Answer:
It's the bottom one.
Step-by-step explanation:
number one makes no snese because inside of you there is no light
number two, heat and thermal are the same thing
number three, there isn't really potential energy inside you, not in the process of the energy transformation of food.
The bottom one makes the most sense because if you think about all of the steps, it goes chemical (stomach acid), there is also some heat in there, and then mechanical when the food moves from place to place
Answer:
x + y ≥ 4
8x + 10y ≤ 70
Step-by-step explanation:
1. State the variables
According to the graph, "Number of green towels" is on the x-axis, and "Number of blue towels" is on the y-axis, so:
let x be the number of green towels.
let y be the number of blue towels
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2. <u>Write an equation for the total number of towels</u>.
The sum of number of green towels and the number of blue towels is the total number of towels.
x + y ≥ 4
"She wants to buy at least 4 towels" means she needs 4 or more. Use the ≥ symbol instead of > (which would mean more than 4 towels, not only 4).
3. <u>Write an equation for the money</u> she will spend.
Multiply each variable by the cost of the towel colour. Add them together. Equate the total as 70 because she is only willing to spend 70.
8x + 10y ≤ 70
"She does not want to spend more than $70" means she is willing to spend 70, but no more. This is why we use ≤ and not < (which would mean she would not spend 70, only less than 70).
The equations are x + y ≥ 4 and 8x + 10y ≤ 70.
The difference in volume is 125.6 cm^3, so the difference in height will be
.. 125.6 cm^3/(3.14*(2 cm)^2) = 10 cm
Eliminate the cubic term by substituting y = x - 3/4:-9 - 4 (y + 3/4)^2 - 3 (y + 3/4)^3 + (y + 3/4)^4 = 0
Expand out terms of the left hand side:y^4 - (59 y^2)/8 - (75 y)/8 - 3123/256 = 0
Subtract -(75 y)/8 - (59 y^2)/8 - 1/8 (3 i) sqrt(347) y^2 from both sides:-3123/256 + 1/8 (3 i) sqrt(347) y^2 + y^4 = (75 y)/8 + (59 y^2)/8 + 1/8 (3 i) sqrt(347) y^2
-3123/256 + 1/8 (3 i) sqrt(347) y^2 + y^4 = (y^2 + 1/16 (3 i) sqrt(347))^2:(y^2 + 1/16 (3 i) sqrt(347))^2 = (75 y)/8 + (59 y^2)/8 + 1/8 (3 i) sqrt(347) y^2
Add 2 (y^2 + 1/16 (3 i) sqrt(347)) λ + λ^2 to both sides:(y^2 + 1/16 (3 i) sqrt(347))^2 + 2 λ (y^2 + 1/16 (3 i) sqrt(347)) + λ^2 = (75 y)/8 + 3/8 i sqrt(347) y^2 + (59 y^2)/8 + 2 λ (y^2 + 1/16 (3 i) sqrt(347)) + λ^2
(y^2 + 1/16 (3 i) sqrt(347))^2 + 2 λ (y^2 + 1/16 (3 i) sqrt(347)) + λ^2 = (y^2 + (3 i sqrt(347))/16 + λ)^2:(y^2 + (3 i sqrt(347))/16 + λ)^2 = (75 y)/8 + 3/8 i sqrt(347) y^2 + (59 y^2)/8 + 2 λ (y^2 + 1/16 (3 i) sqrt(347)) + λ^2
(75 y)/8 + 3/8 i sqrt(347) y^2 + (59 y^2)/8 + 2 λ (y^2 + 1/16 (3 i) sqrt(347)) + λ^2 = (59/8 + (3 i)/8 sqrt(347) + 2 λ) y^2 + (75 y)/8 + 3/8 i sqrt(347) λ + λ^2:(y^2 + (3 i sqrt(347))/16 + λ)^2 = y^2 (59/8 + (3 i)/8 sqrt(347) + 2 λ) + (75 y)/8 + 3/8 i sqrt(347) λ + λ^2
Complete the square on the right hand side:(y^2 + (3 i sqrt(347))/16 + λ)^2 = (y sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ) + 75/(16 sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ)))^2 + (4 (59/8 + 1/8 (3 i) sqrt(347) + 2 λ) (1/8 (3 i) sqrt(347) λ + λ^2) - 5625/64)/(4 (59/8 + 1/8 (3 i) sqrt(347) + 2 λ))
To express the right hand side as a square, find a value of λ such that the last term is 0.This means 4 (59/8 + 1/8 (3 i) sqrt(347) + 2 λ) (1/8 (3 i) sqrt(347) λ + λ^2) - 5625/64 = 1/64 (-5625 - 12492 λ + (708 i) sqrt(347) λ + 1888 λ^2 + (288 i) sqrt(347) λ^2 + 512 λ^3) = 0.Thus the root λ = -1/48 i (-59 i + 9 sqrt(347) + (736 i) (2/(4907 + 9 sqrt(335721)))^(1/3) - (4 i) 2^(2/3) (4907 + 9 sqrt(335721))^(1/3)) allows the right hand side to be expressed as a square.(This value will be substituted later):(y^2 + (3 i sqrt(347))/16 + λ)^2 = (y sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ) + 75/(16 sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ)))^2
Take the square root of both sides:y^2 + (3 i sqrt(347))/16 + λ = y sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ) + 75/(16 sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ)) or y^2 + (3 i sqrt(347))/16 + λ = -y sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ) - 75/(16 sqrt(59/8 + 1/8 (3 i) sqrt(347) + 2 λ))
Solve using the quadratic formula:y = 1/8 (sqrt(2) sqrt(59 + (3 i) sqrt(347) + 16 λ) + 4 sqrt(59/8 - 1/8 (3 i) sqrt(347) - 2 λ + 75/sqrt(118 + (6 i) sqrt(347) + 32 λ))) or y = 1/8 (sqrt(2) sqrt(59 + (3 i) sqrt(347) + 16 λ) - 4 sqrt(59/8 - 1/8 (3 i) sqrt(347) - 2 λ + 75/sqrt(118 + (6 i) sqrt(347) + 32 λ))) or y = 1/8 (4 sqrt(59/8 - 1/8 (3 i) sqrt(347) - 2 λ - 75/sqrt(118 + (6 i) sqrt(347) + 32 λ)) - sqrt(2) sqrt(59 + (3 i) sqrt(347) + 16 λ)) or y = 1/8 (-(sqrt(2) sqrt(59 + (3 i) sqrt(347) + 16 λ)) - 4 sqrt(59/8 - 1/8 (3 i) sqrt(347) - 2 λ - 75/sqrt(118 + (6 i) sqrt(347) + 32 λ))) where λ = 1/48 (-i) (-59 i + 9 sqrt(347) + (736 i) (2/(4907 + 9 sqrt(335721)))^(1/3) - (4 i) 2^(2/3) (4907 + 9 sqrt(335721))^(1/3))
Substitute λ = -1/48 i (-59 i + 9 sqrt(347) + (736 i) (2/(4907 + 9 sqrt(335721)))^(1/3) - (4 i) 2^(2/3) (4907 + 9 sqrt(335721))^(1/3)) and approximate:y = -2.36475 or y = -0.494947 - 1.13703 i or y = -0.494947 + 1.13703 i or y = 3.35465
Substitute back for y = x - 3/4:x - 3/4 = -2.36475 or y = -0.494947 - 1.13703 i or y = -0.494947 + 1.13703 i or y = 3.35465
Add 3/4 to both sides:x = -1.61475 or y = -0.494947 - 1.13703 i or y = -0.494947 + 1.13703 i or y = 3.35465
Substitute back for y = x - 3/4:x = -1.61475 or x - 3/4 = -0.494947 - 1.13703 i or y = -0.494947 + 1.13703 i or y = 3.35465
Add 3/4 to both sides:x = -1.61475 or x = 0.255053 - 1.13703 i or y = -0.494947 + 1.13703 i or y = 3.35465
Substitute back for y = x - 3/4:x = -1.61475 or x = 0.255053 - 1.13703 i or x - 3/4 = -0.494947 + 1.13703 i or y = 3.35465
Add 3/4 to both sides:x = -1.61475 or x = 0.255053 - 1.13703 i or x = 0.255053 + 1.13703 i or y = 3.35465
Substitute back for y = x - 3/4:x = -1.61475 or x = 0.255053 - 1.13703 i or x = 0.255053 + 1.13703 i or x - 3/4 = 3.35465
Add 3/4 to both sides:Answer: x = -1.61475 or x = 0.255053 - 1.13703 i or x = 0.255053 + 1.13703 i or x = 4.10465
Answer:
the answer is 9x + 6 ......