About 4.1 seconds. How long was the ball in the air? We are told that t represents time in seconds since the ball was thrown, so it started to be 'in the air' at t = 0 To answer the question, then, we need to know the time when it stopped being in the air. We are told that the ball hit the ground. So that's what happened when it stopped being airborne. We need to relate that event to the mathematics we're working with. What can we say about h , the height of the ball when the ball hits the ground? Answer: The height will be 0 when the ball stops being in the air. Now translate this back to the mathematics: The ball is in the air from t = 0 until the time t when h = 0 . Find the time t that makes h = 0 . That means: solve: − 5 t 2 + 20 t + 2 = 0 We can solve this by solving: 5 t 2 − 20 t − 2 = 0 (Either multiply both sides of the equation by − 1 , or add 5 x 2 − 20 x and − 2 to both sides and then re-write it the other way around) That's a quadratic equation, so try to factor first. But don't spend too much time trying to factor, because not every quadratic is easily factorable and that's OK, because we still have the quadratic formula if we need it. We do need it. t = − ( − 20 ) ± √ ( − 20 ) 2 − 4 ( 5 ) ( − 2 ) 2 ( 5 ) = 20 ± √ 440 10 = 20 ± √ 4 ( 110 ) 10 = 20 ± 2 √ 110 10 = 2 ( 10 ± √ 110 ) 2 ( 5 ) = 10 ± √ 110 5 We can see that 10 < √ 110 < 11 . In fact ( 10 + 1 2 ) 2 = 10 2 + 10 + 1 4 = 110.25 Using 10.25 as an approximation for √ 110 , we get : for the solution t = 10 − √ 110 5 we'll get a negative t . That doesn't make sense. The other solution gives t ≈ 10 + 10.25 5 = 20.5 5 = 4.1 seconds. So the ball was in the air from t = 0 until about t = 4.1 . The elapsed time is the difference, 4.1 seconds.
It takes 6 minutes to circulate 2.5 gallons of water
Answer:
80
Step-by-step explanation:
Your 4 given numbers equal 295. 5x75 is 375. So take 375-295 and you get 80, your 5th number.
Answer: We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.
We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.
Step-by-step explanation:
Given: A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and .75 quart of grape juice.
Since, for recipe of sparkling grape juice , they should be used in same proportion.
Let x be the amount of sparkling water need to mix with 9 quarts of grape juice, then
We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.
Let y be the amount of grape juice need to mix with 3.75 quarts of sparkling water, then
We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.
