All Questions ⁺⁰237321 Questions

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66

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Pre Calc Problem

1: A particle's position in the plane seconds after it starts moving is:
x=6cos(kt) , y=6sin(kt)
for some constant k . If the particle moves a distance of 120π every second, then what is k ?

accurazy2xgengi Oct 27, 2023

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71

1

+8

Pre Calc Problem

accurazy2xgengi Oct 27, 2023

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54

2

+4

What two numbers multiply to -20 but add to -1

What two numbers multiply to -20 but add to -1

Swatcon Oct 27, 2023

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64

1

+1930

piecewise

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

tomtom Oct 27, 2023

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57

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+1930

floor function

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

tomtom Oct 27, 2023

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74

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+1930

algebra

Let f(x) = \left \lfloor \frac{2 - 3x}{x + 3} + x^2 \right \rfloor.
Find f(1) + f(2) + f(3) + ... + f(999) + f(1000).

tomtom Oct 27, 2023

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86

0

+1930

help hard geo

In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through read more ..

tomtom Oct 27, 2023

+10

40

2

+180

I dont understand these can you explain this please? :D

An equilateral triangle is rotated about one of its altitudes, sweeping out a cone in space. If the height of the equilateral triangle is $3 \sqrt{3},$ then find the volume of the cone. A circular sector is rolled to form a cone. If the radius of the sector read more ..

itsash Oct 27, 2023

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91

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+1930

Minimum value

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

tomtom Oct 27, 2023

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86

1

+1930

Angle bisectors

Help how do I do this
Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle ABC.

tomtom Oct 27, 2023

0

58

1

+1678

help counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

wiseowl Oct 27, 2023

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90

0

+4

math help

During one month, Daniel had 12 online transactions and 3 email money transfers. What were his service charges for that month ?
Up to 6 online transactions for $5.00 per month and $0.90 for each transaction over 6
$1.50 read more ..

jazz.jesso Oct 27, 2023

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60

0

+1678

quick counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

wiseowl Oct 27, 2023

0

60

0

+1348

system

Let the ordered triples $(x,y,z)$ of complex numbers that satisfy
\begin{align*}
x + yz &= 7, \\
y + xz &= -3, \\
z + xy &= -5.<#> \end{align*}<#> be $(x_1,y_1,z_1),$ $(x_2,y_2,z_2),$ $\dots,$ $(x_n,y_n,z_n).$ read more ..

sandwich Oct 27, 2023

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89

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+1348

help with algebra

Let $(x_1,y_1),$ $(x_2,y_2),$ $\dots,$ $(x_n,y_n)$ be the real solutions to
\[x^2 + y^2 = 6y - 4x + 20 \quad \text{and} \quad 4y = x^2 + 4x + 2\]
Find $x_1 + y_1 + x_2 + y_2 + \dots + x_n + y_n.$

sandwich Oct 27, 2023

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79

0

+1348

variables

Let $x,$ $y,$ and $z$ be distinct positive real numbers such that
\[\frac{y}{x - z} = \frac{x + y}{z - 1} = \frac{x + 1}{y}.\]
Find $\frac{x}{y}.$

sandwich Oct 27, 2023

Oct 26, 2023

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83

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+1930

probability

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

tomtom Oct 26, 2023

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88

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+1930

plz help me

The six faces of a cube are painted black. The cube is then cut into $3^3$ smaller cubes, all the same size.
(a) How many of the smaller cubes have exactly one black face?
(b) How many of the smaller cubes do not have any read more ..

tomtom Oct 26, 2023

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87

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+1930

help counting plz

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down at random. What is the probability read more ..

tomtom Oct 26, 2023

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78

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+1348

two variables

If $x$ and $y$ are real numbers satisfying \[x^2+y=10=y^2+3x,\] find all possible values for $x+y$.
Enter all the possible values, separated by commas.

sandwich Oct 26, 2023

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56

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+1348

complex numbers

Let $a,$ $b,$ $c$ be complex numbers such that
\begin{align*}
\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} &= 0, \\
\frac{a^2}{b + c} + \frac{b^2}{c + a} + \frac{c^2}{a + b} &= 1, \\
\frac{a^3}{b + c} + \frac{b^3}{c read more ..

sandwich Oct 26, 2023

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79

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+1348

plz help

Let $x,$ $y,$ $z$ be real numbers such that
\begin{align*}
x + xy + xyz &= 15, \\
y + yz + xyz &= -3, \\
z + zx + xyz &= 17.<#> \end{align*}<#> Find the sum of all possible values of $x + y + z.$

sandwich Oct 26, 2023

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81

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+1348

help hard system

Let $a,$ $b,$ $c$ be real numbers such that
\begin{align*}
a^2 - bc &= 42, \\
b^2 - ac &= -5, \\
c^2 - ab &= 25.<#> \end{align*}<#> Find $a^2 + b^2 + c^2.$

sandwich Oct 26, 2023

0

41

2

+70

help please

I know the person below me probably posted the same question but im prety sure their chart is wrong...
In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), read more ..

sheeshers Oct 26, 2023

0

52

0

+1678

counting

In the array below, in how many different ways can we start with the letter and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
A
RRR
CCCC read more ..

wiseowl Oct 26, 2023

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