Answer:
47378.31625 Liters
Step-by-step explanation:
A fountain holds 12500 7/8 gallons of water. Joe wants to calculate how many liters that is. Which proportion could he use to solve for the number of liters? (1 gal = 3.79 L)
From the above question,
1 gallon = 3.79 Liters
12500 7/8 gallons = x Liters
Cross Multiply
x Liters = 12500 7/8 × 3.79 Liters
x = 47378.31625 Liters
Therefore, the number of liters of water in the fountain is 47378.31625 Liters
Y ' = x(1+y)
dy/dx = x(1+y)
dy/(1+y) = x dx .... separate variables
int[dy/(1+y)] = int[x dx] ... apply integral to both sides
ln(1+y) = (1/2)x^2+C ... see note below
1+y = e^{(1/2)x^2+C}
1+y = e^C*e^{(1/2)x^2}
1+y = Ce^{(1/2)x^2}
y = Ce^{(1/2)x^2}-1
Answer is actually choice C (not choice B)
note: we would use absolute value bars for the natural log on the left side, but because y > -1, this means 1+y > 0. So there's no need to worry about if 1+y is negative
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Checking the answer:
y = Ce^{(1/2)x^2}-1
dy/dx = d/dx[ Ce^{(1/2)x^2}-1 ]
dy/dx = d/dx[(1/2)x^2]*Ce^{(1/2)x^2}
dy/dx = (1/2)*2x*Ce^{(1/2)x^2}
dy/dx = x*Ce^{(1/2)x^2} ... we get some messy expression
x*(1+y) = x*(1+Ce^{(1/2)x^2}-1)
x*(1+y) = x*Ce^{(1/2)x^2} .... we get the same messy expression as before
So this shows that dy/dx = x*(1+y) is a true equation for y > -1 and y = Ce^{(1/2)x^2}-1, which confirms the right answer.
Answer:
25
Step-by-step explanation:
The answer is 25 because if the ratio is 4:5 and there are 20 girls that means they multiplied 4 times 5 to get 20 and that means you have to do the same to the ratio of boy and when you multiply 5 times 5 you get 25
The height of tower A is 1016 feet and tower B is 212 feet.
<u><em>Explanation</em></u>
Suppose , the height of tower B is 
feet.
As the height of tower A is 802 feet more than tower B , so the height of tower B will be : 
Given that, the two towers have a combined height of 1226 feet.
So, the equation will be...
Thus, the height of tower B is 212 feet and height of tower A is (212+802) feet = 1016 feet.
Bread rolls = BR
Ketchup = K
Sausages = S
2BR +1K + 3S = £10 - 45p
2BR + 1K + 3S = £9.55
2BR = 1.40 x 2 = £2.80
1K = £1.80
£2.80 + £1.80 + 3S = £9.55
3S = £9.55 - £2.80 - £1.80
3S = £4.95
£4.95 / 3 = BR
S = £1.65
The answer is £1.65 for one pack of sausages
