Difference between revisions of "User:Zhenghua"
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1. Larry has a pie shaped like a circle. He cuts the biggest square out of the pie and then leaves the leftovers for the ants. How much pie do the ants get if the pie has a diameter of 10 inches? | 1. Larry has a pie shaped like a circle. He cuts the biggest square out of the pie and then leaves the leftovers for the ants. How much pie do the ants get if the pie has a diameter of 10 inches? | ||
| + | <cmath>A) \ \pi \ \ \ B) \ 10\pi-20 \ \ \ C) \ 20\pi-50 \ \ \ D) \ 25\pi-50 \ \ \ E) \ 50pi-100</cmath> | ||
| + | 2. A 16 foot pole is standing at noon. A 4 foot child casts a 2 foot shadow at noon. Assuming that the shadow grows by 2 times each hour, what is the length of the shadow at 3:00pm? | ||
| − | 2. | + | <cmath></cmath> |
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| + | 3. What are the sum of the roots of the quadratic, <math>4x^2-16x+130=0</math>? | ||
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| + | <cmath></cmath> | ||
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| + | 4. <math>\triangle ABC</math> has a median <math>AD</math> of length <math>3\sqrt{2}</math> and height <math>AH</math>. If <math>AB=15</math>, <math>AC=9</math>, and <math>DH=1</math> then what is the area of <math>\triangle ABC</math>? | ||
| + | |||
| + | <cmath></cmath> | ||
Revision as of 22:00, 22 October 2023
An AoPS student that is currently at AIME level. As a somewhat active user on AoPS community and FTW (for-the-win), he basically does only math.
Math Skills
Currently attending AIME level classes or not attending any classes. Before he took AMC 12 Problem Series and is currently taking AIME II as his only math class. His favorite math subject is algebra and he is worst at counting and probability. His geometry skills are also kind of lame.
Profile ID
971407
Problems
1. Larry has a pie shaped like a circle. He cuts the biggest square out of the pie and then leaves the leftovers for the ants. How much pie do the ants get if the pie has a diameter of 10 inches?
![\[A) \ \pi \ \ \ B) \ 10\pi-20 \ \ \ C) \ 20\pi-50 \ \ \ D) \ 25\pi-50 \ \ \ E) \ 50pi-100\]](http://latex.artofproblemsolving.com/1/6/c/16c1560c59fae0ad8d2cfd19b32f6993449a49b4.png)
2. A 16 foot pole is standing at noon. A 4 foot child casts a 2 foot shadow at noon. Assuming that the shadow grows by 2 times each hour, what is the length of the shadow at 3:00pm?
![\[\]](http://latex.artofproblemsolving.com/5/7/f/57f1406b65f9f2e6a365b7356da731780b42cceb.png)
3. What are the sum of the roots of the quadratic, 
?
4. 
has a median 
of length 
and height 
. If 
, 
, and 
then what is the area of ?
