This deals with ratios and proportions. ⊱ ────── ✯ ────── ⊰ A : B = 2 : 3 B : C = 4 : 5. Now, to find A : B : C, we need to make the value of B equal in A : B ratio and B : C ratio. Here, Value of B in A : B ratio is 3; and B : C ratio is 4. LCM of 3 and 4 is 12. Therefore, we multiply 4 to the first ratio and 3 to the second ratio. A : B = 2 × 4 : 3 × 4 A : B = 8 : 12 Also, B : C = 4 × 3 : 5 × 3 B : C = 12 : 15 Now, we can combine A : B and B : C. A : B : C = 8 : 12 : 15.
5 its 4
B
"6" It all depends on the relationship between A B and C. EG if a+b=c the c=6, if axb=c then c=8. you can throw in allsorts of relationships C/A = B So more information is required in the question
I assume you meant "sum". The answer is 60. 60=4 (integers) * 15 (average value of the integers). average of 4 integers = 15 --> (a + b + c + d)/4 = 15 --> (a + b + c + d) = 15 * 4 --> (a + b + c + d) = 60
This deals with ratios and proportions. ⊱ ────── ✯ ────── ⊰ A : B = 2 : 3 B : C = 4 : 5. Now, to find A : B : C, we need to make the value of B equal in A : B ratio and B : C ratio. Here, Value of B in A : B ratio is 3; and B : C ratio is 4. LCM of 3 and 4 is 12. Therefore, we multiply 4 to the first ratio and 3 to the second ratio. A : B = 2 × 4 : 3 × 4 A : B = 8 : 12 Also, B : C = 4 × 3 : 5 × 3 B : C = 12 : 15 Now, we can combine A : B and B : C. A : B : C = 8 : 12 : 15.
Assuming the 10 = Cup A, 4 = Cup B and 3 = Cup C 1) Fill Cup C (A=0, B=0, C=3) 2) Pour Cup C into Cup A (A=3, B=0, C=0) 3) Fill Cup B (A=3, B=4, C=0) 4) Fill Cup C from Cup A (A=3, B=1, C=3) 5) Pour the remainder of Cup B into Cup A (A=4, B=0, C=3) 6) Empty Cup C (A=4, B=0, C=0) 7) Fill Cup B (A=4, B=4, C=0) 8) Fill Cup C from Cup A (A=4, B=1, C=3) 9) Pour the remainder of Cup B into Cup A (A=5, B=0, C=3) 10) Empty Cup C (A=5, B=0, C=0) 11) Fill Cup B (A=5, B=4, C=0) 12) Fill Cup C from Cup A (A=5, B=1, C=3) 13) Empty Cup C (A=5, B=1, C=0) 13) Pour the remainder of Cup B into Cup C (A=5, B=0, C=1) 14) Fill Cup B (A=5, B=4, C=1) so assuming you count the filling of cups as pours your answer is 14
The answer is 4! (4 factorial), the same as 4x3x2x1, which equals 24 combinations. The answer is 24 and this is how: A b c d A b d c A c d b A c b d A d c b A d b c B c d a B c a d B d a c B d c a B a c d B a d c C d a b C d b a C a b d C a d b C b d a C b a d D a b c D a c b D b c a D b a c D c a b D c b a
This is a proof that uses the cosine rule and Pythagoras' theorem. As on any triangle with c being the opposite side of θ and a and b are the other sides: c^2=a^2+b^2-2abcosθ We can rearrange this for θ: θ=arccos[(a^2+b^2-c^2)/(2ab)] On a right-angle triangle cosθ=a/h. We can therefore construct a right-angle triangle with θ being one of the angles, the adjacent side being a^2+b^2-c^2 and the hypotenuse being 2ab. As the formula for the area of a triangle is also absinθ/2, when a and b being two sides and θ the angle between them, the opposite side of θ on the right-angle triangle we have constructed is 4A, with A being the area of the original triangle, as it is 2absinθ. Therefore, according to Pythagoras' theorem: (2ab)^2=(a^2+b^2-c^2)^2+(4A)^2 4a^2*b^2=(a^2+b^2-c^2)^2+16A^2 16A^2=4a^2*b^2-(a^2+b^2-c^2)^2 This is where it will start to get messy: 16A^2=4a^2*b^2-(a^2+b^2-c^2)(a^2+b^2-c^2) =4a^2*b^2-(a^4+a^2*b^2-a^2*c^2+a^2*b^2+b^4-b^2*c^2- a^2*c^2-b^2*c^2+c^4) =4a^2*b^2-(a^4+2a^2*b^2-2a^2*c^2+b^4-2b^2*c^2+c^4) =-a^4+2a^2*b^2+2a^2*c^2-b^4+2b^2*c^2-c^4 (Eq.1) We will now see: (a+b+c)(-a+b+c)(a-b+c)(a+b-c) =(-a^2+ab+ac-ab+b^2+bc-ac+bc+c^2)(a^2+ab-ac-ab-b^2+bc+ac+bc-c^2) =(-a^2+b^2+2bc+c^2)(a^2-b^2+2bc-c^2) =-a^4+a^2*b^2-2a^2*bc+a^2*c^2+a^2*b^2-b^4+2b^3*c-b^2*c^2+2a^2*bc-2b^3*c+(2bc)^2-2bc^3+a^2*c^2-b^2*c^2+2bc^3-c^4 =-a^4+2a^2*b^2+2a^2*c^2-b^4+(2bc)^2-c^4-2b^2*c^2 =-a^4+2a^2*b^2+2a^2*c^2-b^4+2b^2*c^2-c^4 (Eq.2) And now that we know that Eq.1=Eq.2, we can make Eq.1=(a+b+c)(-a+b+c)(a-b+c)(a+b-c) Therefore: 16A^2=(a+b+c)(-a+b+c)(a-b+c)(a+b-c) A^2=(a+b+c)(-a+b+c)(a-b+c)(a+b-c)/16 =[(a+b+c)/2][(-a+b+c)/2][(a-b+c)/2][(a+b-c)/2] And so if we let s=(a+b+c)/2 A^2=s(s-a)(s-b)(s-c)
Well, isn't that just a happy little math problem! If A is less than B and B plus C equals 10, then it must be true that A plus C is less than 10. Just remember, in the world of numbers, everything adds up beautifully in the end.
here's the notes for i gotta feeling on the recorder by the black eyed peas: d' d' d' d' c' c' bb c'c'c'c' c'c'c'c' b b b b b b b b a ( 4 beats) g ( 4 beats) a ( 4 beats) g ( 4 beats) c' a ( 4 beats) g ( 4 beats) a ( 4 beats) g ( 4 beats) E A G C' B..........E E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' B E E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' B E E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' B E E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' B A...G. Thats the begining thnks ;)
Here's the notes for i gotta feeling on the recorder ( can also be played on the keyboard with the same notes) by the black eyed peas:d' d' d' d' c' c' bb c'c'c'c' c'c'c'c' b b b b b b b b c'c'c'c' c'c'c'c'a ( 4 beats) g ( 4 beats)a ( 4 beats) g ( 4 beats) c'a ( 4 beats) g ( 4 beats)a ( 4 beats) g ( 4 beats)E A G C' B..........E E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' BE E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' BE E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' BE E C' B A G E C' B ......... E E C' B A G E D' B E E D' B A G E D' D' B A G ... C' BA...G. Thats the begining thnks ;)
PLEASE NOTE ~ |= MEASURE SEPARATION ALL OF THE Ds ARE HIGH D AND OPEN D WILL BE WRITTEN IN ITALICS ( D )4/4 B B B B B B| B D G A B| C# C# C# C# C# B B|B A A B D|B B B B B B| B D G A B| C# C# C# C# C# B B B| D D C# A G| D B A G D | D B A G E | E C# B A F | D D C# A B| D B A G D | D B A G E | E C# B A D D D D | E-(high) D C# A G D| B B B B B B| B D G A B| C# C# C# C# C# B B|B A A B D| B B B B B B| B D G A B| C# C# C# C# C# B B B| D D C# A G|
Well. Multiply both sides by 'c'. After that you should have something like ac=b-4 then you add 4, to get this result 4+ac=b.
a+(b+c)=b+(a+c) 2+(7+4)=7+(2+4)
1.A 2.d 3.b 4.a 5.c 6.a 7.c 8.c 9.b 10.c 11.b 12.b 13.a 14.a 15.a
x=(-b+sqrt(b^2-4*a*c))/(2a) and (-b-sqrt(b^2-4*a*c))/(2a) (This is called the quadratic formula)