1)The equation y=−4.9x2+8.82x+1.96 represents the height of the trajectory of a ball x seconds after it was released. The solutions to 0=−4.9x2+8.82x+1.96 are x=−0.2 and x=2. Which of these solutions represents the time it takes the ball to hit the ground?(1 point)
a) both x=−0.2 and x=2
b) x=−0.2
c) x=2
d) Neither of the solutions represents the correct time.
2) The equation y=−4.9x^2+19.5x+1.75 represents the height of the trajectory of a ball x seconds after it was released. At what time is the ball 10 meters above the ground?(1 point)
a) The ball never is never 10 meters above the ground.
b) approximately 0.5 seconds and 3.5 seconds
c) approximately 3.5 seconds
d) approximately 0.5 seconds
(A) x = -0.2 is before the ball was thrown, so what do you think?
(B) You want to solve
−4.9x^2+19.5x+1.75 = 10
4.9x^2 - 19.5x + 8.25 = 0
Now just solve using the quadratic formula.
so it sounds like for number one its (a)
and for number 2 its (b)
#1 is definitely NOT (a)
#2 is b
then then #1 would be b
how could #1 be B if A is wrong? (And I told you why A is wrong ...)
Do a little thinking here!
omg im stupid its d) im so sorry for you having to deal with me
*sigh* it's c)
They told you there are two solutions, but x = -0.2 makes no sense, so it must be x = 2
If your seeing this your a legend stay safe :)
To find the answers to these questions, we need to solve the quadratic equation given and interpret the solutions in the context of the problem.
1) For the first question, we are looking for the solution that represents the time it takes for the ball to hit the ground. In the equation y = -4.9x^2 + 8.82x + 1.96, the value of y represents the height of the ball at a given time x. When the ball hits the ground, its height is 0.
To find the time it takes for the ball to hit the ground, we need to set y = 0 in the equation and solve for x. So, we have:
0 = -4.9x^2 + 8.82x + 1.96
To solve this quadratic equation, we can use the quadratic formula or factor it. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -4.9, b = 8.82, and c = 1.96. Plugging these values into the formula, we get:
x = (-8.82 ± √(8.82^2 - 4(-4.9)(1.96))) / (2(-4.9))
Simplifying this expression, we find:
x = (-8.82 ± √(89.44 + 38.24)) / (-9.8)
x = (-8.82 ± √(127.68)) / (-9.8)
x = (-8.82 ± 11.31) / (-9.8)
Now, we have two values for x, -0.2 and 2. Checking these values for their relevance to the problem, we find that x = 2 represents the time it takes for the ball to hit the ground. Therefore, the correct answer is:
c) x = 2
2) For the second question, we are looking for the time at which the ball is 10 meters above the ground. In the equation y = -4.9x^2 + 19.5x + 1.75, the value of y represents the height of the ball at a given time x. We want to find the value of x when y = 10.
So, we set y = 10 in the equation:
10 = -4.9x^2 + 19.5x + 1.75
To solve this equation for x, we need to re-arrange it to the standard quadratic form:
-4.9x^2 + 19.5x + 1.75 - 10 = 0
-4.9x^2 + 19.5x - 8.25 = 0
To solve this equation, we can again use the quadratic formula or factor it. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -4.9, b = 19.5, and c = -8.25. Plugging these values into the formula, we get:
x = (-19.5 ± √(19.5^2 - 4(-4.9)(-8.25))) / (2(-4.9))
Simplifying this expression, we find:
x = (-19.5 ± √(380.25 - 162.36)) / (-9.8)
x = (-19.5 ± √(217.89)) / (-9.8)
x = (-19.5 ± 14.75) / (-9.8)
Now, we have two values for x, approximately 0.5 seconds and 3.5 seconds. These are the solutions to the equation and represent the times when the ball is 10 meters above the ground. Therefore, the correct answer is:
b) approximately 0.5 seconds and 3.5 seconds