MATHEMATICS HIGH SCHOOL

A van travels 220 miles on 10 gallons of gas. Find how many gallons the van needs to travel 550 miles.31 gallons of gas
121 gallons of gas
25 gallons of gas
115 gallons of gas

Answers

Answer 1
Answer: The van will need 25 gallons of gas for it to travel 550 miles. This is calculated by dividing 10 gallons to 220 miles to get the miles per gallons, which in this case is 22 miles per gallon. Then we have to divide 550 miles by 22 miles per gallon to get the total gas consumption, which is 25 gallons.
Answer 2
Answer:

Answer:

Step-by-step explanation:

To calculate how many gallons the van needs to travel 550 miles you should multiply the number of miles by the relationship between the number of gallons of gas it needs to travel 220 miles, (it is important to put the quantity in miles on the denominator) as follows:

550miles*(10gallons)/(220miles)=25

Therefore the van needs 25 gallons of gas to travel 550 miles

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For the given differential equation Y'' - Y' - 30 = sin(9t), with initial conditions Y(0) = 6 and Y'(0) = 4, what is the Laplace transform equation for Y(s)? a) Y(s) = (s^2 + 4s + 6)/(s^2 + s - 30) - (9s)/(s^2 + 81) b) Y(s) = (s^2 - 4s - 6)/(s^2 - s + 30) + (9s)/(s^2 - 81) c) Y(s) = (s^2 + 4s - 6)/(s^2 - s - 30) - (9s)/(s^2 + 81) d) Y(s) = (s^2 - 4s + 6)/(s^2 + s + 30) + (9s)/(s^2 + 81)

Answers

Answer:

None of the answer choices (a, b, c, d) match this result exactly, but the correct choice closest to this result would be:

a) Y(s) = (s^2 + 4s + 6)/(s^2 + s - 30) - (9s)/(s^2 + 81)

Step-by-step explanation:

To find the Laplace transform of the given differential equation, we'll first take the Laplace transform of each term in the equation. Let's denote Y(s) as the Laplace transform of Y(t).

The differential equation is:

Y''(t) - Y'(t) - 30Y(t) = sin(9t)

Taking the Laplace transform of each term, we get:

L{Y''(t)} - L{Y'(t)} - 30L{Y(t)} = L{sin(9t)}

Using the properties of the Laplace transform, we can find the Laplace transforms of the derivatives as follows:

L{Y''(t)} = s^2Y(s) - sy(0) - y'(0)

L{Y'(t)} = sY(s) - y(0)

So the equation becomes:

s^2Y(s) - sy(0) - y'(0) - sY(s) + y(0) - 30Y(s) = 9/(s^2 + 81)

Now, substitute the initial conditions Y(0) = 6 and Y'(0) = 4:

s^2Y(s) - 6s - 4 - sY(s) + 6 - 30Y(s) = 9/(s^2 + 81)

Now, group like terms:

(s^2 - s - 30)Y(s) - 6s - 4 + 6 = 9/(s^2 + 81)

(s^2 - s - 30)Y(s) - 6s + 2 = 9/(s^2 + 81)

Now, solve for Y(s):

Y(s) = [9/(s^2 + 81) + 6s - 2] / (s^2 - s - 30)

Factoring the denominators:

Y(s) = [9/(s^2 + 81) + 6s - 2] / [(s - 6)(s + 5)]

Now, we have the Laplace transform equation for Y(s):

Y(s) = [9/(s^2 + 81) + 6s - 2] / [(s - 6)(s + 5)]

None of the answer choices (a, b, c, d) match this result exactly, but the correct choice closest to this result would be:

a) Y(s) = (s^2 + 4s + 6)/(s^2 + s - 30) - (9s)/(s^2 + 81)
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