Linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, conic sections, binomial, surds, graphs and transformations of graphs, equation- and system-solving, and other symbolic-manipulation topics.

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-4
votes
1answer
31 views

how to solve $2^{2x}-12(2^x)+36=0$

Today I had an exam with the question: solve for $x$: $2^{2x}-12(2^x)+36=0$ I just can't figure out how to solve it, can someone please show me.
0
votes
2answers
33 views

How do I solve inequality $\frac{2x-3}{x+1}\leq 1$?

How do I solve inequality $\frac{2x-3}{x+1}\leq 1$? Here is my thought process: $2x-3 \leq x+1$ so $x \leq 4$ So in interval notation, this is $(-\infty$,4]$ but apparently this is not ...
0
votes
4answers
44 views

Is it okay to use the quadratic equation in an inequality?

I've been trying to solve this problem: A chicken cost $38$ units. The weekly cost of preparing $x$ chickens is given by the equation: $P = -0.1x^2 + 1190 + 28x$. How many chickens must be sold ...
2
votes
0answers
20 views

Coming up with a function or a single graph, given its characteristics (pre-calculus)

Give an example of a function or a single graph which has the following characteristics: Hole at $(3,-1)$ Domain is all real numbers except $3$ Local minimum at $(-1,-2)$ Local ...
2
votes
1answer
36 views

Is my answer wrong?

As their father told them, the elder son took half of the money that was in the box and 200 Dhs. After that, the junior son came and did the same thing. Finally, the little son came, did the same ...
1
vote
5answers
45 views

How do I solve $x^4-3x^2+2=0$?

How do I solve $x^4-3x^2+2=0$ ? I would appreciate some kind of hint here. I have no clue how to start this problem.
1
vote
1answer
20 views

Identifying the formula for a quartic graphic

I am attempting to help someone with their homework and these concepts are a bit above me. I apologize for the terrible graph drawing. I am using a surface pro 3 and it has an awful camera so I can't ...
-2
votes
2answers
34 views

Please help me with this sigma notation [on hold]

Use the properties of summation to evaluate the following: $$\displaystyle \sum^{4}_{i=1}(i^2-3i)$$
0
votes
3answers
31 views

Why is the limit of this graph not 4.3?

I just took an online exam as part of a Precalculus course, and one of the problems on my test was as follows: Estimate $\lim \limits_{x \to 2} f(x)$ from the graph below. The available ...
4
votes
3answers
53 views

How do you factor $\frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}=$?

\begin{align} & \frac{2x^2-x-1}{x^2-9} \cdot \frac{x+3}{2x+1}= \frac{2x^2-x-1}{(x-3)(x+3)} \cdot \frac{x+3}{2x+1} \\[10pt] = {} & \frac{2x^2-x-1}{(x-3)} \cdot \frac{1}{2x+1}= ...
-5
votes
3answers
32 views

one number is six more than another.The sum of the two numbers is 28. What are the numbers? [on hold]

one number is two more than another.The sum of the two numbers is 20. What are the numbers?
-1
votes
2answers
28 views

Need help to understand a math task about algebraic and parametric equations

Can anybody please explain this for me?: Find the algebraic and parametric equations of the circle with centre (-2,3) that passes through (1,-1) How do I find the algebraic and parametric ...
5
votes
3answers
489 views

How to find out which number is larger without a calculator?

So I have a question which is: Which is larger? $$2.2^{3.3} \text{ or } 3.3^{2.2} $$ Now I need to find out with using a calculator but the answer is $3.3^{2.2}$. The only thing I could think of ...
-4
votes
1answer
22 views

Word problem including time [on hold]

Two vans are 420 miles apart when they begin traveling toward each other. One can goes 50 mph while the other goes 55 mph. How long do they drive before they meet?
-1
votes
3answers
26 views

Guaranteed Profit on a Roulette wheel: Does $N$ exist?

I'm looking for a good answer that can be explained to someone without much maths. If a casino spins a roulette wheel enough times, the probability the casino makes a profit $\to$ 1 as $N \to \infty$ ...
5
votes
4answers
109 views

How many ways to write $2010$?

Let $ N$ be the number of ways to write $ 2010$ in the form $ 2010 = a_3 \cdot 10^3 + a_2 \cdot 10^2 + a_1 \cdot 10 + a_0$, where the $ a_i$'s are integers, and $ 0 \le a_i \le 99$. An example of ...
0
votes
2answers
34 views

Inverse functions: what is the difference between $\tan^{-1}(x)$ and $\tan(x)^{-1}$?

I’ve never really been taught about inverse functions, and I figured this is a pretty simple question, but I couldn’t find any explanation in my math textbook about this. What is the difference ...
0
votes
3answers
31 views

Trying to show $|\overrightarrow{a}\times\overrightarrow{b}|^2=|\overrightarrow{a}|^2|\overrightarrow{b}|^2-(\overrightarrow{a}⋅\overrightarrow{b})^2$

If $\overrightarrow{a} = \langle a_1, a_2, a_3 \rangle$ and $\overrightarrow{b} = \langle b_1, b_2, b_3 \rangle$, then the cross product of $\overrightarrow{a}$ and $\overrightarrow{b}$ is the ...
2
votes
0answers
14 views

Generalised equation/Notation for writing down products of sets of combinations

I am trying to write a generalized equation to solve a fairly simple probability problem (c & k are constants) $$y_{1} = (1 - cx_{1})^k$$ $$y_{2} = \frac{(1 - cx_{2})^k - ...
2
votes
1answer
43 views

Simplified is 0? $\log_{3} 9x^4 - log_{3}(3x)^2 $

I have tried to solve this multiple ways, but I keep getting $2\log_{3}x$. According to the answer key, it is supposed to work out to 0, but I'm not seeing it. Can someone point me in the right ...
1
vote
1answer
39 views

Convert from base 10 to base 5

I understand the integer part, keep dividing by 5 and I get 112, but for the fraction part I need a help. The number is: $$ (32.\bar 5)_{10} = (112, ??)_{5} $$ $$ 0,5 * 5 = 2,5\\ 0,5 * 5 = 2,5\\ ...
-7
votes
0answers
36 views

Prove the following statement by contradiction: [on hold]

Prove the following statement by contradiction: if $x,y >0$ then $(x + y)^2 \ne x^2 + y^2$.
0
votes
0answers
25 views

Range edge attraction of strength n [on hold]

Basically I want a function that takes a domain $m$ that goes from [0, $n$] where $n$ is a real number, a position/value $x$ within that domain, and an edge attraction strength $t$. If I say ...
2
votes
0answers
35 views

Algebric equation problems

Find $a, b, c \in \Bbb Q$ such that: $\sqrt[3] a + \sqrt[3] b + \sqrt[3] c = \sqrt[3]{\sqrt[3] 2 - 1}$.
0
votes
1answer
33 views

Problem of Mathematical Induction [on hold]

Show that $n!\leq 2^{-n}(n+1)^n$ for all $n\in\mathbb{N}$ and equality holds if and only if $n=1$.
-3
votes
2answers
76 views

Solve equation $x^3 - 3x = \sqrt{x + 2}$ [on hold]

Solve :  $$x^3-3x=\sqrt{x+2}$$ For any real number x.
0
votes
0answers
18 views

Additive exponential function

I am trying to solve the following for $x$: $$ ax = b(P-P^x)$$ where $a$, $b$ are positive constants, and $P \in (0, 1)$. I already know that the left hand side is linear and the right hand side ...
-3
votes
1answer
16 views

ATV business and percentages [on hold]

I have 12 ATVs. My friend owns 2 of them. Through rental, we make $2,020$ \$. What percent of that amount is of my friend? How much is it?
0
votes
1answer
11 views

Modulus of Z (Normal distribution)

The random variable $Z$ is distributed such that $Z \sim N(0,1)$ find the probability of $P(\left|Z\right| >2.4)$. How to solve this modulus type of question ?
2
votes
2answers
22 views

Finding $P$ knowing $\overrightarrow{PQ}×\overrightarrow{b}$, $\overrightarrow{PQ}⋅\overrightarrow{c}$, $\overrightarrow{b}$, and $\overrightarrow{c}$

Let $Q$ be the point $(1,2,3)$, let $\overrightarrow{b} = \langle -1, 0, 1\rangle$, and let $\overrightarrow{c} = \langle 2, 1, 5\rangle$. It is known that $\overrightarrow{PQ} \times ...
1
vote
2answers
41 views

Equality in AM GM Inequality

In AM GM inequality for nonnegative real numbers $a_1,a_2,\ldots,a_n$, How to show that if equality holds then $a_1=a_2=\ldots=a_n,$ using method of induction?
0
votes
0answers
11 views

Why is Distribution Prioritized Over Combining?

In every algebra (or basic analysis) book that I've seen, three properties of real numbers are taken as axiomatic: commutativity, association, and distribution of multiplication over addition [a(b + ...
0
votes
0answers
16 views

What are the loci of points z which satisfy the following relations?

a) |Z-Z1|=|Z-Z2| b) 0< Re(iZ)<1 c) |z|=ReZ+1 d) Im((Z-Z1)/(Z-Z2))=0 The professor did not explain loci in class and the text does not have any examples, so I am completely lost.
0
votes
2answers
19 views

How do I complete composite functions that use cos(x) and a polynomial? [on hold]

Let $f(x)= \cos(x)$ and $g(x)= 3x^3+4x^2-7$. Find $g(f(x))$ and $f(g(x))$
-1
votes
0answers
16 views

simplifying distance equation

The optimal angle for throwing a ball from a cliff is $$\sin \theta = \frac{1}{(2+ \beta)^{1/2}}$$ the original distance equation is $$ x = \cos \theta (\sin \theta + (\sin^{2} \theta + ...
2
votes
4answers
39 views

Solving for b for equation $3a−5=−4b+1$ [on hold]

I have a math problem, and I'm trying to solve for 'b'. The problem answer shows that the first step is going from Step 1 to Step 2. I don't understand how they are doing this. How does the $-4b$ ...
4
votes
2answers
60 views

Why $\tan x>\sin x$ in this question?

The question asks me to prove the identity $\tan ^2x-\sin ^2x=\tan^2 x \sin^2 x$ and use this result to explain why $\tan x>\sin x$ for $0<x<90$ I've proved the identity and I can't explain ...
2
votes
2answers
45 views

How do you factor $3x^{3/2} -9x^{1/2}+6x^{-1/2}$?

How do you factor $3x^{3/2} -9x^{1/2}+6x^{-1/2}$ ? I factored out a 3 to get: $3(x^{3/2} -3x^{1/2}+2x^{-1/2})$, but it seems this can be factored further.
0
votes
2answers
33 views

Domain and range of $f(x,y)=\sqrt{1+x-y^2}$

I need to find the domain and range of $f(x,y)=\sqrt{1+x-y^2}$. Can someone walk me through the proper reasonings in solving this problem? My attempt Domain From looking at the function I get: ...
2
votes
1answer
31 views

How do you factor $x^3-3x^2-4x+12$

How do you factor $x^3-3x^2-4x+12$ ? I tried to factor $x(x^2-3x-4) + 12$ instead and I got $x(x-4)(x+1)+12$ but apparently this can be factored further.
3
votes
1answer
32 views

Largest Triangular Number less than a Given Natural Number

I want to determine the closest Triangular number a particular natural number is. For example, the first 10 triangular numbers are $1,3,6,10,15,21,28,36,45,55$ and thus, the number $57$ can be ...
-5
votes
2answers
24 views

Modifying a recipe, changing it from 8 to 10 servings.

A recipe that makes 8 servings calls for 3/5 cup flour. Jeff modifies the recipe so that it can serve 10. How many cups of flour does he need?
3
votes
4answers
87 views

Why doesn't quadratic formula lead to a the correct factored form of the original equation?

Applying the quadratic formula to $2x^2-3x+1$ we have \begin{eqnarray*} a&=&2 \\ b&=&-3 \\ c&=&1 \end{eqnarray*} which gives me two roots: \begin{eqnarray*} x_1&=&1 ...
2
votes
3answers
66 views

Why does the a*c cheat work when factoring trinomials?

When factoring a trinomial, in the form $ax^2 + bx + c$, I am told that one can multiply $a$ and $c$ which gives a product whose factors add to $b$. So if I have $2x^2 + 5x -3$ that gives me $-6$. ...
-2
votes
1answer
35 views

Solve the quadratic equation $(2-y)^4=3(2-y)^2+1$

Solve $$(2-y)^4=3(2-y)^2+1$$ The answer is supposed to be $y=4\pm \sqrt{6+\frac{13}2}$. I have tried to work this problem out but I cannot get the answer that is in the book.
-1
votes
1answer
24 views

Adding two variables with subscripts [on hold]

What is the explanation to why $x_{3k} + x_{3k+1}$, is equal to $x_{3k+2}$. Isn't that incorrect because there is no value 1 in the subscript $x_{3k}$? I saw this in a prove in ...
0
votes
1answer
26 views

Two variables in one equation

I am currently having some trouble getting through the following exercise: "There are $25$ apples in a basket in which teacher eats an $X$ amount of them and gives the remaining apples to Y amount of ...
22
votes
1answer
453 views

Parabolas in sequences of digits from the Fibonacci sequence

In preperation for an exam, I was studying Haskell. Therefore I was solving an old assignment where you had to define the fibonacci series. After solving the task (see 1] for source code) and ...
4
votes
4answers
79 views

Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$

Tell me please, how calculate this expression: $$ \sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}} $$ The result should be a number. I try this: $$ \frac{\left(\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - ...
0
votes
0answers
33 views

For the classical diffusion equation ut = r (5ru) (in 3 space dimensions)

fi nd TWO changes of variables which changes the di ffusion constant from 5 to D = 1 for the new coordinate system?