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Nuetrik [128]
3 years ago
15

In the diagram below AB is parallel to CD what is the value of X?

Mathematics
1 answer:
Delicious77 [7]3 years ago
4 0
Where is the diagram?
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A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) =- 5<img src="https://tex.z-dn.net/?f=t%5E%7
DanielleElmas [232]

Answer:

Part A)

No

Part B)

About 2.9362 seconds.

Step-by-step explanation:

The equation  \displaystyle h(t)=-5t^2+14t+2  models the height h in meters of the ball t seconds after its launch.

Part A)

To determine whether or not the ball reaches a height of 14 meters, we can find the vertex of our function.

Remember that the vertex marks the maximum value of the quadratic (since our quadratic curves down).

If our vertex is greater than 14, then, at some time t, the ball will definitely reach a height of 14 meters.

However, if our vertex is less than 14, then the ball doesn’t reach a height of 14 meters since it can’t go higher than the vertex.

So, let’s find our vertex. The formula for vertex is given by:

\displaystyle (-\frac{b}{2a},h(-\frac{b}{2a}))

Our quadratic is:

\displaystyle h(t)=-5t^2+14t+2

Hence: a=-5, b=14, and c=2.

Therefore, the x-coordinate of our vertex is:

\displaystyle x=-\frac{14}{2(-5)}=\frac{14}{10}=\frac{7}{5}

To find the y-coordinate and the maximum height, we will substitute this value back in for x and evaluate. Hence:

\displaystyle h(\frac{7}{5})=-5(\frac{7}{5})^2+14(\frac{7}{5})+2

Evaluate:

\displaystyle \begin{aligned} h(\frac{7}{2})&=-5(\frac{49}{25})+\frac{98}{5}+2 \\ &=\frac{-245}{25}+\frac{98}{5}+2\\ &=\frac{-245}{25}+\frac{490}{25}+\frac{50}{25}\\&=\frac{-245+490+50}{25}\\&=\frac{295}{25}=\frac{59}{5}=11.8\end{aligned}

So, our maximum value is 11.8 meters.

Therefore, the ball doesn’t reach a height of 14 meters.

Part B)

To find out how long the ball is in the air, we can simply solve for our t when h=0.

When the ball stops being in the air, this will be the point at which it is at the ground. So, h=0. Therefore:

0=-5t^2+14t+2

A quick check of factors will reveal that is it not factorable. Hence, we can use the quadratic formula:

\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Again, a=-5, b=14, and c=2. Substitute appropriately:

\displaystyle x=\frac{-(14)\pm\sqrt{(14)^2-4(-5)(2)}}{2(-5)}

Evaluate:

\displaystyle x=\frac{-14\pm\sqrt{236}}{-10}

We can factor the square root:

\sqrt{236}=\sqrt{4}\cdot\sqrt{59}=2\sqrt{59}

Hence:

\displaystyle x=\frac{-14\pm2\sqrt{59}}{-10}

Divide everything by -2:

\displaystyle x=\frac{7\pm\sqrt{59}}{5}

Hence, our two solutions are:

\displaystyle x=\frac{7+\sqrt{59}}{5}\approx2.9362\text{ or } x=\frac{7-\sqrt{59}}{5}\approx-0.1362

Since our variable indicates time, we can reject the negative solution since time cannot be negative.

Hence, our zero is approximately 2.9362.

Therefore, the ball is in the air for approximately 2.9362 seconds.

5 0
3 years ago
Read 2 more answers
The perimeter of a 5-sided figure is 45.56 meters. Two of the sides have the same length. The sum of the other three side length
balandron [24]
10.68 each for the 2 same length sides. The total of the 5 sides is 45.56 less the 3 sides which total 24.2 leaves 21.36 remaining for the 2 equal length sides. So divide 21.36 by 2 = 10.68
(45.56 - 24.2)/2 = 10.68
4 0
3 years ago
Read 2 more answers
Need help with task! Show work if possible~~
Inessa [10]

Answer:

Please see attached picture for full solution.

Sorry, I'm not sure how to do Q7 :(

6 0
3 years ago
242 X 38 1 9 36 9,1 96 Which digits belong in the blue boxes shown on the multiplication problem?
babymother [125]

Answer:

C. 726

Step-by-step explanation:

9196-1936=7260 and take away the 0 so your answer will be 726

4 0
2 years ago
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What is the range of f(x) = 3X + 9?<br> {yly&lt;9}<br> {yly&gt;9}<br> {yly&gt; 3}<br> {yly&lt;3}
4vir4ik [10]

Answer:

the set of all real numbers

Step-by-step explanation:

f(x) = 3X + 9 is a polynomial, and so both the domain and the range are "the set of all real numbers."  

None of your answer choices match this.  Check with your teacher if you can.

7 0
3 years ago
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