Answer: The equation of the sphere is:
(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2
Step-by-step explanation:
The centre of the sphere is the midpoint of the diameter, which is
1/2
[(-4,7,6) + (8,-3,5)] =(2,2,5/2)
The length of the diameter is
=sqrt |(8,-3,5) - (-4,7,6)|^2
=sqrt (12^2 + (-10)^2 + (-1)^2)
=sqrt (144+100+1)
=sqrt(245)
so the radius of
the sphere is:
1/2(sqrt(245)) = sqrt(245)/2.
The equation of the sphere is:
(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2
To do it without a calculator:
10% of 67 is 6.7
6.7 x 8 is 53.6 (80%)
1% of 67 is .67
<span>53.6 - .67 is 52.93 (79%)</span>
Answer:
Red: 1/5 or 0.2 or 20% (depends if the question asked you to give the answer in fraction/decimal/percentage. Either way, it's still correct)
Black: 0
Blue: 2/5 or 0.4 or 40%
Step-by-step explanation:
In total, the bag contains 10 balls,
- There are no black marbles so you have 0 chance of pulling them out.
Consider the digit expansion of one of the numbers, say,
676₉ = 600₉ + 70₉ + 6₉
then distribute 874₉ over this sum.
874₉ • 6₉ = (8•6)(7•6)(4•6)₉ = (48)(42)(24)₉
• 48 = 45 + 3 = 5•9¹ + 3•9⁰ = 53₉
• 42 = 36 + 6 = 4•9¹ + 6•9⁰ = 46₉
• 24 = 18 + 6 = 2•9¹ + 6•9⁰ = 26₉
874₉ • 6₉ = 5(3 + 4)(6 + 2)6₉ = 5786₉
874₉ • 70₉ = (8•7)(7•7)(4•7)0₉ = (56)(49)(28)0₉
• 56 = 54 + 2 = 6•9¹ + 2•9⁰ = 62₉
• 49 = 45 + 4 = 5•9¹ + 4•9⁰ = 54₉
• 28 = 27 + 1 = 3•9¹ + 1•9⁰ = 31₉
874₉ • 70₉ = 6(2 + 5)(4 + 3)10₉ = 67710₉
874₉ • 600₉ = (874•6)00₉ = 578600₉
Then
874₉ • 676₉ = 578600₉ + 67710₉ + 5786₉
= 5(7 + 6)(8 + 7 + 5)(6 + 7 + 7)(0 + 1 + 8)(0 + 0 + 6)₉
= 5(13)(20)(20)(1•9)6₉
= 5(13)(20)(20 + 1)06₉
= 5(13)(20)(2•9 + 3)06₉
= 5(13)(20 + 2)306₉
= 5(13)(2•9 + 4)306₉
= 5(13 + 2)4306₉
= 5(1•9 + 6)4306₉
= (5 + 1)64306₉
= 664306₉
<u>Direct Variation:</u> 
when y = 7: 
14 = 15x
<u>Inverse variation:</u> y*x = k
15 * 2 = k
30 = k
when y = 7: 7 * x = 30
