sin(2Θ) = 2cosΘsinΘ
sinΘ=opposite/hypotenuse=8/17
adjacent = (17^2 - 8^2)^1/2 =15
sin(2Θ) = 2cosΘsinΘ = 2 *(15/17)*(8/17)= 240/289
opposite of 2Θ equals 240
hypotenuse of 2Θ equals 289
adjacent of 2Θ = (289^2 - 240^2)^1/2 = 161
cos(2Θ) = 161/289
tan(2Θ) = 240/161
Answer: Shirts are $9 each and hats are $8 each
Step-by-step explanation:
Let S be the price of a Shirt, and H the price of a Hat.
First Week: 4S + 9H = $108
Today: 17S + 21H = $321
We have 2 equations and 2 unknowns (S and H). Rearrange one of the equations to isolate one of the unknowns. I'll rearrange the first for S:
4S + 9H = $108
4S = $108 - 9H
S = ($108 - 9H)/4
S = 27 - 2.25H
Now use this value of S in the second equation:
17S + 21H = $321
17(($27 - 2.25H) + 21H = $321
Solve for H:
459 -38.25H + 21H = $321
-17.25H = - 138
H = $8
Each hat was $8.
Use this value in the first equation to find S:
4S + 9H = $108
4S + 9*($8) = $108
4S + $72 = $108
S = $9
Each shirt was $9.
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Check to see if the numbers give the correct results:
4*($9) + 9*($8) = $108
17*($9) + 21*($8) = $321
Both yield the correct amounts. Shirts are $9 each and hats are $8 each.
Answer: 4a
Explanation If ‘a’ represents his age today, and you have to find his age in four years you take 4 multiplied a. (4 x a) putting it together and you would get 4a
Is -1-2-3-4-5-6= - (1+2+3+4+5+6)=-21
It is an arithmetic sum
2/3 miles per hour, because you would divide the distance of 1 1/3 miles by the time it took, which was 2 hours.