The prime factorisation of 600 is given by
Therefore, a = 3, b = 3, c = 5 and d = 2.
Answer:
Step-by-step explanation:
Given the equation
Sin(5x) = ½
5x = arcSin(½)
5x = 30°
Then,
The general formula for sin is
5θ = n180 + (-1)ⁿθ
Divide through by 5
θ = n•36 + (-1)ⁿ30/5
θ = 36n + (-1)ⁿ6
The range of the solution is
0<θ<2π I.e 0<θ<360
First solution
When n = 0
θ = 36n + (-1)ⁿθ
θ = 0×36 + (-1)^0×6
θ = 6°
When n = 1
θ = 36n + (-1)ⁿ6
θ = 36-6
θ = 30°
When n = 2
θ = 36n + (-1)ⁿ6
θ = 36×2 + 6
θ = 78°
When n =3
θ = 36n + (-1)ⁿ6
θ = 36×3 - 6
θ = 102°
When n=4
θ = 36n + (-1)ⁿ6
θ = 36×4 + 6
θ = 150
When n =5
θ = 36n + (-1)ⁿ6
θ = 36×5 - 6
θ = 174°
When n = 6
θ = 36n+ (-1)ⁿ6
θ = 36×6 + 6
θ = 222°
When n = 7
θ = 36n + (-1)ⁿ6
θ = 36×7 - 6
θ = 246°
When n =8
θ = 36n + (-1)ⁿ6
θ = 36×8 + 6
θ = 294°
When n =9
θ = 36n + (-1)ⁿ6
θ = 36×9 - 6
θ = 318°
When n =10
θ = 36n + (-1)ⁿ6
θ = 36×10 + 6
θ = 366°
When n = 10 is out of range of θ
Then, the solution is from n =0 to n=9
So the equation have 10 solutions in the range 0<θ<2π
Answer:Answer:a) Area=f(x)= 24x-x^2
b) f(x) ranges from 0 to 144
c) Area max = 144 ft^2
Step-by-step explanation: shown in the attachment
Answer:
38
Step-by-step explanation:
We can express the 8th term as x and the 12th term as y.
This would mean that 8x=12y
Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y
Now we can use this to substitute y with x in the first equation. This would give us:
8x=12(x-8)
Which we can expand and solve:
8x=12x-96
-4x=-96
Therefore x=24
This means the 8th term is 24 and the 12th term is 16 (24-8).
To test if this is correct we can do:
8x24=12x16
Which indeed are equal, both sides multiply to 192.
Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)
24+14=38.
The first term is 38.
Hope this helped!
Answer:
The data provide strong evidence that young men weigh more on average than old men in the U.S
Step-by-step explanation:
Given :
The null hypothesis ; H0 : μ1 = μ2
The alternative hypothesis ; H1 : μ1 > μ2
T score = 5.3 ; Pvalue = < 0.0001
The decision region :
If Pvalue < α ; We reject the Null
If Pvalue > α ; We fail to reject the Null
When the α - level isn't stated, we usually assume a α - level of 5%
However, even at lower alpha level of 1% = 0.01 ;
The Pvalue < α
Hence, we can conclude that there is significant evidence that there is difference in the mean weight of young men and old men in the U.S
