All categories

2 years ago

Jacob throws an acorn into the air. It lands in front of him. The acorn's path is

Mathematics

2 answers:

iren2701 [21]2 years ago

5 0

The acorn hits the ground at x = 1.232 and x = -2.232

Also, only one solution is reasonable which is x = 1.232 since the acorn lands in front of him.

To answer the question, we need to solve the quadratic equation.

<h3>How to solve the quadratic equation?</h3>

Since the acorn's path is described by y = -3x² + 6x + 6, where x is the acorn's horizontal distance from him and y is the height of the acorn.

We solve -3x² + 6x + 6 = 0 to see where the acorn hits the ground.

So, -3x² + 6x + 6 = 0

Using the quadratic formula, we have

$x = \frac{-(-3) +/- \sqrt{6^{2} - 4X(-3)X6} }{2 X (-3)} \\x = \frac{3 +/- \sqrt{36 + 72} }{-6} \\x = \frac{3 +/- \sqrt{108} }{-6} \\x = \frac{3 +/- 10.39 }{-6} \\x = \frac{3 - 10.39 }{-6} or x = \frac{3 + 10.39 }{-6} \\x = \frac{-7.39 }{-6} or x = \frac{13.39 }{-6} \\x = 1.232 or x = -2.232$

So, the acorn hits the ground at x = 1.232 and x = -2.232

Also, only one solution is reasonable which is x = 1.232 since the acorn lands in front of him.

Learn more about quadratic equation here:

brainly.com/question/25841119

#SPJ1

Burka [1]2 years ago

3 0

Answer:

hits the ground at x = -0.732, and x = 2.732
only the positive solution is reasonable

Step-by-step explanation:

The acorn will hit the ground where the value of x is such that y=0. We can find these values of x by solving the quadratic using any of several means.

<h3>graphing</h3>

The attachment shows a graphing calculator solution to the equation

-3x^2 + 6x + 6 = 0

The values of x are -0.732 and 2.732. The negative value is the point where the acorn would have originated from if its parabolic path were extrapolated backward in time. Only the positive horizontal distance is a reasonable solution.

<h3>completing the square</h3>

We can also solve the equation algebraically. One of the simplest methods is "completing the square."

-3x^2 +6x +6 = 0

x^2 -2x = 2 . . . . . . . . divide by -3 and add 2

x^2 -2x +1 = 2 +1 . . . . add 1 to complete the square

(x -1)^2 = 3 . . . . . . . . written as a square

x -1 = ±√3 . . . . . . . take the square root

x = 1 ±√3 . . . . . . . add 1; where the acorn hits the ground

The numerical values of these solutions are approximately ...

x ≈ {-0.732, 2.732}

The solutions to the equation say the acorn hits the ground at a distance of -0.732 behind Jacob, and at a distance of 2.732 in front of Jacob. The "behind" distance represents and extrapolation of the acorn's path backward in time before Jacob threw it. Only the positive solution is reasonable.

You might be interested in

Which type of statement switches and negates the hypothesis and the conclusion of the original conditional statement?

valentinak56 [21]

Inverse

Inverse - is a conditional statement that NEGATES both the hypothesis and the conclusion of the original conditional statement.

8 0

3 years ago

please look at the problem and help. I tried to ask my teacher for help earlier but she ignored me so please don't ignore this.

Alchen [17]

36*40+36*40-6*6=2844ft^2

we had to subtract the area of the closet so it wasn't counted twice :P

8 0

3 years ago

12. The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each.

Debora [2.8K]

Answer:

The number of tickets they have sold in advance are summed up with the following equation and solution:

Equation: $\frac{6842.50}{17.50}$ [the final answer should be in dollars]

Solution: The Opera sold 391 tickets in advance.

Step-by-step explanation:

First: Review some background information:

Let's see what the problem gives us to answer it. I'll bold out the important parts:

The Opera is collecting monies in advance for ticket sales. The tickets cost $17.50 each. If they have collected $6842.50 already, then how many tickets have they sold in advance?

We know how much the tickets cost and how much money they have earned from selling tickets, we can find out how much tickets they have sold.

Second: Solve the problem:

We can solve this problem using many ways, but I'm just going to pick one. We will use proportions to answer this. Now thoughts might be going through your head like this: What is this guy saying? What in the world is proportions? Well hopefully you learn from this example (Please don't take offense if you <em>do</em> know how to do proportions).

First we set up two fractions. One ticket costs $17.50, so we will use it to set up our first fraction: $\frac{1}{17.50}$ . We don't know how many tickets all together cost $6842.50 so we will use the variable: x. Now, we can set up our second fraction. x tickets costs $6842.50 so our second fraction will be: $\frac{x}{6842.50}$ . Now we must use cross multiplication. We multiply the numerator of the first fraction times the denominator of the second fraction, and then we multiply the denominator o the first fraction times the numerator of the second fraction. That's what we would do usually. But now, since we have a variable, we must use cross multiplication to solve for this variable. So we multiply the the numerator of the first fraction times the denominator of the other fraction and then we divide that answer times the denominator of the first fraction (You don't have to set it up like this).So let's solve this question: