HELPPP!!!!!!
A falling object travels a distance given by the formula d=3t+5t2, where d is measured in feet and t is measured in seconds. How many seconds will it take for the object to travel 84 feet?
3t+5t^2 = 84
5t^2 + 3t - 84 = 0
solve as usual.
Why did the object fall in love with the ground? Because it couldn't resist its irresistible gravitational pull!
Now, let's solve the problem.
Given the formula d = 3t + 5t^2 and the desired distance d = 84 feet, we can set up the equation:
84 = 3t + 5t^2
To make the equation easier to solve, we rearrange it:
5t^2 + 3t - 84 = 0
Now, you have a quadratic equation! You can solve it using methods like factoring, completing the square, or using the quadratic formula. It's up to you to choose the method you find most amusing!
Once you find the solutions for t, you will have the number of seconds it takes for the object to travel 84 feet. Just remember to consider both positive and negative solutions, as time can't be negative!
To find the number of seconds it will take for the object to travel 84 feet, we need to solve the equation d = 84, where d is the distance traveled by the object.
The equation given is d = 3t + 5t^2.
So, we can substitute 84 for d in the equation:
84 = 3t + 5t^2.
To solve this equation, we need to rearrange it and set it equal to zero:
5t^2 + 3t - 84 = 0.
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula, which is:
t = (-b ± √(b^2 - 4ac)) / (2a).
For the equation 5t^2 + 3t - 84 = 0, the values of a, b, and c are:
a = 5, b = 3, c = -84.
Now, we can substitute these values into the quadratic formula and calculate t:
t = (-3 ± √(3^2 - 4 * 5 * -84)) / (2 * 5).
Simplifying further:
t = (-3 ± √(9 + 1680)) / 10.
t = (-3 ± √(1689)) / 10.
To determine the values of t, we need to find the square root of 1689. Using a calculator, we get:
t ≈ (-3 ± 41.14) / 10.
Therefore, there are two possible solutions:
1. t ≈ (-3 + 41.14) / 10 ≈ 3.11 seconds.
2. t ≈ (-3 - 41.14) / 10 ≈ -4.114 seconds.
Since time cannot be negative, the only valid solution is t ≈ 3.11 seconds.
Hence, it will take approximately 3.11 seconds for the object to travel 84 feet.
To find the number of seconds it will take for the object to travel 84 feet, we need to solve the equation d = 3t + 5t^2, where d is the distance traveled in feet and t is the time in seconds.
Given that we want to find the time when the distance traveled is 84 feet, we can rewrite the equation as follows:
84 = 3t + 5t^2
Now, we have a quadratic equation. To solve it, we need to rearrange it into the standard form:
5t^2 + 3t - 84 = 0
We can solve this equation using factoring, completing the square, or the quadratic formula. In this case, let's use factoring to solve for t.
First, let's try to factor out any common factors from the equation:
t(5t + 3) - 84 = 0
Now, we can factor the quadratic expression (5t + 3):
(t - 4)(5t + 21) = 0
Setting each factor equal to zero, we have:
t - 4 = 0 or 5t + 21 = 0
Solving these two equations, we find:
t = 4 or t = -21/5
Since time cannot be negative in this case, we discard the solution t = -21/5.
Therefore, it will take 4 seconds for the object to travel 84 feet.