P = Av^2 + (B/v)

(where A and B are positive constants.)

(a) What speed vP minimizes power?

(b) What power does the speed in (a) require?

(c) Suppose that an electric car has a usable store E of energy. How far dP can the electric car travel at the

speed found in (b)?]]>

P = Av^2 + (B/v)

(where A and B are positive constants.)

(a) What speed vP minimizes power?

(b) What power does the speed in (a) require?

(c) Suppose that an electric car has a usable store E of energy. How far dP can the electric car travel at the

speed found in (b)?]]>

ok this is an observation question but many seem to miss the answer

What theorms would rely on to get the correct answer]]>

Let's consider the function \begin{align*}f:\mathbb{R}^2&\rightarrow \mathbb{R} \\ (x,y)&\mapsto \sqrt{|x|\cdot |y|}\end{align*}

Show that $f$ is partially differentiable in $(0,0)$ but not total differentiable.

I have done the following:

We prove that $f$ is partially differentiable in each direction:

Let $0 \neq v =(r, s) \in \mathbb{R}^2$ be the direction and $0 \neq h \in \mathbb{R}$ :

\begin{align*}\frac{1}{h}\cdot \left (f\left ((0,0)+hv\right )-f(0,0)\right...

f is partially differentiable in (0,0) but not total differentiable]]>

We have the function $$f(x,y)=\begin{cases}x^2\sin\left (\frac{1}{x}\right )+y^2\sin\left (\frac{1}{y}\right ) & \text{ if } xy\neq 0 \\ x^2\sin\left (\frac{1}{x}\right ) & \text{ if } x\neq 0, y=0 \\ y^2\sin\left (\frac{1}{y}\right ) & \text{ if } x= 0, y\neq 0 \\ 0 & \text{ if } (x,y)=(0,0)\end{cases}$$

I want to calculate the partial derivatives $\frac{\partial{f}}{\partial{x}}$ and$\frac{\partial{f}}{\partial{y}}$ for each point $(x,y)\in \mathbb{R}^2$.

For that do...

Piecewise function: differentiable but not continuously differentiable]]>

x' & = -x - 4y\\

y' & = 3x - 2y

\end{array}$

and initial values are

$x(0) = 20\quad y(0) = 20$

so since $x=-x'-4y$

then

$y'=3(-x'-4y)-2y=-3x'-12y-2y=-3x'-14y$

just seeing if this combined eq is ok....i think y also could have been substituted

$4y=-x-x'$ or $y=-\dfrac{x}{4}-\dfrac{x'}{4}$

then

$y'=-3x'+\dfrac{7x}{2}-\dfrac{7x'}{2}$

not that sure ]]>

Hello, I feel like I am struggling with this more than I should. I can tell intuitively what the infimum and supremum are, but I am pretty sure that I need a more formal proof style answer. How would one actually prove this question?]]>

A wooden board with an area of 4.55m^2 is dropped into the dead sea (

My understanding is that the volume (V sub) of the submerged object over the total volume (V) of the object is equal to the density (

[ATTACH...

Physics - Archimedes principle]]>

Hello! I have been trying to work through this but I have never really been able to use the definition correctly to find a limit sequence. Any help would be greatly appreciated!]]>

I have a code in C where the user has to give information (id, name, surname, grade) of a student.

The id must be 5 characters, the name and the surname at most 50 characters.

The code is:

Code:

```
#include <stdio.h>
#include <stdlib.h>
struct student
{
char id[5];
char name[50];
char surname[50];
float grade;
};
void GetInformation(struct student *ptr){
printf("Enter ID of the student: ");
scanf("%s", ptr->id);
printf("Enter the name of the...
```

-----

A person is working on a jigsaw puzzle that contains 1000 pieces. It is found that it takes 3 minutes to put the first two pieces together and that when $x$ pieces have been connected it takes $\dfrac{3(1000-x)}{1000+x}$ minutes to connect the next piece. Determine an accurate estimate of time (in hours) it takes to complete the puzzle.

-----

Remember to read the...

Problem Of The Week #466 May 3rd 2021]]>

-----

Real numbers $x,\,y$ and $z$ satisfy $x+y+z=4$ and $\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=\dfrac{1}{3}$. Find the largest and smallest possible value of the expression $x^3+y^3+z^3+xyz$.

-----

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

Yes I know its insulting

But how many seconds did it take you to see the solution]]>

I have a question....

https://dyclassroom.com/c/c-passing-structure-pointer-to-function

At the

When do we use & at pointers?]]>

0.123456876…

0.254896487…

0.143256876…

0.758468126…

0.534157162…]]>

I am new to math forums and am not even sure I’m in the right thread but will give it a go!

I am trying to determine how many days it will take to mow 295 hectares when my mower has a blade 12’ wide and can move at 4km/hour.

Attached is what I believe to be correct but am uncertain if you can cross multiply squared numbers.

Thanks in advance!]]>

We define the sequence of functions $f_n:[0,1]\rightarrow \mathbb{R}$ by $$f_{n+1}(x)=\begin{cases}0 & \text{ if } x\in \left[ 0, \frac{1}{2n+3}\right ]\\ |2(n+1)x-1| & \text{ if } x\in \left [\frac{1}{2n+3}, \frac{1}{2n+1}\right ] \\ f_n(x) & \text{ if } x\in \left [\frac{1}{2n+1}, 1\right ] \end{cases}$$ where $f_1$ is given by $$f_1(x)=\begin{cases}0 & \text{ if } x\in \left [0, \frac{1}{3}\right ]\\ |2x-1| & \text{ if } x\in \left [\frac{1}{3}, 1\right ]\end{cases}$$...

Uniform convergence - Length of graph]]>

R=2000cos6= 1989N

F=1000-(0.4×1989+2000sin6),

By using F=m×a, I get a=-0.023m/s^2

V^2=u^2+2as, u=2m/s, s=10m, I get v=1.88m/s...

Mechanics- friction]]>

Does the sequence $x_n=\frac{1}{n}$ converges as for the cofinite topology on $\mathbb{R}$ ? If it converges,where does it converge?

Could you explain to me what exactly is meant by "cofinite topology on $\mathbb{R}$" ? Do we have to define first this set and then check if we have convergence inside that set? ]]>

- The blood groups of 200 people are distributed as follows: 40 have type A blood, 75 have type B blood, 60 have type O blood, and 25 have type AB blood. If a person from any of the group is selected at random, what is the probability that this person has an O blood type? How about the AB blood type? i hope you will help me.

- The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?

a) Find the acceleration of the wheelbarrow

I got the ans for this a = 1.29m/s^2

b) what happens when the wheelbarrow had 20kg of soil in it and the gardener exerts the same force at the same angle?

I don't understand how...

Mechanics- friction]]>

-----

Solve the system of equation

$3x+7y+14z=252\\xyz-u^2=2016$

for non-negative real numbers.

-----

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

Solve for x:

and

Simplify the following:

]]>

a. green ball

b. purple ball

c. red ball

d. white ball]]>

PS: I JUST NEED THE ANSWER AND SOLUTIONS]]>

128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |

I already know \(\displaystyle 128+64+32= 224\) so then \(\displaystyle 16+1=17\), meaning...

Question: Binary & Hexadecimal]]>

Given the covariance of x and y is -12 and the variance of x is 6,5, using the least squares line of best fit connecting x and y yo estimate the value of x when y=15

x | 2 | 5 | 9 | 7 | 9 | 10 | 7 |

y | 25 | 17 | 11 | 10 | 8 | 7 | 13 |

]]>

- (a) Nathan and Nelle (twins) got an inheritance of $550,000 upon turning twenty one. Nathan decides to invest his money with ABC Financial. If ABC Financial pays simple interest at a rate of 6.75% per annum, how long in years, will it take Nathan’s money to grow to $720,000?

(b) Nelle decided to invest her money with XYZ Financial. If XYZ Financial doubles the inheritance in the same amount of time that Nathan got his money, what was the interest rate...

Business Maths I need help please ]]>

I am looking at the Riemann integral and I have two questions.

Theorem: Let $f: [a,b] \to \mathbb{R}$ bounded and $c \in (a,b)$. Then $f$ is integrable in $[a,b]$ iff it is integrable in $[a,c]$ and in $[c,b]$. In this case we have $\int_a^b f=\int_a^c f + \int_c^b f$.

At the proof, we use the Riemann criterion to conclude that $\mathcal{U}(f,P)-\mathcal{L}(f,P)<\epsilon$, so $f$ is integrable.

Then the following is stated:

We note that the quantities

$$\int_a^b f...

Riemann Integral-Questions]]>

boyce 7.1 exercises

boyce 7.1 answers

Boyce Book

(a) Transform the given system into a single equation of second order.

(b) Find $x_1$ and $x_2$ that also satisfy the given initial conditions.

(c) Sketch the graph of the solution in the $x+1x_2$-plane...

b.7.1.8 IVP with system of eq]]>

Question

\[ \int dx_1dx_2...dx_d e^{(x^2_1+x^2_2+...+x^2_d)^{r/2}} = \frac{\pi ^{d/2}(d/r)!}{(d/2)!} \]

How can I derive this answer?]]>

Question:

Find the minimum of $6\sin x+8\cos x+5$. Hence, find the minimum of $(6\sin x+8\cos x)^2+5,\,(6\sin x+8\cos x)^3+5$ and $(6\sin x+8\cos x)^4+5$.

It is important to stress that students are expected to solve it via trigonometry route but not other methods.

I...

Linear combination of sine and cosine function]]>

I recently started a youtube channel on which I would be posting lectures on undergraduate mathematics.

Here is the link: https://www.youtube.com/channel/UCuDg-ezFuAfjlHWsoTlZMVw

Thank you.]]>

$\begin{array}{rl}x' & = 2x + 2y\\y' & = -4x + 6y\\x(0) & = 2\\y(0) & = -3

\end{array}$

assume we can proceed with this first

$A=\left[\begin{array}{rr}2&2\\-4&6\end{array}\right]\\

A-rI=\left[\begin{array}{rr}2-r&2\\-4&6-r\end{array}\right]=r^{2} -8r + 20 = 0 \quad r_1 = 4 -2 i \quad r_2=4+2i$

so...

3.4.5.5 solve IVP]]>

Upper bound definition for sequences: $ M \in \mathbb{R} $ is an upper bound of sequence $ (a_n)$ if $ \forall n \in \mathbb{N}. a_n \leq M$

Suppose we look at the set $ A = \{ a_n | n \in \mathbb{N} \} $ .

I've been pondering for a while about the following 2 questions related to mathematical-writing , logic and set builder notation:

Questions:

1. How do we...

Transition from Upper Bound definition for Sets to Sequences using Logical transitions & Set-Builder notation]]>

Approaching -3 from the left means that the values of x must be slightly less than -3.

I created a table for x and f(x).

x...............(-4.5)..........(-4)...............(-3.5)

f(x).......... 0.088..........0.142....….....0.3076

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?]]>

-----

Find all prime numbers $p$ such that $2p^3+4p^2-3p+12$ is the fifth power of an integer.

-----

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

a) The box is pulled horizontally to the right by a force of 40N

b) the box is pushed to the left by a force of 50N at 15 degree above the horizontal .

c) the box is pushed to the left by a force of 50N at 15 degree below the horizontal.]]>

$[x]^2=[2x]-1$ where [x] is the floor value of the x real No

hint : start by puting x=n+b where n is an integer and $0\leq b<1$

-----

Prove that every positive real number satisfies $(x+1)(x+2)(x+5)\ge 36x$.

-----

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

source

Find the general solution of each of the linear system

\begin{align*}

x' & = -3 x + 4y\\

y' & = 3x - 2y

\end{align*}

$A=\begin{pmatrix}-3&4\\ 3&-2\end{pmatrix}

=\left[\begin{array}{rr}- \lambda - 3 & 4\\3 & - \lambda - 2\end{array}\right]

=\lambda^{2} + 5 \lambda - 6 = 0

\quad \lambda_1=-5\quad \lambda_2=6$

\textit{ eigenvector:}$\left[...

3.2.5.3 General Solution if system]]>

A: 3x - 2y = 8.

I believe this to be correct because it makes an identical line to one of her correct answers (6x - 4y = 16) and nowhere did it specify that it had to be new. Could you tell me my mistake?]]>

a) Find the angle between the forces

b) The two given forces of magnitude 8N act on a particle of mass m kg, which remains at rest on a horizontal surface with no friction. The normal contact force between the surface and the particle has magnitude 7N. Find m and the acute angle that one of the 8N forces makes with the surface.]]>

Change the second-order IVP into a system of equations

$\dfrac{d^2x}{dt^2}+\dfrac{dx}{dt}'+4x=\sin t \quad x(0)=4\quad x'(0)= -3$

ok I presume we can rewrite this as

$u''+u'+4u=\sin t$

Let $x_1=u$ and $x_2=u'$ then $x_1'=x_2$

substituting

$x_2'+x_2+4x=\sin t$

$\begin{array}{lllll}

&let &x_1=u &and &x_2=u'\\

&then &x_1'=x_2 &and &x_2'=u''

\end{array}$

so

$\begin{array}{llll}...

5.1.c trig IVP]]>

I wanted to ask you if you are familiar with html, css, javascript and php... What is it about?

Here is for example an exercise:

Implement in HTML and CSS the site that is shown below (the specifications are marked with red). The site will be without functionality. How would we proceed? ]]>

-----------------------------------------------------------

1m^2 = 9.33 $

1m = ?]]>

What is the probability the tile is worth 3

points given the tile is a consonant?

and

A player selects two tiles blindly without replacement. What is the probability the

second tile is a vowel given the first tile is a consonant?

Is this like the Urn example with ball replacement? would I solve it the same way? any examples would be nice. Thank you

]]>

x+[x]+[2x]+................................[nx}

Prove that there exists an A such that the equation: x+[x]+[2x]+..........................[nx]=A has a solution for all $n\geq 1$]]>

x+[2x]+[3x]=7]]>

the same time, the shadow of a tree measures 28 ft. Draw a diagram to represent

the situation. How tall is the tree?]]>

$[x]=2x+1$,where [x] is the floor function]]>

(A) 30 K

(B) 18 K

(C) 50 K

(D) 42 K

My answer is 42 K. Is this answer correct?]]>

$x^2+y^2+xy=3\\y^2+z^2+yz=4\\z^2+x^2+xz=1$

Evaluate $x+y+z$.]]>

x.....22 29 35 40 44 48 53 58 65 76

y.....53 74 57 66 79 90 76 93 83 99

(a) Sketch a scatter plot of the data.

(b) Find the entrance test score of any student with a final exam score in the 80s.

(c) Does a higher entrance test score imply a higher final exam score? Explain.

Let me see.

Part (a) is just plotting points on the xy-plane.

Part (b)

The...

Exam Scores]]>

I don't know how to set the number to be divisible by 225, so if anyone can help]]>

Here I understand that the even number in the last place is an even number, that is, it has 4 possibilities, but won't the numbers repeat themselves?]]>

For all A,B we define the floor value of A denoted by [A] to be an iteger B such that : $[A]=B\Leftrightarrow B\leq A<B+1$

And in symbols $\forall A\forall B ( [A]=B\Leftrightarrow B\leq A<B+1\wedge B\in Z)$,then prove:

For all A $ [A]\leq A<[A]+1$]]>

I need to prove the above statement. I have a very strong gut feeling that the above equation is not true, and so I need to find a case where the graph diameter is greater than the average pairwise distance.

First off, I would like to clarify about the average pairwise distance, which is given below

Given that the denominator is C(n,2), I am assuming that the average pairwise distance will be taking the maximum number of...

Graph: showing that diameter is greater than average pairwise distance]]>

[$x^2+1$]=[2x] ,where [x] is the floor value of x]]>

$\dfrac{1}{s^3-22s^2+80s-67}=\dfrac{A}{s-p}+\dfrac{B}{s-q}+\dfrac{C}{s-r}$ for all $s\not \in \{p,\,q,\,r\}$. What is $\dfrac{1}{A}+\dfrac{1}{B}+\dfrac{1}{C}$?]]>

$y''+y'-2y=0\quad y(0)= 2\quad y'(0)=0$

let $x_1=y$ and $x_2=y'$ then $x_1'= x_2$ and $y''=x_2'$

then by substitution

$x_2'+x_2-2x_1=0$

then the system of first order of equations

$x_1'=x_2$

$x_2'=-x_2+2x_1$

hopefully so far..]]>

(A) $x_1$ , a , $x_2$ are in G.P.

(B) $y_{1} \over 2$ ,a, $y_2$ are in G.P.

(C) -4 , $y_{1} \over y_{2}$ , $x_{1} \over x_{2}$ are in G.P.

(D) $x_1$ $x_2$ + $y_1$ $y_2$ = $a^2$]]>

Change the second-order IVP into a system of equations

$y''+y'-2y=0 \quad y(0)= 2\quad y'(0)=0$

let $u=y'$

ok I stuck on this substitution stuff]]>

Change the second-order initial-value problem into a system of equations

$x''+6x'-2x= 0\quad x(0)=1\quad x'(0)=1$

ok my first step was to do this

$e^{rt}(r^2+6r-2)=0$

using quadratic formula we get

$r=-3+\sqrt{11},\quad r=-3-\sqrt{11}$

just seeing if I going down the right road]]>

Decided to solve the problems from last year's exams. I came across this example. Honestly, I didn't understand it. Who can help a young student?

Find characteristic equation of the matrix A in the form of the polynomial of degree of 3 (you do not need to find eigenvalues) and associated eigenvectors of the matrix. Eigenvalues of the matrix: -2, -2, 1.

А= 7 0 -3

-9 -2 3

18 0 -8]]>

Approaching 2 from the left means that the values of x must be slightly less than 2.

I created a table for x and f(x).

x...............0.....0.5.....1.....1.5

f(x)...........0......-1.....-3......-9

I can see that f(x) is getting smaller and smaller and possibly without bound.

I say the limit is negative infinity.

Yes?]]>

Top degree does not = bottom degree.

Top degree is not less than bottom degree.

If top degree > bottom degree, the horizontal asymptote DNE.

The problem for me is that 2x^2 lies within the radical. I can rewrite the radical using a fractional degree (2x^2 - x + 10)^(1/2) but leads no where, I think.]]>

Approaching 2 from the right means that the values of x must be slightly larger than 2.

I created a table for x and f(x).

x...............2.1.....2.01................2.001

f(x)...........12......124.68............1249.68

I can see that f(x) is getting larger and larger and possibly without bound.

I say the limit is positive infinity.

Yes?]]>

f (x) = x3 − 4x + 2; interval: (1, 2)

I don't understand the instructions. How is this done?]]>

Seeking a hint or two. Does the graph of the given function help in terms of finding the limit?]]>