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LeoIsTheBest
Nom d'utilisateur
LeoIsTheBest
But
142
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Questions
19
Réponses
19
19 Questions
19 Answers
0
752
0
+142
Find all angles theta, 0<=theta<=2pi with the following property:
Find all angles theta, 0<=theta<=2pi with the following property: For all real x, 0<=x<=1: x^2 * cos theta - x(1 - x) + (1 - x)^2 * sin theta > 0
LeoIsTheBest
18 août 2019
0
1049
2
+142
In equilateral triangle ABC let points D and E trisect BC. Find sin DAE.
In equilateral triangle ABC let points D and E trisect BC. Find sin DAE.
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LeoIsTheBest
18 août 2019
0
1004
7
+142
Compute
Compute
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LeoIsTheBest
13 août 2019
0
1061
6
+142
Stuart has drawn a pair of concentric circles, as shown. He draws chords AB, BC,... of the large circle, each tangent to the small one. If
Stuart has drawn a pair of concentric circles, as shown. He draws chords AB, BC,... of the large circle, each tangent to the small one. If
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LeoIsTheBest
12 août 2019
0
872
1
+142
Geometry+Algebra
Let A=(10,-10) and O=(0,0). Determine the sum of all x and y-coordinates of all points Q on the line y=-x+6 such that angle OQA = 90.
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LeoIsTheBest
4 août 2019
0
2021
2
+142
A shop sells 500 smartphones a week for $450 each...
A shop sells 500 smartphones a week for $450 each. A market survey shows that each decrease of $5 on the price will result in the sale of an additional 10 smartphones per week. What price of the smartphone would result in maximum revenue, in dollars?
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LeoIsTheBest
28 juil. 2019
0
1510
1
+142
Jo adds up all the positive integers from 1 to 100...
Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values. What is the positive
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LeoIsTheBest
28 juil. 2019
+1
1811
3
+142
For a give-away at the mall, the color of the entry forms...
For a give-away at the mall, the color of the entry forms changes every hour on the hour, and once a color has been used, it is not used again that day. To limit the number of entries, a person may not fill out more than one form of any color. Using the
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LeoIsTheBest
4 juil. 2019
+1
1526
2
+142
What is the median of the distinct positive values...
What is the median of the distinct positive values of all of the fractions less than or equal to 1 with positive integer denominators less than or equal to 5? Express your answer as a common fraction.
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LeoIsTheBest
4 juil. 2019
+1
923
1
+142
Let and be nonzero complex numbers such that . Find the sum of all possible values of .
Let and be nonzero complex numbers such that . Find the sum of all possible values of .
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LeoIsTheBest
29 juin 2019
0
3086
1
+142
In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown.
In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown.
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LeoIsTheBest
28 juin 2019
0
2843
3
+142
Help with Geo
A circle with center $O$ has radius $8$ units and circle $P$ has radius $2$ units. The circles are externally tangent to each other at point $Q$. Segment $TS$ is the common external tangent to circle $O$ and circle $P$ at points $T$ and $S$, respectively.
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LeoIsTheBest
22 juin 2019
+2
830
1
+142
Complex
Let $a$ and $b$ be nonzero complex numbers such that \[|a| = |b| = |a + b|.\]Find the sum of all possible values of $\frac{a}{b}.$
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LeoIsTheBest
13 juin 2019
+2
966
7
+142
Complex Numbers
Let \[\omega\] be a nonreal root of \[z^3 = 1.\] Let \[a_1, a_2, \dots, a_n\] be real numbers such that \[\frac{1}{a_1 + \omega} + \frac{1}{a_2 + \omega} + \dots + \frac{1}{a_n + \omega} = 2 + 5i.\]Compute \[\frac{2a_1 - 1}{a_1^2 - a_1 + 1} + \frac{2a_2
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LeoIsTheBest
12 juin 2019
+1
1599
5
+142
Help On Complex Numbers
The four consecutive digits a, b, c and d are used to form the four-digit numbers abcd and dcba. What is the greatest common divisor of all numbers of the form abcd+dcba?
hectictar
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LeoIsTheBest
12 juin 2019
0
920
5
+142
Complex Numbers
Find all values of the real number so that the four complex roots of form the vertices of a parallelogram in the complex plane. Enter all the values, separated by commas.
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LeoIsTheBest
6 juin 2019
0
778
2
+142
A square $DEFG$ varies inside equilateral triangle $ABC$ so that $E$ always lies on side $\overline{AB},$ $F$ always lies on side
A square $DEFG$ varies inside equilateral triangle $ABC$ so that $E$ always lies on side $\overline{AB},$ $F$ always lies on side $\overline{BC},$ and $G$ always lies on side $\overline{AC}.$ The point $D$ starts on side $\overline{AB}$
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LeoIsTheBest
18 avr. 2019
0
1523
4
+142
Help please?
Right $\triangle ABC$ has hypotenuse $AB$. Square $BCDE$ has $BC$ as one of its sides. Suppose that the area of $BCDE$ is a prime number. If $AB$ and $AC$ are each integers less than $20$, how many possibilities are there for their lengths?
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LeoIsTheBest
17 avr. 2019
0
844
1
+142
Help on question!!!
At a certain amusement park, there is a bulk discount for tickets. If you buy up to 60 tickets in one order, the price for each ticket is $\$70$. However if you buy more than 60 tickets in a single order, the price of every ticket is reduced by $\$1$ for
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LeoIsTheBest
30 mars 2019
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