Vocab
3 legs and a 90 degree angle
right triangle
what do pythagorean triples only apply to
only right triangles
An isosceles right triangle has a hypotenuse of 10. What is the area of the triangle?
25
Louis Charles Nathaniel Johnson has an equilateral triangle with side length 5. Ernest has a different right triangle with bases 8 and 3. Whose triangle has a larger area?
Ernest
Take the derivative of f(x)= 5x^2 +7x+13
10x+7
4 legs
giraffe
smallest pythagorean triple with integers
3,4,5
An isosceles triangle has side lengths of 18 and 41. What is the area of this triangle?
360
If a right triangle has legs ⅗ and ⅘, what is the length of its hypotenuse?
1
What does 1+x+x^2+x^3+... equal
1/(1-x)
a/sin a = b/sin b
law of sines
how many pythagorean triples have the number 5 in them
2
A right triangle is inscribed in a circle. One angle of the triangle measures 30o and the length of the side opposite that angle is 10 mm. In millimeters, what is the circle’s diameter?
20
Find 162 +92
625
Based on the 2nd derivative of f, when does the original function f have a point of inflection.
Where the 2nd derivative of f changes signs.
What does it mean for two triangles to be similar
They have angles that are congruent and sides that are in the same ratio.
What number is missing in the triple 41, __ , 40
9
What type of triangle has side lengths 4,3, and 12
This triangle does not exist.
A triangle has sides with length 11 and 60. What is the length of the hypotenuse?
61
Find dy/dx given 7xy+2x=19
dx/dy= (-7y-2)/(7x)
what is a circumcenter
the point where the three perpendicular bisectors of the triangle's sides intersect
List all pythagorean triples (a, b, c) where c = 25
(7,24,25), (15,20,25), or variations thereof
What is the relation between the circumcenter and the vertices of a triangle.
Equidistant from each vertex.
How many mls of water do you need to add to a 2 molar 100 ml solution to get a 0.2 molar solution
900 ml
What is the sum of this series?
1+1/2+1/4+1/8+1/16+...
S= 2