Answer:666 hours
Step-by-step explanation: The reason is that if you turn the problem into an equation it would be h=Lx. h= hours. L=how long the log lasts and x=how many logs. So when you plug in the numbers you get 101010=L*151515. So we need to find L. What you do is you divide both sides by 151515 since it is the opposite of multiplication. 151515/151515 gets crossed out and 101010/151515 is .6666666666666 irrational. So the equation now looks like .666666 irrational=L. So .66666 irrational is your L. Know you plug .666666 irrational into your original equation. Which is now h=.6666 irrational*x. So to find how long the fire keeps on burning with 999 logs you just plug 999 into x and now your equation looks like this h=.6666 irrational*999. If you multiply .6666 irrational by 999 your final answer is 666.
Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
c^2 = a^2 + b^2 - 2*ab*Cos(C)
c = 16; a = 17; b = 8 (what you call a and b don't really matter. c does). Substitute.
16^2 = 17^2 + 8^2 - 2*17*8*Cos(C) Add the first 2 on the right.
256 = 289 + 64 - 282*cos(C)
256 = 353 - 282*cos(C)
Whatever you do, don't do any more combing on the right side. Subtract 353 from both sides.
-97 = -282 * cos(C )
Divide by 282
0.34397 = cos(C)
cos-1(0.34397) = C ; C = 69.88 degrees.
Do you need more help on this question? All of these are done the same way.
