Two ants start at the origin of the rectangular grid shown above where each unit represents an inch. They roam around in different directions for exactly 30 seconds. Ant A ends at point (-3,5) while Ant B ends at points (4,-2). How far apart are the two ants at the end of 30 seconds?
* is this right? (1,3)
A small fishing boat's outboard motor requires a mixture of gasoline and oil for fuel. The mixture called for in the owner's manual is 1 gallon of oil for every 50 gallons of gas. If the boat's gas tank holds approximately 6 gallons of gas, approximately how much oil must be added to the gasoline?
2007-06-04 05:00:15 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
For your first question, you are not correct. Your answer will be a single number representing a distance, not an ordered pair. You must take the square root of the sum of the squares of the respective differences of the x and y coordinates. This is an application of the Pythagorean theorem. The difference in the x-coordinates is (-3) - 4 = -7. The difference in the y-coordinates is 5 - (-2) = 7. The square root of the sum of the squares is sqrt((-7)^2 + 7^2) = sqrt(49 + 49) = sqrt(98) = sqrt(2)*sqrt(49) = 7*sqrt(2) = 9.899 inches.
The second question is a little unclear. I assume the oil and gasoline are added together into one tank with a total capacity of 6 gal. The volume of the mixture will be 1/51 oil and 50/51 gasoline. If the total volume is 6 gal, the volume of oil will be (1/51)*6 = 0.118 gal. If, instead, the gasoline is held in a compartment with a capacity of 6 gal, and the oil is added somewhere else, the amount of oil is instead (1/50)*6 = 0.12 gal.
2007-06-04 05:06:28 · answer #1 · answered by DavidK93 7 · 0⤊ 0⤋
Consider the differences in the x and y locations of the Ants.
x2 - x1 = -3 -4 = -7 (That is, +7 inches, distance is positive).
y2 - y1 = 5 - (-2) = 7.
Now you have a right angle triangle of horizontal and vertical lengths of 7 inches each. The distance between them is the hypotenuse of the triangle. The question asks for the distance between them, not for a reference point.
d² = a² + b²
d = √(a² + b²)
d = |√(7² + 7²)|
d = |√(98)|
d = 9∙899 494....
d ≈ 9∙9 inches.
1 gallon (oil) = 50 gallons (gas) (÷ 50)
1/50 gallon (oil) = 1 gallon (gas) (x 6)
6/50 gallon (oil) = 6 gallons (gas)
3/25 gallon (oil) = 6 gallons (gas)
2007-06-04 05:21:59 · answer #2 · answered by Sparks 6 · 0⤊ 0⤋
I am not sure about the 1st question but the second one is .12 gallons. You get this by using the formula 1/50 = x/6 You cross multiply and get 6 = 50x you then divide each side by 50 and the answer is .12 .... as for the 1st question .. i would need to see the grid to understand what it is asking
2007-06-04 05:07:15 · answer #3 · answered by Rick 1 · 0⤊ 0⤋
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2016-12-12 11:11:27 · answer #4 · answered by ? 4 · 0⤊ 0⤋
twelve
2007-06-04 05:07:10 · answer #5 · answered by Anonymous · 0⤊ 0⤋