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Naval Operations. Two warning flares are fired upward at the same time from different parts of a ship. The height of the first flare is $\left(-16 t^{2}+128 t+20\right)$ feet and the height of the higher-traveling second flare is $\left(-16 t^{2}+150 t+40\right)$ feet, after $t$ seconds.a. Find a polynomial that represents the difference in the heights of the flares.b. In 4 seconds, the first flare reaches its peak, explodes, and lights up the sky. How much higher is the second flare at that time?

a. $(22 t+20) \mathrm{ft}$b. $108 \mathrm{ft}$

Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

02:19

The staging platform for a…

02:21

A fireworks shell is shot …

02:41

A set of fireworks mortar …

09:23

Trajectory of a Flare. The…

00:52

A fireworks display is pla…

00:58

Use a graphing calculator …

02:12

Fireworks are typically la…

01:35

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07:41

At the Bakersville Fourth …

04:42

Trajectory of a Launched O…

01:29

Suppose that a flare is la…

03:40

A projectile is fired upwa…

01:10

Solve.Fireworks Displa…

04:32

02:46

A model rocket is launched…

02:20

Solve each problem.Hit…

02:53

A model rocket is launche…

03:25

Rocket-Propelled Grenade I…

07:30

Two rockets start from res…

01:31

In the following exercises…

in this problem. We're being told that a ship is setting off to different players, and the height of these flares can very represented by two different Paulino meals. Well, the height of the smaller flare is represented by negative 16 t squared post 1 2080 plus 20 in the height of the larger flair is represented by the polynomial negative 16 t squared plus 1 50 t plus 40. And keep in mind, TV represents the height. So in part A, they want us to determine the difference in the height between the higher flair versus the smaller flair. Well, that simply means we need to subtract the higher flair, minus the smaller flair. Well, the higher flare is represented by the polynomial negative 16 T Square plus 1 50 t plus 40 and the smaller flare is represented by the polynomial negative 16 T Square plus 1 28 T plus 20. So now all we need to do is simplify this well for being asked to subtract Paulino meals, which in this case means that we just need to bring down the terms. In the first polynomial, which are negative. 16 t squared plus 1 50 T plus 40 now for a second Paulino meal because it's getting subtracted by the first. What we need to do is change the signs of each of those terms, and then we can drop the parentheses. So, in other words, that means negative 16 t squared will become positive. 16 t squared, the positive 1 2080 will become negative 1 2080 and the positive 20 is going to become negative. 20. So now we just need to combine like terms. So let's look at our first term of negative 16. T squared. Well, it's like term is positive. 16. T squared. Well, negative 16 plus 16 0 So those terms will cancel each other up. Next, we have positive. 1 50 t. It's like term is negative. 1 2080 while 1 50 minus 1 28 is 22 so we'll have 22 tea. Next we have positive. 40. Who's like term is negative. 20. Well 14 minus 20 is equal to 20 so we'll have plus 20. So 22 T plus 20 represents the distance in the height between the higher flair and the smaller flare at any particular time. So now we're gonna move on to part B. So I'm going to go on to my second page here, and I again put the polynomial is to represent the smaller in the higher flare, just in case we need it. Well, in part B, we're told that in four seconds, the smaller of the two flares is going to heat hit its peak. Meaning is gonna hit its highest point. What they're asking us, though, is defined. How much higher is the second flare at this time? We'll remember in part a. We found that the difference in the heights and the two flares is represented by the polynomial 22 tea plus 20. Well, because this tells us the difference in the height of the two flares for this particular problem, we just need to figure out what the difference in the height would be after four seconds. So for part B, all we're going to dio is substitute for and for teeth. So we'll have 22 times four because it's after four seconds plus 20 well, 22 times four is 88 plus 20 in 88 plus 20 is 108. So that means the difference in their heights is 100 and eight

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