Rewrite in simplest terms:(10x+3y)−(2x−4y)
1 answer:
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9514 1404 393
Answer:
58. 2 real roots; see attached for a graph
59. -6, 3
Step-by-step explanation:
58. A graphing calculator graphs this easily. The graph is shown in the attachment. There are 2 x-intercepts, hence 2 real roots.
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59. The x-intercepts are (-6, 0) and (3, 0), so the x-values x=-6 and x=3 satisfy the equation y = 0.
Ok, so we know that teh diameters of the 3 tennis balls added up equals the height of the canister
also, since the tennis balls touch the sides, the diameter of the tennis ball=diameter of the base
so what we do is
canister volume-3tennisballvolume=wasted space
normally alot of the equations are using radius so
2.7=diameter
diameter=2r
d/2=r
2.7/2=r
1.35=r
since we are to aprox volume to hundreth. use 3.14=pi
volume of cylinder=hpir^2
volume of sphere (tennis ball)=volume of spere=
first find volume of cylinder
h=3 times diameter of 1 tennis ball=3 times 2.7=8.1
r=1.35
vofcylinder=8.1 times 3.14 times 1.35^2
v=25.434 times1.8225
v=46.353465 (keep as many digits a possible for accuracy)
volume of tennis balls=volume of shpere times 3
v= times 3
and we can see that the 4/3 and the 3 cancel to get 4
v=
v=
v=4(3.14)(2.460375)
v=30.90231
so we have
volume of canister=46.353465 in^3
volume of tennis balls=30.90231 in^3
subtract
wasted space=46.353465-30.90231
wasted space=15.451155
round to hundreth
15.45
wasted space=15.45 in^3
also, since the tennis balls touch the sides, the diameter of the tennis ball=diameter of the base
so what we do is
canister volume-3tennisballvolume=wasted space
normally alot of the equations are using radius so
2.7=diameter
diameter=2r
d/2=r
2.7/2=r
1.35=r
since we are to aprox volume to hundreth. use 3.14=pi
volume of cylinder=hpir^2
volume of sphere (tennis ball)=volume of spere=
first find volume of cylinder
h=3 times diameter of 1 tennis ball=3 times 2.7=8.1
r=1.35
vofcylinder=8.1 times 3.14 times 1.35^2
v=25.434 times1.8225
v=46.353465 (keep as many digits a possible for accuracy)
volume of tennis balls=volume of shpere times 3
v=
and we can see that the 4/3 and the 3 cancel to get 4
v=
v=
v=4(3.14)(2.460375)
v=30.90231
so we have
volume of canister=46.353465 in^3
volume of tennis balls=30.90231 in^3
subtract
wasted space=46.353465-30.90231
wasted space=15.451155
round to hundreth
15.45
wasted space=15.45 in^3