Ask question

Ask question

All categories

3 years ago

8

For the problem, use the discriminant to determine the number of real solutions for the equation. Then, find the solutions and c

heck to see if they make sense in the context of the problem.
A soccer player kicks the ball to a height of 2 meters inside the goal. The equation for the height h of the ball at time t is h = −4.9t^2 − 4t + 4. Find the time the ball reached the goal. Enter the time to two decimal places.

1 answer:

Ksivusya [100]3 years ago

8 0

Answer:

Discriminant = 55.2 > 0 -> 2 real solutions

Solutions: t1 = -1.1663 s and t2 = 0.35 s

The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.

So the solution is t2 = 0.35 s

Step-by-step explanation:

To find the time when the ball will reach the height of 2 meters, we just need to use the value of h = 2 in the equation given. So, we have that:

−4.9t^2 − 4t + 4 = 2

−4.9t^2 − 4t + 2 = 0

For this equation, we have the constants a = -4.9, b = -4 and c = 2. So the discriminant Delta is:

Delta = b^2 - 4ac = 16 + 39.2 = 55.2

sqrt(Delta) = 7.4297

As Delta > 0, we have 2 real solutions

t1 = (-b + sqrt(Delta)) / 2a = (4 + 7.4297) / (-9.8) = -1.1663 s

t2 = (-b - sqrt(Delta)) / 2a = (4 - 7.4297) / (-9.8) = 0.35 s

Number of real solutions: 2

Solutions: t1 = -1.1663 s and t2 = 0.35 s

The solution t1 doesn't make sense for this problem, as we can't have a negative value for the time.

So the solution is t2 = 0.35 s

You might be interested in

Suppose f(x) = 12x – 1,400 and g(x) = 12x – 1,535. Describe the transformation of the graph of f to the graph of g. Group of ans

m_a_m_a [10]

The graph is translates down 135 units, because you can see how the y-intercept decreased by 135 units from f(x) to g(x).

3 0

3 years ago

1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?

ziro4ka [17]

PART A (1 in diagram)

Each mapping diagram represents a function because none of the elements in the inputs maps on to two different elements in the outputs.

1. The domain of the given function f(x) is the set {10, 20, 30}.

All we can say about

${f}^{ - 1} (x)$

is that, it has a range of {10, 20, 30}.

This is because the domain of a function becomes the range of its inverse function.

2. If the graph of a function f(x) includes the point (3, 0), then the graph of the inverse function ,

${f}^{ - 1} (x)$

will contain the point (0,3).

Reason:The point on the graph of the inverse function is obtained by reflecting the corresponding point on the graph of the function in the line y=x. We just have to swap the coordinates.

In simple terms the domain of the function becomes the range of the inverse function and vice versa.

3. If the first term in an arithmetic sequence is 2.

Then we have a=2.

If the twelfth term is 211, then

$a + 11d = 211...(1)$

Put a=2 into this equation.

$2 + 11d = 211$

Solve for d.

$11d = 211 - 2$

$11d = 209$

$d = \frac{209}{11} = 19$

If

$a_n = 135$

then

$a + (n - 1)d = 135$

Substitute a=2 and d=19

$2 + (n - 1)19 = 135$

$19(n - 1) = 133$

$(n - 1) = \frac{133}{19}$

$n - 1 = 7$

$n = 7 + 1 = 8$

Therefore n=8

4 0

3 years ago

Your family drives 126 miles from Key West to the Florida mainland. About 15% of this distance is spent on bridges. How many mil

a_sh-v [17]

<span>How many sixth graders were late? 6 sixth graders. Your family drives 126 miles from Key West to the Florida mainland. About 15% of this distance is spent on bridges. How many miles of bridges do you travel over? 18.9 miles or 18 9/10 miles.

</span>
i hope this helps u! and if u can will u make me the <span>Brainliest answer thank you :) </span>

8 0

3 years ago

Read 2 more answers

Solving a trigonometric equation involving an angle multiplied by a constant

PIT_PIT [208]

In these questions, we need to follow the steps:

1 - solve for the trigonometric function

2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.

3 - Complete these angles with the complete round repetition, by adding

$2k\pi,k\in\Z$

4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for <em>x</em> to get the solutions.

1 - To solve, we just use algebraic operations:

$\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}$

2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:

The value for the angle that give positive

$+\frac{\sqrt[]{3}}{3}$

is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of

$-\frac{\sqrt[]{3}}{3}$

Are:

$\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}$

3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:

$\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}$

Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:

$\theta=\frac{5\pi}{6}+k\pi,k\in\Z$

4 - Now, we need to solve for <em>x</em>, because these solutions are for all the interior of the tangent function, so:

$\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}$

So, the solutions are:

$x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z$

4 0

1 year ago

What is the Y intercept of the line described for the equation below?y=4x-9

Vladimir [108]

Answer: Assuming that it's already in the standard form - y=mx+b | Your Y-Intercept is going to be -9

Step-by-step explanation:

Using the equation y=mx+b, anything that is in place of the (b) is your Y-Intercept and your slope is (m)

8 0

3 years ago

Read 2 more answers