Answer:
3/5
Step-by-step explanation:
60/100 can be reduced down to 6/10 by dividing by 10, and then you can simplify even more by dividing 6/10 by 2, which leaves you with 3/5.
I hope this helps :)
Answer:
Write the equation as n + 31 = 113 and subtract 31 from both sides. The answer is 82.
Step-by-step explanation:
The sum of a number and 31 would be 'n + 31'. The sum equaling 113 would be '= 113'.
You would get 'n' by subtracting 31 for each side.
The statement: "Write the equation as n + 31 = 113 and subtract 31 from both sides. The answer is 82." should be the correct answer.
Answer:
x=1
Step-by-step explanation:
simplify and create a chart of denominators until you find the common one.
Answer:
3300 was on 3% and 6700 on 2,5%
Step-by-step explanation:
We can say that 'a' represents the price that will go on 3% interest and 'b' 2,5% interest.
Therefore;
a + b = 10 000
And
0,03a + 0,025b = 283.5 (0,03 means 3% etc)
You can move 'b' to the other side to leave 'a' on the LHS
0,03a = 283.5 - 0,025b - - > (divide both sides by 0,03)
a=9450 - 0,8333b
Substitute this equation as 'a' in the first equation to get:
9450 - 0,8333b + b = 10 000 (move 9450 to the RHS to leave values with b on the LHS)
-0,8333b + b = 10 000 - 9450
0,1666b = 550 (divide both sides by 0,1666)
b = 3,300
Therefore 'a' will be :
a= 10 000 - 3 300
a = 6700
I hope this helps.
Prove we are to prove 4(coshx)^3 - 3(coshx) we are asked to prove 4(coshx)^3 - 3(coshx) to be equal to cosh 3x
= 4(e^x+e^(-x))^3/8 - 3(e^x+e^(-x))/2 = e^3x /2 +3e^x /2 + 3e^(-x) /2 + e^(-3x) /2 - 3(e^x+e^(-x))/2 = e^(3x) /2 + e^(-3x) /2 = cosh(3x) = LHS Since y = cosh x satisfies the equation if we replace the "2" with cosh3x, we require cosh 3x = 2 for the solution to work.
i.e. e^(3x)/2 + e^(-3x)/2 = 2
Setting e^(3x) = u, we have u^2 + 1 - 4u = 0
u = (4 + sqrt(12)) / 2 = 2 + sqrt(3), so x = ln((2+sqrt(3))/2) /3, Or u = (4 - sqrt(12)) / 2 = 2 - sqrt(3), so x = ln((2-sqrt(3))/2) /3,
Therefore, y = cosh x = e^(ln((2+sqrt(3))/2) /3) /2 + e^(-ln((2+sqrt(3))/2) /3) /2 = (2+sqrt(3))^(1/3) / 2 + (-2-sqrt(3))^(1/3) to be equ
= 4(e^x+e^(-x))^3/8 - 3(e^x+e^(-x))/2
= e^3x /2 +3e^x /2 + 3e^(-x) /2 + e^(-3x) /2 - 3(e^x+e^(-x))/2
= e^(3x) /2 + e^(-3x) /2
= cosh(3x)
= LHS
<span>Therefore, because y = cosh x satisfies the equation IF we replace the "2" with cosh3x, we require cosh 3x = 2 for the solution to work. </span>
i.e. e^(3x)/2 + e^(-3x)/2 = 2
Setting e^(3x) = u, we have u^2 + 1 - 4u = 0
u = (4 + sqrt(12)) / 2 = 2 + sqrt(3), so x = ln((2+sqrt(3))/2) /3,
Or u = (4 - sqrt(12)) / 2 = 2 - sqrt(3), so x = ln((2-sqrt(3))/2) /3,
Therefore, y = cosh x = e^(ln((2+sqrt(3))/2) /3) /2 + e^(-ln((2+sqrt(3))/2) /3) /2
= (2+sqrt(3))^(1/3) / 2 + (-2-sqrt(3))^(1/3)