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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

Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken

AlekseyPX

Ken's distance is: d(t)=1.7t

Ken's shadow is:

(14-6)/d(t)=14/s

8/d(t)=14/s

s=14d(t)/8

s=1.75d(t) and using the value for d(t) we have:

s=1.75(1.7t)

s=2.975t and if you want it in terms of d, d=1.7t, t=d/1.7 so

s=2.975(d/1.7)

s=1.75d

5 0

3 years ago

Write in equation of the line in the graph

salantis [7]

To write the equation of a line, we use the equation: y = mx +b.

m is the slope of the line, which can be calculated using the equation:
m = (y2 - y1)/(x2 - x1)
We can choose any two points on the line to put into this equation. The red dots are at (0,0) and (-6,-2), so we will use those, but you would get the same answer by using any other pair of coordinates on the blue line.
m = (-2 - 0)/(-6 - 0) = 2/6 = 1/3

b is the y-intercept of the line. The y-intercept is the y-coordinate when the line crosses the y-axis. It crosses the y-axis at (0,0), so the y-intercept is 0.

Now, we plug our values back into the full equation to get the equation of the line.
y = mx + b
y = (1/3)x + 0

So the final answer is y = (1/3)x or y = x/3, depending on how you want to write it.

6 0

3 years ago

Read 2 more answers

Solve #3 Find the length of the missing side.a) A right triangle has a side length 2.4 cm and 6.5 cm. What is the length of the

Snezhnost [94]

Answer:

A) ≈ 6.93

B) ≈ 0.02

Step-by-step explanation:

A)

Formula : a² + b² = c²

2.4² + 6.5² = c²

5.76 + 42.25 = c²

c = √48.01

c ≈ 6.93

B)

Formula = c² - a² = b²

1/3² - 1/4² = b²

1/9 - 1/16 = b²

b = √7/144

b ≈ 0.02

If my answer is incorrect, pls correct me!

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-Chetan K

3 0

2 years ago

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The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a r

muminat

x + 1 minus StartFraction 4 Over x cubed + 3 x squared + 8

Step-by-step explanation:

Volume of the prism is given by the product of its base area and height. To get the height, divide the volume by the base area

Perform long division of the volume polynomial by the polynomial for base area to get the polynomial for height

x³+3x²+8 √x⁴+4x³+3x²+8x+4

-x⁴+3x³+8x

---------------------------

1x³+3x²+0+4

- 1x³+3x²+8

------------------------

-4

The answer will be : x+1 + -4/(x³+3x²+8)

Learn More

Dividing polynomials : brainly.com/question/11792208

Keywords : volume, rectangular prism, area,height

#LearnwithBrainly

3 0

2 years ago

Read 2 more answers