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Results tagged with algebra-precalculus
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user 164587
For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.
4
votes
Find an equation of a quartic function with 2 points and a tangent point
The tangent point represents a repeated root. Thus you have been given all four roots of the quartic.
- 1,509
0
votes
Evaluate the piecewise defined function
The last two are correct. You are doing something very wrong for the first three, but I don't know what because you have given no working.
You need to pay close attention to the ranges to which each …
- 1,509
0
votes
Solution of $|1-2|x||\le3$
$$-3 \le 1-2|x| \le 3 \implies -4 \le -2|x| \le 2 \implies 2 \ge |x| \ge -1$$
- 1,509
1
vote
Finding the sum of $\sin(0^\circ) + \sin(1^\circ) + \sin(2^\circ) + \cdots +\sin(180^\circ)$
Wikipedia says
$$\sum_{k=0}^n \sin{(\gamma + k\alpha)} = \frac{\sin\tfrac{(n+1)\alpha}{2} + \sin{(\gamma + \tfrac{n\alpha}{2})}}{\sin\tfrac\alpha2}$$So we may write $\gamma = 0$, $n=180$ and $\alpha=\ …
- 1,509
0
votes
1
answer
63
views
Where does the third solution come from?
There's a well known trick with polynomials. If we have
\begin{align*}
&&(x-r_1)(x-r_2) &= 0 \\
&& x^2 -(r_1+r_2)x + r_1r_2 &=0 \tag{*}\label{*} \\
&\text{so}& x^2 &= (r_1+r_2)x - r_1r _2 \tag{**}\lab …
- 1,509
6
votes
Accepted
System of Equations and Pumpkins? I Think Not.
You have already spotted that $a_1 + a_2 = 110$ and $a_4 + a_5 = 121$. But we also have $a_1 + a_3 = 112$ and $a_3 + a_5 = 120$.
- 1,509
1
vote
Property of a system of two inequalities
You can sum them, yes. But you can't subtract them.
$$a+b \gt 1 \implies a+b= 1 + \alpha^2 \\a-b \gt 1 \implies a-b = 1+\beta^2 \\[12pt]2b = \alpha^2 - \beta^2$$but we don't know the values of $\alpha …
- 1,509