48. Calculate the number of sides of a regular polygon whose interior angle is

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.

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3 years ago

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Kazeer [188]

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3 0

2 years ago

How many quarter, a pound burgers can Kristina make out<br> of 75 pounds of ground beef?<br> 1

antoniya [11.8K]

Answer:

1 quarter pound = 0.25 of a pound.

Give that:

Total amount of ground beef = pound

From 3.5 pound of beef we have to make burgers using 0.25 pound of beef in one burger

We have to find how many burgers can be made:

We have to divide 3.5 pound by 0.25 pound

i.e,

⇒14 quarter pounds burger can be made.

Therefore, 14 quarter pound burgers can George make out of 3 1/2 pounds of ground beef

Step-by-step explanation:

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3 years ago

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I need help on this. The portrait studio can buy photographs on canvas. The small canvas photograph print is $20 and the large c

Whitepunk [10]

<h3>Answer:</h3>

6 large prints
12 small prints

<h3>Step-by-step explanation:</h3>

<em>Numerical Reasoning</em>

Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...

... 2×$20 +45 = $85

To have revenue of at least $510, the studio must sell ...

... $510/$85 = 6

sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.

_____

<em>With an equation</em>

Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...

... 20·2x +45·x ≥ 510

... 85x ≥ 510

... x ≥ 510/85

... x ≥ 6

The studio needs to sell at least 6 large prints and 12 small prints.

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3 years ago

HELP ASAP ILL GIVE A THANKS AND BRAINLIEST

larisa [96]

Answer:

-3 < x ≤ -1

Step-by-step explanation:

we know that

The solution of the graph is equal to the interval

All real numbers greater than -3 and less than or equal to -1

so the combined inequality is equal to -3 < x ≤ -1!!!!

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3 years ago