Answer:

Step-by-step explanation:
Hi there!

Open up the parentheses

Combine like terms

I hope this helps!
Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
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<em>Comment on the geometry</em>
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
Hi. 2=(7+h)/4 ; 2 * 4 = 7+h ; 8=7+h ; 8-7=h ; 1=h. The answer is h=1.
Answer:
1.5 seconds
Step-by-step explanation:
The height equation is supposed to be ...
h(t) = -16t^2 +22t +3
We want to find the positive value of t where h(t) = 0.
0 = -16t^2 +24t -2t +3 . . . . facilitate factoring
0 = -8t(2t -3) -1(2t -3) . . . . . factor by pairs
0 = -(8t +1)(2t -3) . . . . . . . . complete the factoring
The solutions to this are ...
t = -1/8, 3/2
The ball will reach the ground in 1.5 seconds.
Step-by-step explanation:
it is 50 km in total.
30 km are already covered by the initial rental amount (4000).
what is left is 50-30 = 20 km.
for these 20 km he has to pay 200 for every 5 km.
how many 5 km units are in 20 km ?
well, 20/5 = 4
so, he needs to pay additionally 200×4 = 800php.
therefore, the total cost will be
4000 + 800 = 4800php