets
Answered

garkochenvz
2022-08-12

Vectors
Answered

Taliyah Reyes
2022-08-12

$r=|{\overrightarrow{r}}_{1}-{\overrightarrow{r}}_{2}|$

and distance vector namely

${\overrightarrow{r}}_{12}={\overrightarrow{r}}_{1}-{\overrightarrow{r}}_{2}$

Finding volume
Answered

Passafaromx
2022-08-12

I'm having problems finding the triple integrals of equations. I guess it has to do with the geometry. Can someone solve the two questions below elaborately such that I can comprehend this triple integral thing once and for all:

Compute the volume of the solid enclosed by

1. $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1,x=0,y=o,z=0$

2. ${x}^{2}+{y}^{2}-2ax=0,z=0,{x}^{2}+{y}^{2}={z}^{2}$

Finding volume
Answered

traucaderx7
2022-08-12

Let R be the area laying beneath the curve $f(x)=8-{x}^{2}$ and above the line $y=7$. Find the volume of the solid of revolution which is created when R is revolved around the x-axis.

I graphed the functions and found out I have to integrate from -1 to 1. I want to use the disc method, but I don't know how to only get the discs with radii higher than $y=7$ and lower than f(x). I thought it would be logical if the radii of the discs would be $8-{x}^{2}-7=1-{x}^{2}$, but this approach gives me the wrong answer when i plug it into the formula.

Vectors
Answered

Garrett Sheppard
2022-08-12

$\begin{array}{rl}{u}_{1}& =(1,t,t)\\ {u}_{2}& =(2t,t+1,2t-1)\\ {u}_{3}& =(2-2t,t-1,1)\end{array}$

Till now I have tried using the Gram-Schmidt process but did not really reach anywhere. Can you please provide a hint or some theory that may help me get the solution for this question?

Polynomials
Answered

Max Macias
2022-08-12

Bar Magnet
Answered

betterthennewzv
2022-08-12

Finding volume
Answered

Matonya
2022-08-12

Suppose I want to find the volume between $z=2{x}^{2}+3{y}^{2}$ and $z=4$. Is there a way finding that with a double integral? I tried to use $4-2{x}^{2}-3{y}^{2}$ inside the integral and then convert it to polar coordinates...

Regression
Answered

pominjaneh6
2022-08-12

The question is how I can utilize this knowledge of the upper bound on values to improve the regression result?

My intuition is to run a "normal" linear regression on all coordinates in $S$ giving $g(x)$ and then construct ${g}^{\prime}(x)=g(x)+c$, with $c$ being the lowest number such that $\mathrm{\forall}x,y((x,y)\in S\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}y\le {g}^{\prime}(x))$, e.g. such that ${g}^{\prime}(x)$ lies as high as it can whilst still touching at least point in $S$. I do, however, have absolutely no idea if this is the best way to do it, nor how to devise an algorithm that does this efficiently.

Other
Answered

schnelltcr
2022-08-12

A bottle has a mass of 1700 g? What is its mass in kilograms?

A person has a mass of 74 kg. What is their weight in pounds?

A person has a weight of 60 lbs. What is their mass in kilograms?

Vectors
Answered

muroscamsey
2022-08-12

for T is a scalar and r is radial component of a vector in spherical coordinate.

(1) $\mathbf{r}\cdot \mathbf{[}\mathbf{(}\mathbf{r}\cdot \mathrm{\nabla}\mathbf{)}\mathrm{\nabla}T+2\mathrm{\nabla}T]=\mathbf{r}\cdot \mathrm{\nabla}T+\mathbf{r}\cdot \mathrm{\nabla}\mathbf{(}\mathbf{r}\cdot \mathrm{\nabla}T)$

(2) ${\mathrm{\nabla}}^{2}(T\mathbf{r}\mathbf{)}=\mathbf{r}{\mathrm{\nabla}}^{2}T+T{\mathrm{\nabla}}^{2}\mathbf{r}+2\mathrm{\nabla}T\cdot \mathrm{\nabla}\mathbf{r}$

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