dx/dt+4x=2sin(3t) ; x(0)=0

Now I know that for the natural response I set the right side of the equation equal to 0, so I get

dx/dt+4x=0, thus the characteristic equation is m+4=0 and I get -4 as the root and the solution to the natural response is Ae^-4t and since x(0)=0, A must be 0.

So the natural response is just 0.

However, im not sure about how to...

Natural and forced response of a differential equation]]>

screen shot to avoid typos

OK the key said it was D

I surfed for about half hour trying to find a solution to this but $f'(0)$ doesn't equal any of these numbers

$e^0=\pm 1$ from the $e^{(x^2-1)^2}$

kinda ???]]>

I'm doing an 3rd year economics course in university and I'm already running into difficulty trying to show proofs of the following:

Now I certainly don't wish to ask for spoon feeding just some direction or source to where I can look up and read for the solution. My knowledge on these are still weak and the deadline is by the end of this Friday. I'm going to try the text book tomorrow to see...

Econometrics Questions]]>

α (t) = (cos(t), t^2, 0)

How would I go about finding the euclidean coordinate functions for this curve? I know how to find euclidean coord. fns. for a vector field, but I am a bit confused here.

(Sorry about the formatting)]]>

Here N, a, and b are integer constants. M is also an integer but changes for every value of x, which makes the index of the second summation dependent on the first. The problem is the relationship M(x) is analytically difficult to define. Is there a way to solve/simplify this expression?]]>

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Let $a<b<c$ be real numbers such that $a+b+c=6$ and $ab+bc+ca=9$. Prove that $0<a<1<b<3<c<4$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!]]>

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If all the roots of $x^4-8x^3+24x^2+bx+c=0$ are positive reals, find the value of $b$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!]]>

I'm stuck again and not sure how to solve this question been at it for a few hours. Any help is appreciated as always.

Q: (1) Let the sum S = 3- 3/2 + 3/4 - 3/8 + 3/16 - 3/32 +...- 3/128. Determine integers

[IMG alt="r/askmath - Summation and geometric...

Summation and geometric sums]]>

The vertical circular cylinder has radius r ft and height h ft.

If the height and radius both increase at the constant rate of 2 ft/sec,

Then what is the rate at which the lateral surface area increases?

\een

$\begin{array}{ll}

a&4\pi r\\

b&2\pi(r+h)\\

c&4\pi(r+h)\\

d&4\pi rh\\

e&4\pi h

\end{array}$

ok here is my setup

\begin{array}{lll}

\textit{given rates}

&\dfrac{dr}{dt}=2 \quad \dfrac{dh}{dt}=2

&(1)\\ \\

\textit{surface area eq}

&2\pi rh

&(2)\\ \\

\end{array}

so far]]>

See picture below:

There exist an infinite plane with infinite number of dots. For sake of argument, let's assume they are 1 inch away from each other.

However, below(on your far left) you can see 3 lines already made. The last line is the yellow one.

What you see on the left, are all combinations of possible moves. Move is defined as structure of lines until you reach an empty dot.

Thus, there are 6 combinations of single line(on top). While...

#s of Combinations and Permutations of lines?]]>

It is so embarrassing to ask because I would think there is a trick to solve this problem without going through the trigonometric formulas like sine rule for example (because this is a primary math problem) but for some reason, I can't see through it...if you can solve it without using any of the trigonometric formulas, can you please enlighten me? Many thanks!

The figure is made up of a circle, identical semicircles and a square of side 12 cm. What is the area of the regions...

Find area of shaded region]]>

$$

\int_{0}^\infty \frac{e^{3x} - e^x}{x(e^x + 1)(e^{3x} + 1)}\ dx

$$

I substituted $y=e^x$, thus $dx = dy/y$, which turns the above integral to

$$

\int_{1}^\infty \frac{y^2 - 1}{(\log y)(y+1)(y^3+1)}\ dy = \int_{1}^\infty \frac{y-1}{(\log y) (y^3+1)} \ dy

$$

I am unable to make progress.

Thanks.]]>

point D is such that the vector AD = Vector BC + (2x) vector AB + (3y) vectorAC = vector AB + (2x) vectorAC + (3y) vector BC

find coordinates of D]]>

$a \le 1 \\a+4b \le 17\\a+4b+16c \le273\\a+4b+16c+64d \le4369$

Find the minimum value of $\dfrac{1}{d}+\dfrac{2}{4c+d}+\dfrac{3}{16b+4c+d}+\dfrac{4}{64a+16b+4c+d}$.]]>

ok I thot this was just observation to get b.

but maybe not

I saw some rather hefty substations to get different answers]]>

Thanks a lot!]]>

$\displaystyle\int^1_0{xe^x\ dx}$

$A.\ \ {1}\quad B. \ \ {-1}\quad C. \ \ {2-e}\quad D.\ \ {\dfrac{e^2}{2}}\quad E.\ \ {e-1}$

\textit{IBP}

&uv-\displaystyle\int v' dv

&\tiny{(1)}\\ \\

\textit{substitution}

&u=x,\ v'=e^x

&\tiny{(2)}\\ \\

\textit{calculate}

&I=xe^x-\displaystyle\int \ e^xdx\biggr|^1_0

=xe^x-e^x\biggr|^1_0=1

&\tiny{(3)}

\end{array}$

ok I think this is ok possible typos

but curious if this could...

4.2.5 AP Calculus Exam IBP]]>

$x = \sqrt{(x-667)(x-736)}+\sqrt{(x-736)(x-928)}+\sqrt{(x-928)(x-667)}$]]>

screenshot to avoid typos

I picked B just could see the others as definite

insights?]]>

\[ \mathscr{L}^{-1} \frac{a(s+2 \lambda)+b}{(s+ \lambda)^2- \omega^2} \]]]>

$$\frac{(x+y)^2}{16}+\frac{(x-y)^2}{9}=1$$

Solution given:-

Let $x+y= 4\cos{\alpha},x-y=3\sin{\alpha}$ Then $x=\frac{4\cos{\alpha}+3\sin{\alpha}}{2}$ $\Rightarrow dx=\frac{3\cos{\alpha}-4\sin{\alpha}}{2}d\alpha$

$y=\frac{4\cos{\alpha}-3\sin{\alpha}}{2}$. So, $ydx=\left(3-\frac{25}{8}*\sin{2\alpha}\right)*d\alpha$

Hence the required area is

Needs explanation for the solution of question relating to the area of ellipse]]>

2nd grade math app is one of the best cool math games, it offers wonderful interesting quick math lessons of the second grade math for kids (grade 2 math).

Get it Free from Google Play: Cool Math Games | 2nd Grade Math | Grade 2 Math - Apps on Google Play

Buy no Ads version...

Math App: Cool Math Games]]>

Suppose that the prices of a product have platycurtic and positive asymmetry. The minister of commerce decides to define maximum value of product equal to the mean value. The minister probably:

- will decrease the price at more than 25% of the products

- will decrease the price at less than 50% of the products

- no of the options that are given

- will decrease the price at less than 75% of the products

- will decrease the price at more than 50% of the products

I have...

What will the minister do?]]>

Suppose that we calculate the calories and the quantity of sugar at the package of a product. For the calories we have mean value $10$ and standard variation $4,90$. For the quantity of sugar we have corresponding values $5,85$ and $3,38$, respectively. (Use CV). I want to find the relative variance between the calories and the quantity of sugar.

I have thought the following:

$$CV_{\text{cal}}=\frac{4,90}{10} 100%=49%$$

$$CV_{\text{sug}}=\frac{3,38}{5,85} 100%=57,77%$$

So...

Relative variance]]>

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Let $P_1(x)=ax^2-bx-c,\,P_2(x)=bx^2-cx-a,\,P_3(x)=cx^2-ax-b$ be three quadratic polynomials where $a,\,b$ and $c$ are non-zero real numbers. Suppose there exists a real number $k$ such that $P_1(k)=P_2(k)=P_3(k)$, prove that $a=b=c$.

-----

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Problem Of The Week #434 September 14th, 2020]]>

f(x) = 8x - 5 is continuous on R]]>

screenshot to avoid typos

ok I assume f(x) is the eq of a sloped line.. well at the simplest option

at $2\ge x \ge 8$ so $y=\dfrac{7.3}{6}$ but I don't know how to get the slope so $\displaystyle\int_2^4 f(x) = 5.9$]]>

#include <iostream>

using namespace std;

int main() {

int amountToChange;

int numFives;

int numOnes;

cin >> amountToChange;

numFives = amountToChange / 5;

/ Your Input Goes Here/

cout...

2.11.2: Compute change.]]>

$a.\quad \tan^{-1}e^x+C$

$b.\quad 1+e^x-\ln(1+e^1)+C$

$c.\quad x-x+\ln |1+e^x|+C$

$d.\quad e^x+\frac{1}{(e^x+1)^2}+C$

$e.\quad {none}$

ok I was going to use $u=1+e^x\quad du=e^x dx$ but maybe not best

btw I tried to use array on the choices but its was all underlined in preview]]>

a) There is at least one consonant between every vowel

b) There is at least least two consonants between every vowel

Thanks for your help!]]>

but is it possible to auto post an event to google calendar when we post a new post

like the title wold show up in the calendar event

I just created a new calendar called mhb to overlay with 2 other calendars

it seems there is options to do this with other programs

anyway..

would be a really cool feature if is offered]]>

Note: I could have used any trig function.

I know that tan^2 (x) means (tan x)^2.

What does tan (x)^2 mean? Is it proper notation?]]>

The options are

\(\displaystyle rank(B)+null(B)=n\)

\(\displaystyle tr(ABA^{−1})=tr(B)\)

\(\displaystyle det(AB)=det(A)det(B)\)

I'm thinking that since it's invertible, I would focus on the determinant =/= 0. I believe the first option is out, because null (B) would be 0 which won't be helpful. The second option makes the point that \(\displaystyle AA^{−1}\) is \(\displaystyle I\), so it's suggesting invertibility. So I'm deciding between the second and last option. Does anyone have any...

Connecting linear algebra concepts to groups]]>

Evaluate $\int(e^{t^2}+16)te^{t^2} dt$

ok I was going to distribute but not sure if a substitution would be better

the answer looks like it is done by observation

W|A returned

]]>

"The map

Group homomorphism]]>

i) Calculate the angle between the vectors \(\displaystyle \vec j\) and \(\displaystyle \vec E\) if the angle between \(\displaystyle \vec E\) and \(\displaystyle \vec n\) is α

ii) Now assume that \(\displaystyle \vec n=\vec...\)

Calculate the angle between the E-field and Current vectors in an anisotropic conductive material]]>

\(\displaystyle log_2(x+2)+log_{(x-2)}4=3\)

I said I had no idea because one is x + 2 and the other one is x - 2. If both are x + 2 or x - 2, I can do it. He said that if that's the case, even at his level he could solve it. This is what I've done so far regarding the question.

\(\displaystyle log_2(x+2)+log_{(x-2)}4=3\)

\(\displaystyle \frac{log(x+2)}{log2}+\frac{log4}{log(x-2)}=3\)

\(\displaystyle \frac{log(x+2)log(x-2)+log4log2}{log2log(x-2)}=3\)...

[ASK] Logarithmic Equation]]>

Something that I relate the gap radius with the distances between the light and dark fractions of the diffraction figure.]]>

The value of constant $k_1$ depends upon the amount of the gas, temperature of the gas and the units in which p and V are expressed. $p \times V= k_1$

If a fixed amount of gas at constant...

What is the explanation of the given table of effect of pressure on the volume of 0.09 mol CO₂ gas at 300 K?]]>

For what values of m do the line $y=mx$ and the curve $y=\dfrac{x}{x^2+1}$ enclose a region.

Find the area of the region

ok I could only estimate this by observation but it looks $m\ne 1$

not sure how you solve by calculation]]>

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Show that if $a+b+c=0$, then $\left(\dfrac{a}{b-c}+\dfrac{b}{c-a}+\dfrac{c}{a-b}\right)\left(\dfrac{b-c}{a}+\dfrac{c-a}{b}+\dfrac{a-b}{c}\right)=9$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!]]>

I'm not very sure whether a predicate can be neither true or false, and I haven't seen any example so far.

The second choice is false because it is the truth set that is the set of all values which make the predicate true.

A predicate has finite variables, so the third choice is false too.

I believe the truth set of a predicate can be empty, so the last choice is true.]]>

Evaluate $I=\displaystyle\int_1^3 \dfrac{y^3-2y^2-y}{y^2}\ dy$

\begin{array}{lll}\displaystyle

\textit{expand}

&I=\displaystyle\int_1^3 y \ dy

-\displaystyle\int_1^3 2 \ dy

-\displaystyle\int_1^3 \dfrac{1}{y} \ dy

\end{array}

just want to see if I am on the right horse before I cross the stream]]>

a) Determine the area that includes the point (x, y) = (0, 0) where the coordinate system

is well defined. Express the area both in the Cartesian coordinates (x, y) and in

the new coordinates (s, t).

b) Calculate the tangent basis vectors \(\displaystyle \vec...\)

Determine the area, calculate the basis vectors and determine the inner product]]>

Find the Slant asymptote

$y=\dfrac{4x^3-10x^2-11x-1}{x^2-3x}$

Ok the last time I did a slant asymptote was decades ago in Algrebra but this is a calculus problem

the example started with this $\displaystyle\lim_{x \to \infty}[f(x)-(mx+b)]=0$

long division returns $4x+2+\dfrac{-5x-1}{x^2-3x}$ and a desmos graph looks like y=x+3 is sorta close to the SA

so far.. anyway.. but next???]]>

I didn't understand the geometry of molecules in which central atom has no lone pairs of electrons. for example, in $CH_4, NH_4^+$ molecular shape is tetrahedral and bond angle is $109.5^\circ$. How is that bond angle computed? $CH_4$ stands for liquid methane and $NH_4^+$ is a polyatomic cation.

Now my other question involve mathematics as well.

If i want to compute other angles of this tetrahedral, how can i compute it?

If any member knows the answer to these question, may...

Computation of bond angles and other angles in tetrahedral]]>

Find y' $\sqrt{x}+\sqrt{y}=1$

\begin{array}{lll}

\textit{isolate }y

&\sqrt{y}=1-\sqrt{x}

&(1)\\ \\

\textit{square both sides}

&y=(1-\sqrt{x})^2

&(2)\\ \\

\textit{differentiate both sides}

&y'=2\left(1-\sqrt{x}\right)\left(-\dfrac{1}{2\sqrt{x}}\right)&

(3)\\ \\

\textit{simplify}

&y'=-\dfrac{1-\sqrt{x}}{\sqrt{x}}

&(4)

\end{array}

well we could rationalize the denominator but why?

hopefully correct]]>

Find y' of $2x^2+x+xy=1

$\begin{array}{lll}

\textit{separate variables}

&xy=2x^2+x+1 \implies y=\dfrac{2x^2+x+1}{x}\implies 2x+1+x^{-1}

&(1)\\ \\

\textit{differencate both sides}

&y'=2-\dfrac{1}{x^2}

&(2)

\end{array}

ok it seems we can do any implicit differentiation by separation or not?

I think I got the right answer hopefully]]>

Evaluate

$\displaystyle\lim_{x \to 2}

\dfrac{\sqrt{6-x}{-2}}{\sqrt{3-x}-1}$

ok so if you plug in 2 directly you get $\dfrac{0}{0}$

So we either use L'H rule or use conjugate

or is there better way]]>

\[ n(x) = \int_{a}^{b} \frac{d \omega}{\omega ' ^2 - x^2} \] Where $ a<x<b $

I case $a = 0, b = 3, x = 1$ We get

\[ n(1) = \int_{0}^{3} \frac{d \omega}{\omega ' ^2 - 1^2} = −0.3465735902799727 \] The result shown is the Cauchy principal value.

You can check this answer with...

Cauchy principal value.]]>

Primality test]]>

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An object in the plane moves from one lattice point to another. At each step, the object may move one unit to the right, one unit to the left, one unit up, or one unit down. If the object starts at the origin and takes a ten-step path, how many different points could be the final point?

-----

Remember to read the POTW submission guidelines to find out how...

Problem Of The Week #432 August 31st, 2020]]>

The sigma $(\sigma)$ molecular orbitals are symmetrical around the bond-axis while pi $(\pi)$ molecular orbitals are not symmetrical. For example, the linear combination of 1s orbitals centered on two nuclei produces two molecular orbitals which are symmetrical around the bond-axis. Such molecular orbitals are of the $\sigma$ type and are designated as $\sigma1s$ and $\sigma^*1s$ [Fig. 4.20(a)].

If internuclear axis is taken to be in the z-direction, it can be seen that a linear...

Molecular orbital theory question about energy level diagrams]]>

I've got a question here which I'm really unsure what the wording is asking me to do, I've calculated (5), so worked out the steady states. However question 6 has really thrown me off with it's wording, any help would be appreciated.]]>

1.) Find the critical point on the graph ?

2.) Find the interval of the increasing function on the graph ?

3.) Find the interval of the decreasing function on the graph ?

4.) Find the point which is the absolute maximum on the graph ?

5.) Find the point which is the absolute minimum on the graph ?

]]>

Please help me

I have tried to solve the answer many times but I cannot do it

Thank you in advice]]>

In the differential equation:

\[ \frac{d^4y(x)}{dx^4}=\frac{1}{\text{EI}}q(x) \]

In which

\[ q(x)= P \delta(x-\frac{L}{2}) \]

P represents an infinitely concentrated charge distribution

The problem can be solved through developments in Fourier sine series, suppose that

\[ y(x)=\sum_{n=1}^{\infty} b_n \sin (\frac{n \pi x}{\text{L}}) \]

Demonstrate and explain step by step to obtain...

Dirac Delta and Fourier Series]]>

[ATTACH type="full"...

Extrapolating sofa dimensions]]>

]]>

]]>

ok from the $ \dfrac{60\%}{40\%}$ ration we have $\dfrac{3}{2}=\dfrac{m}{w}$

by changing the ratio $\dfrac{3+1.5(3)}{2+1}=\dfrac{15}{6}=\dfrac{5}{2}=\dfrac{m}{w}$

$\dfrac{m}{m-45}=\dfrac{5}{2}\quad m=75$

howeve when I tried to appy this it...

ratio to ratio club membership]]>

]]>

]]>

I have a question about how to solve for x near the end of the problem:

\[ 1+2\sinh^{2}(z)=0 \]

Here is the solution and work:

\[ 1+2\sinh^2(z)=0 \\ \sinh^2(z)=\frac{-1}{2}\\ \sqrt{\sinh^2(z)}=\pm \sqrt{\frac{-1}{2}}\\ \sinh(z)=\pm i\frac{1}{\sqrt{2}}\\ \]

Then we can split the positive complex number and the negative complex number.

\[ \sinh(z)= \frac{i}{\sqrt{2}}\ \text{or} \sinh(z)= \frac{-i}{\sqrt{2}} \]

Let's focus on the positive complex number. (The method will be...

Solving a complex value equation]]>

y^2+12y+16x+68=0

The form we have been using is (y-k)^2=4p(x-h)

Any explanation would help too, I'm really stuck on this one.

Thank you!]]>

maybe application Residue theorem integral ? because this problem same the kramers kronig relation?]]>

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Find all positive integers $(x,\,n)$ such that $x^n+2^n+1$ is a divisor of $x^{n+1}+2^{n+1}+1$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!]]>