Blizzardshine

51 Questions
15 Answers

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What is the total area of the region between the curves y=6x^2-18x and y=-6x from x=1 to x=3?

What is the total area of the region between the curves y=6x^2-18x and y=-6x from x=1 to x=3?
I keep getting 4, but it's not right. How do you do this?

Blizzardshine Feb 22, 2025

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Analytical geometry

Trapezoid $ABCD$ has vertices $A(-1,0)$, $B(0,4)$, $C(m,4)$ and $D(k,0)$, with $m>0$ and $k>0$. The line $y = -x + 4$ is perpendicular to the line containing side $CD$, and the area of trapezoid $ABCD$ is 34 square units. What is the value of $k$ read more ..

Blizzardshine Jun 22, 2023

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geometry help

In the diagram below, $\angle PQR = \angle PRQ = \angle STR = \angle TSR$, $RQ = 8$, and $SQ = 3$. Find $PQ$. [asy] pair A,B,C,D,E; A = (0, 0.9); B = (-0.4, 0); C = (0.4, 0); D = (-0.275, 0.16); E = (0.11, 0.65); draw(A--B); draw(A--C); draw(B--C); draw(B--E);read more ..

Blizzardshine Mar 5, 2023

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When the same constant is added to the numbers $60,$ $100,$ and $160,$ a three-term geometric sequence arises. What is the common ratio of t

Ive gotten to (60+x)/(100+x) = (100+x)(100+x).
Cross multiply to get 9600+x^2+200x = 10000 +200x + x^2.
Then 400 = 20x
The sequence is 80, 120, 180. read more ..

Blizzardshine Oct 1, 2022

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Let\[f(x) = \left\{ \begin{array}{cl} -x - 3 & \text{if } x \le 1, \\ \frac{x}{2} + 1 & \text{if } x > 1...

Let\[f(x) = \left\{ \begin{array}{cl} -x - 3 & \text{if } x \le 1, \\ \frac{x}{2} + 1 & \text{if } x > 1. \end{array} \right.\]Find the sum of all values of $x$ such that $f(x) = 0$.

Blizzardshine Sep 23, 2022

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If $y= \frac{x^2+2x+8}{x-4}$, at what value of $x$ will there be a vertical asymptote?

If $y= \frac{x^2+2x+8}{x-4}$, at what value of $x$ will there be a vertical asymptote?

Blizzardshine Sep 23, 2022

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What is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4$ and the like terms are combined?

What is the coefficient of $x^3$ when $7x^4-3x^3 -3x^2-8x + 1$ is multiplied by $8x^4+2x^3 - 7x^2 + 3x + 4$ and the like terms are combined?

Blizzardshine Aug 27, 2022

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Suppose that $f$ is a polynomial and $h$ is a polynomial of degree $5$ or less such that\[(x^2+3x-3)\cdot f(x)+h(x)= -6x^6+72x^4 -50x^3 + 13

Suppose that $f$ is a polynomial and $h$ is a polynomial of degree $5$ or less such that\[(x^2+3x-3)\cdot f(x)+h(x)= -6x^6+72x^4 -50x^3 + 13x^2 +38x -44.\]What is the degree of $f$?

Blizzardshine Aug 24, 2022

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We have that $3 \cdot f(x) + 4 \cdot g(x) = h(x)$ where $f(x),$ $g(x),$ and $h(x)$ are all polynomials in $x.$ If the degree of $f(x)$ is $8

We have that $3 \cdot f(x) + 4 \cdot g(x) = h(x)$ where $f(x),$ $g(x),$ and $h(x)$ are all polynomials in $x.$ If the degree of $f(x)$ is $8$ and the degree of $h(x)$ is $9$, then what is the minimum possible degree of $g(x)$?

Blizzardshine Aug 24, 2022