This is geometry through and through. Plus a little trig thrown in for fun. If you inscribe an equilateral triangle inside a circle and the triangle has side lengths of 12, you have part of what you need to use Pythagorean's Theorem to find the hypotenuse of the triangle which is also the radius of the circle. First, use the formula 360/3 to find that the central angle measure of each angle INSIDE a triangle is 120. So you have 3 triangles within the large one, each with a top angle of 120 and a base of 12. If you extract that one triangle and then split it in half, you have a right triangle with a base of 6. This is a 30-60-90 triangle and this is important so you can check your work. Now use the apothem formula for a right triangle as it relates to a side in an equilateral triangle, which is a = sqrt3/6 * s. Our values are a = sqrt3/6(12) which simplifies to 2sqrt3. That's our apothem. If you're familiar with a 30-60-0 triangle, you could check this to see it's correct. Now you have the base leg of 6 and the height of 2sqrt3, now use Pythagorean's Theorem to find the hypotenuse, which is also the radius of the circle. This was really a difficult one to explain.
Answer:
27
Step-by-step explanation:
V_cylinder = pi r^2 h
h = 36
V_cylinder = 36 pi r^2
V_Sphere = 4/3 * pi * r^3
But the volumes are given as equal
36pi r^2 = (4/3) pi r^3 divide by pi r^2
36 = 4/3 r Multiply both sides by3/4
36 * 3/4 = r
r = 27
So remember that the area of a circle is A = π * r^2, with r = radius. In this case, the radius is 1.5, and with that info our equation is A = π * 1.5^2 .
For this, all you need to do is solve the exponents, and your answer is A = 2.25π yds^2
I think that maria picked up 43 apples i’m not sure
Answer:
general solution=
+5
Step-by-step explanation:
using linear differential equation method
y'' + y' + y = 5
writing down the characteristics equation.
using quadratic formula
we get
now Complementary function(CF)
now for particular integrals
putting D=0
we get
P.I.=5
general solution=CF+PI
general solution=+5
