Tagged Questions
0
votes
0answers
19 views
Solve the cubic equation for min $r$ and max $k$
I need to find the minimum $r$ and the maximum $k$ of the following cubic equation for which there does not exist three distinct real roots.
$rx^3-rkx^2+(r+k)x-rk=0$.
Is it possible to find such $r$ ...
1
vote
0answers
25 views
Uniqueness of solution for boundary value problem
In the article : "Third order semipositone boundary value problems"
They assume that $w(t)$ is nondecreasing and $w(t)>0$ on $(q,1]$ .
and they found the Green's function ...
0
votes
4answers
140 views
1
vote
3answers
32 views
I need help with this word problem.
A pet store owner wants to mix together an high quality dry cat food costing 1.10
per pound with a lower quality dry cat food costing 0.85 per pound. How many
pounds of each should be mixed together ...
1
vote
1answer
28 views
Solving for $f(n+1)$ when $f(k)$ is known for $k=0,1,…,n$
I posted earlier about polynomials but this is different type of problem I think. I seem to have an answer but I mistrust it....
A polynomial $f(x)$ where deg[$f(x)$]$\le{n}$ satisfies $f(k)=2^k$ ...
4
votes
3answers
70 views
Oceans and volume [closed]
What would be the math formulas to calculate the increase in the height of the ocean if one drop of water were released into it. Assuming that everything is static. How would you solve that ...
1
vote
2answers
57 views
How to solve this system of equations?
How to solve this system of equations?
$$\begin{cases}
1+\sqrt{2 x+y+1}=4 (2
x+y)^2+\sqrt{6 x+3 y},\\
(x+1) \sqrt{2 x^2-x+4}+8 x^2+4
x y=4.
\end{cases}$$
12
votes
4answers
488 views
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
I have to give a combinatorial proof of
$$\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}.$$
I find it difficult to solve such problems. I'm not a brilliant person and never will be so I need to have ...
1
vote
1answer
85 views
Worded problems.
There are 9 chocolates in a selection box: 3 white, 3 milk & 3 dark chocolates. There are 3
soft centres, 3 truffles & 3 pralines. Each chocolate is different. Using the clues below,
arrange ...
-1
votes
1answer
80 views
Word problem: List all acceptable possibillities
Ingrid, Jean, Karen, Philippa and Shirley are sharing a box of chocolates.
There are 5 chocolates left in the box:
a Coffee Cream
a Orange Fondant,
a Hazelnut Praline
a Toffee Crunch
a Nougat ...
2
votes
2answers
181 views
a word problem algebra
Fred and George are to share a chocolate bar made up of
an 8 by 6 square rectangular array. The top-left top-right
squares each contain a visible nut.
They take it in turns, starting with Fred, to ...
2
votes
2answers
107 views
which problems do you recommend it to me to solve it? [closed]
i study abstract algebra from dummit and foote .
i started to solve some problems in section 3 in chapter 4
there is 36 problems
i study the subject myself , so there is no proffesor to ...
1
vote
2answers
582 views
Solving equations that contain summations
My previous algebra course did not go over summation at all, and now that I'm in my new course, Discrete Math for Information Technology, we have been introduced to summation. I understand summation ...
0
votes
2answers
73 views
Area of a function is the same as the area of the inverse function
The area of between the function $f(x)=x^2$ and the $x$-axis from $1\to a$ is the same as the area between $f^{-1}(x)$ and the $y$-axis from $1 \to b$ when $f(a)=b$
It says write two equations of $a$ ...
18
votes
6answers
1k views
Helping my daughter with her homework: solving an algebra word problem.
Three bags of apples and two bags of oranges weigh $32$ pounds.
Four bags of apples and three bags of oranges weigh $44$ pounds.
All bags of apples weigh the same. All bags of oranges weigh the ...
1
vote
1answer
35 views
Ratio isn't answering correct for this problem
Assume there are 2 products A and B made by different companies. Product A costs 1.2006 USD and Product B costs 2.8298 USD. They decided to exchange their products equally without using Money as a ...
0
votes
2answers
134 views
Help solving probability problem!
Can you help solve this problem?
Place contains $N$ coupons $(N>3)$. $3$ tickets have prizes $ \$10000, \$1000, \$500$ respectively. $X$ is the number of coupons drawn before a prize-containing ...
2
votes
5answers
142 views
How to show $A-B \subseteq C \Rightarrow A\cup B \subseteq B\cup C$?
I really need help with this logical proof.
Show that $A-B \subseteq C \Rightarrow A\cup B \subseteq B\cup C$.
Please show the steps to the solution. Thank you!
4
votes
1answer
108 views
Showing a function is not of a bounded variation.
$V_a^b(P,f):=\sum_{i=1}^k|f(x_i)-f(x_{i-1})|$, where $P$ is a partition.
$$f(x)= \begin{cases}
x^2\sin(\frac{1}{x^2}), &\text{if } x\neq0, \\
0, &\text{if } x=0
\end{cases}
...
1
vote
2answers
328 views
Factorial Word Problem
Here is the problem:
"The traditional French greeting is to kiss the other person on each cheek.
So, when two traditional French friends meet, one kisses the second on
both cheeks and the second ...
0
votes
4answers
98 views
How to solve the equation?
I want to solve this equation
$$\sin\dfrac{(x+1)\pi}{4x^2 -4x + 2} = \cos\dfrac{(x-2)\pi}{4x^2 -4x + 2}.$$ The equation has solutions $x = 1$, $x = \dfrac{1 \pm \sqrt{5}}{2}$ and $x = \dfrac{5\pm ...
1
vote
2answers
122 views
Multiplying Reciprocal Exponents
This is the problem I have:
$$y^{\frac{3}{2}} = 5y$$
What I tried so far was raising $y^{\frac{3}{2}}$ to the $\frac{3}{2}$, making it equal $1$, but I had trouble raising $5y$ to that power.
1
vote
1answer
36 views
Four golfers in a square in two teams of two - who tees off second given that one person is diagonal from another?
I am not sure if I am interpreting the question correctly per se. I drew a picture in which Clark was diagonal from Diana. So, that means Chris could either face Clark OR Diana.
If Chris is facing ...
1
vote
3answers
494 views
200 ft race (with turnaround) where two people have different jump lengths but jump the same distance in equal time - who wins and by how much?
This problem is from Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr.
I decided to draw a picture from the segment of 90 ft ...
2
votes
1answer
49 views
Determining probability that blue is part of an outfit based on five shirts and four ties along with a constraint for the possibilities
This problem is from Problem Solving Strategies - Crossing the River with Dogs and Other Mathematical Adventures by Ken Johnson and Ted Herr.
I first let capital letters denote shirts, and ...
1
vote
1answer
223 views
Problem Solving - Ways to add 6 even, positive, non-zero integers to get 26
I believe I have gotten all of the ways now - thanks for the hints below Yun, Andre Nicolas, and Gerry Myerson. If anyone could confirm my answer (I feel there should be more possibilities, but ...
0
votes
1answer
278 views
Problem Solving Question - Can't eliminate possibilities based on clues given
The problem gets cut off. The rest of the problem is supposed to say
She said, "Okay, I'll tell you the sum of all the digits." She whispered the information in his ear. "Thanks!" Ed said, ...
1
vote
2answers
138 views
Constrained optimization problem
I'm having problems with this assignment:
$$\begin{array}{rl}
\min & x^3 + 2xyz - z^2 \\
\text{subject to} & x^2 + y^2 + z^2 \leq 1 \\
\end{array}$$
Disregarding the constraint, find all ...
3
votes
1answer
123 views
What does the underscore stand for in the following analogies?
This is taken from the Miller Analogies Test. No explanation or context is given. My assumption is that the underscore stands for the same operation/number/whatever in both, but I don't know what it ...
2
votes
3answers
440 views
What is the highest number that can be got from 4383 by moving exactly 2 matches?
What is the highest number that can be got from 4383 by moving exactly 2 matches?
Number 1 has got 2 matches, so I thought it will be 47831 as I remove two matches from second number (3), but it ...
3
votes
3answers
283 views
grid puzzle about combinatorics
Here is a puzzle about combinatorics.
Suppose you have a square grid with $n^2$ points. You want to go from the origin $(0, 0)$ to $(n-1, n-1)$. Assuming you can only go right or up, in how many ways ...
1
vote
3answers
139 views
Easy marketing problem
I am a bit weak at math, and I am hoping you can help me find the fastest way to solve a problem. (I hope I came to the right place). This maybe sounds ridiculous, but I want to mathematically solve ...
