0
votes
2answers
16 views

simplifying 3 different equations with 3 different variables

I am stuck trying to get the values for x, y, and z. I keep moving variables around but I end up getting answers like x = x or z = z and I do not think that is what I want. It's really just algebra ...
0
votes
0answers
14 views

Descartes rule of signs

I'm trying to write an algorithm that gets a polynomial and gives how many roots does it have in the interval [0 $x_0$]. I'm supposed to do it by Descartes law, I know that by Descartes law you Know ...
0
votes
2answers
39 views

$-5| 2+4x | = -32(x+3/4)- | x | + 1$

This was my attempt: $$-5| 2+4x | = -32\left(x+\frac34\right)- | x | + 1\\ \implies|2+4x|=\frac{-32x-24- | x | + 1}{-5}\\ \implies2+4x=\pm \frac{-32x+-24- x + 1}{-5}\\ \implies4x=\pm \frac{-33x+-23 ...
0
votes
1answer
10 views

Linear programming problem answer

Big Seas makes regular ice cream and non fat ice cream. The ice cream mixer can make at most 300 gallons. Each regular ice cream requires 5 ounces of milk, and each non fat ice cream requires 2 ounces ...
0
votes
1answer
15 views

What expression represents the total cost?

A customer calculated the cost of a new jacket , c, including a 7% sales tax, by multiplying 0.07 times the cost of the jacket and adding the product to the cost of the jacket. What is another way to ...
0
votes
2answers
67 views

How to solve this inequality?

I have the following problem in an assignment and have been struggling to do it. $2 + 2x - x^2 \geq 2 \sqrt{1+2x}$ I have tried solving for $x$ but have not been able to do so. Any hints to solve ...
0
votes
1answer
20 views

Maximizing the area of the rectangular part of a running track only

Question: A high school is planning to build a new playing field surrounded by a running track. The track coach wants two laps around the track to be 1000 m. The football coach wants the rectangular ...
1
vote
2answers
47 views

Finding roots of cubing equation

Find all roots of the following polynomial: $$x^3 + x^2 + 1$$
4
votes
7answers
195 views

Which is bigger: $\sqrt{1001} - \sqrt{1000}$, or $\frac{1}{10}$?

Which is bigger: $\sqrt{1001} - \sqrt{1000}$, or $\frac{1}{10}$? I can calculate the answer using a calculator, however I suspect to do so may be missing the point of the question. The problem ...
0
votes
1answer
56 views

Hint finding exact value of half-angle when $\tan (\theta) = {3}$

Unlike others I've tried, I'm having a hard time with this half-angle exercise: If $tan(\theta)={3}$ and $\theta$ is in QIII, find $\tan\left(\frac{\theta}{2}\right)$ Here's what I know (or think I ...
0
votes
1answer
16 views

System of inequalities. Points of intersection?

$x^2+y^2<=81$ $y<x$ Is this correct? My answer: (-9sqrt(2)/2,-9sqrt(2)/2), (9sqrt(2)/2,9sqrt(2)/2)
1
vote
1answer
18 views

Intersection of graphs, and no solution for trig functions.

All I know is the c=asin(x-b) I don't know how to check the values of b for 'no solutions,' in the case of trig functions. Can someone people provide an algebraic method to solve this.
0
votes
1answer
102 views

Proof for A majorizes B

$\alpha = [\alpha_i] \in\mathbb R^n$ and $\beta = [\beta_i]$ where $\beta_1 = \beta_2 = ......=\beta_n = \frac{1}{n}\sum\alpha_i$ How can i show that $\alpha$ majorizes $\beta$ I tried to get a ...
-1
votes
1answer
31 views

question about rational expressions

i can't understand how to do this 5 question please help me ! Thank you
0
votes
3answers
49 views

Sequence problem.

Help for this problem would be much appreciated, as I am expected to solve it without being properly taught how. Suppose a single cell of bacteria divides into three every 12 hours. Suppose that the ...
0
votes
4answers
52 views

A seemingly basic PEMDAS problem… [duplicate]

There's one of those meme-type images posted on Facebook with the equation 6/2(1+2), challenging you to solve it. So, parenthesis first, ...
4
votes
1answer
40 views

Calculate depth using triginometry

I was asked a question like this on an exam today and I'm wondering if I got it right or not. ...
2
votes
5answers
41 views

Calculate the height of a building

This question I really need help with, I simply do not know where to start! Anyone can help, all I can offer is supreme thanks. Please include method. I don't want simple answers which don't help me ...
0
votes
0answers
17 views

Substitution in multiple integrals, rewriting variables

I have this problem that seems almost laughably simple, but has stumped me for some time. For the variables $ u = x^2 - y^2 $ $ v = x$ $y$ Under the condition $ u > 0 $ We're simply asked to ...
0
votes
2answers
31 views

The zoo car park

In the zoo car park there were 780 vehicles. Most of the vehicles were cars,but one section contained coaches only.the ratio of cars to coaches was 11:2. How many vehilces were cars and how many were ...
10
votes
10answers
2k views

How to solve $4\sin \theta +3\cos \theta = 5$

Another problem that I already wasted hours on. Given $$4\sinθ +3\cosθ = 5$$ Find $$4\cosθ -3\sinθ$$ Help me guys (PS:I'm not that good in maths)
0
votes
1answer
17 views

How to handle a double inequality where all 3 spots have unknowns

Given the problem $4x \lt 2x + 1 \le 3x + 2$ solve for x. I'm not sure how to go about solving this problem. No matter how I subtract or add the x's or multiply/divide the coefficients I cannot ...
0
votes
1answer
41 views

Proving that $\frac 1 2 t^3+\frac 1 2 t, (t\in \mathbb N)$ will always be a whole number

Is there any way to show that $\dfrac 1 2 t^3+\dfrac 1 2 t$ will always be a whole number? Assuming that t is always a whole number greater than or equal to one? If i think about it logically it seems ...
1
vote
3answers
71 views

Solution for $x$ with exponents?

I am trying to solve the following, $$7^{(2x+1)} + (2(3)^x) - 56 = 0$$ Should I put the 56 on the other side and get the log of both sides and is there a better way to solve this.
3
votes
2answers
71 views

If $(b-a) = (ba^2 - ab^2)$, show that $a=b$ where $a,b \in \mathbb R$

I am slightly stuck on this seemlingly simple problem that I encoutered as part of a problem to show that the orthogonality condition of $M_{2\times2}$ matrices given by $\sum_i a_{ij}a_{jk} = ...
1
vote
1answer
16 views

population of a city based on another [hw]

I've been struggling with understanding how to solve a particular branch of population problems. The question reads as follows: City P had a population of 20,000 in the year 2005. The population ...
1
vote
7answers
296 views

Factoring a fourth degree polynomial

How would I go about factoring $$x^4-x^2-12=0$$ I'm supposed to find the roots of this without the use of calculators (well we do have TI's but some don't so I suppose they're assuming we can solve ...
-1
votes
1answer
22 views

Help with if x = y at z the what does x equal if q [closed]

If it takes 30 minutes to get to your destination at 60 mph then how longs does it take at 70 mph?
2
votes
2answers
62 views

how to multiply infinite power series

I am doing an assignment for my precalculus 2 class. I am expanding two infinite power series and multiplying them together to prove that $\exp(ax)\exp(by) = \exp(ax+by)$ I'm not sure what I am ...
2
votes
1answer
25 views

How do I simplify this difference of angles expression using conjugates?

I'm trying to fill in the gaps in my knowledge of simplifying rational expressions using conjugates, but this one stumps me. Given $\tan(\frac{\pi}{4}-\frac{\pi}{6})$, I can work the formula down to: ...
0
votes
1answer
47 views

Need help with simple algebra question

I've been stuck at this simple algebra question for quite a while already. I would appreciate some help. Given that: a + b + c + d + e = 200 a + c + d = 85.841 2d + 2e = a find the value of c + 2d. ...
0
votes
1answer
48 views

question on time, distance and overtaking

P, Q and R start from the same place X at (a) kmph, (a+b) kmph and (a+2b) kmph respectively. If Q starts p hours after P, how many hours after Q should R start, so that both Q and R overtake P at ...
0
votes
1answer
67 views

How do I simplify a radical within a radical in this half-angle problem?

I don't understand how to simplify the following radicals and arrive at the final answer below. I can make it to this point: $$\sin\left(-\frac{3\pi}{8}\right)=\pm\sqrt{1+\frac{\sqrt2}{2}\over2}$$ ...
2
votes
2answers
57 views

Solve $8p^2 + 5p = 0$ by factorising

How can we solve this by factorising? $$8p^2 + 5p = 0$$ I know how to factorise it, $$p(8p + 5) = 0$$ However I do not know how to solve it. Any help would be appreciated.
0
votes
1answer
43 views

Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? I'm getting 8/5 ft. Is this correct? Appreciated!
-1
votes
1answer
55 views

General Mathematics

Maths was never my subject. I can't answer this, could anyone help?. Is there some sort of formula that can be applied to scenarios like this? Thanks. A building firm employs 60 employees at a cost ...
1
vote
1answer
41 views

In $1 < k < n-10^6$, what is $k$? (details in question)

This is a homework question of mine, I am not searching for the solution but rather what it means. It seems pretty straight forward but I am a little confused as to what the $k$ in $1 < k < ...
-4
votes
1answer
47 views

7=x√3 Solve this equation for X without using a calculator [closed]

7=x√3 solve for x DO NOT find the decimal answer of the √3 but keep it as a square root simplifying completely (this is from a 30, 60, 90 triangle)
0
votes
2answers
40 views

Is this a typo, or am I missing something?

I have a handout for my precalc II class. It says $\sinh(-x) = -\sin(x)$ It should be $\sinh(-x) = -\sinh(x)$ right? I don't see how a negative input could make a hyperbolic function circular.
1
vote
3answers
64 views

Solution of an equation, $x(\log\log9-\log\log x)=\log8$

How to find the solution of this equation analytically $x(\ln(\ln(9))−\ln(\ln(x)))=ln(8)$ Note:- I already know that the solution if this equality is 3, but I don't know how to find it analytical ( ...
1
vote
1answer
25 views

Making $-{{\pi i}\over n} e^{\alpha i}({{1 - e^{2 n \alpha i}\over{1-e^{2 \alpha i}}}})={\pi \over {n sin(\alpha)}}$; $\alpha={{2m+1}\over{2n}} \pi$

As part of a (much) longer problem in complex analysis, I need to show that the equality mentioned in the title makes sense, but I can't seem to find the right algebra tricks to get from point A to ...
4
votes
2answers
61 views

Is limits $\lim_{x\to\infty}{(x-2)^2\over2x+1}=\dfrac{1}{2}$?

$$\lim_{x\to\infty}{(x-2)^2\over2x+1}=\dfrac{1}{2}$$ I used an online calculator and it said it was actually $=\infty$ Here's how I calculate it: ...
-2
votes
1answer
28 views

planet x 1 hr equivalent for earth [closed]

I'm not a mathematician, so I need help, please show how to answer this question. If 1 day on earth = 1000 years in planet x then how many days will it be on earth if 1 hr passes on planet x? Update ...
0
votes
3answers
28 views

How do you solve a equation by converting to logarithm form for the problem$3e^{x-4} +2=83$?

$3e^{x-4} +2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.
3
votes
2answers
75 views

Evaluating $\lim_{x\to1}\frac{x^2}{(x-1)^2}$

$\lim_{x\to1}\frac{x^2}{(x-1)^2}$ How do I calculate this limit? I can't use L'Hospital's rule here and dividing by $x^2$ doesn't work either. Thanks
0
votes
2answers
36 views

how do i write an equation in standard form by completing the square for $x^2 -9y^2-4x-18y=14$

I'm really having trouble with completeing squares i can solve for circles and ellipses but i can't seem to understand hyperbolas or parabolas, help would be deeply appreciated.
1
vote
2answers
37 views

Parabola problem involving depth.

The equation for the parabola, I found, is $$y^2=3.2x$$ What is the depth of the reflector? I'm getting $\dfrac {25}{3.2}$.
-1
votes
0answers
40 views

Parabola word problem. Depth? [duplicate]

I did the first part of this problem correctly, coming up with the equation of y^2=3.2x However, for the second part, where it wants to know the depth of the reflector, I’m having trouble. I ...
0
votes
0answers
35 views

Question about an exponential funtion

Now we have a function: $f(x)=e^x, x\in \mathbb R$ Question: 1) Assume that $x>0$, discuss the number of the intersects between $f(x)$ and $y=mx^2,m>0$ under different situation. 2)Assume ...
1
vote
1answer
44 views

Solve this simple polynomial

$$\text{Problem: }{x^3-x^2-x-2 \over x^2 + x - 6}$$ My textbook was able to come up with $(x-2)(x^2+x+1)$ $$\text{Textbook: }{(x-2)(x^2+x+1) \over (x-2)(x+3)}$$ I've tried grouping and using the ...