A passenger on a stranded lifeboat shoots two distress flares into the air. The first flare travels a maximum height 196 feet and lands in the water after 7 seconds. The height (feet) of the second flare above the water is given by f(t) = -16t(t-8), where t is time (seconds) since the flare was shot. Which flare travels higher? Which remains in the air longer?

Answers

Answer 1

Answer:

The second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare

Step-by-step explanation:

The given parameters are;

The height of the first flare = 196 feet

The duration the first flare spends in the air = 7 seconds

The function representing the height of the second flair is f(t) = -16t(t - 8)

Where;

t = The time since the passenger shot the second flare

The time the flair stays i the air is given by the time it takes for the height, f(t),  to be 0 as follows;

f(t) = 0 = -16t(t - 8)

-16t(t - 8) = 0

t = 0, or t = 8

The time the second flare stays in the air = 8 seconds

The maximum height reached by the second flair is given by the finding the maximum point of the curve of the function as follows;

d(f(t))/dt = 0 = d(-16t(t - 8))/dt = -32t + 128 at the maximum point (the coefficient of t² is negative in the quadratic equation)

-32t + 128 = 0

128 = 32t

32t = 128

t = 128/32 = 4

t = 4 at maximum height and f(4) = -16 × 4 × (4 - 8) = 256 feet

The maximum height reached by the second flare f(4) = -16 × 4 × (4 - 8) = 256 feet.

Therefore, the second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare, with maximum height of 196 feet, and time in the air of 7 seconds.


Related Questions

The amounts below show the change (measured in feet) in water level over four months. What is the average monthly change in water level?

3/4, -9/4, -11/4, 5/4

Answers

Answer:

The average change in water level is: -3/4

Step-by-step explanation:

The average is calculated by adding up all the values and then dividing the sum by total number of values.

Given values are:

3/4, -9/4, -11/4, 5/4

The sum of values will be:

[tex]=\frac{3}{4}+(-\frac{9}{4})+(-\frac{11}{4})+\frac{5}{4}\\=\frac{3}{4}-\frac{9}{4}-\frac{11}{4}+\frac{5}{4}\\=\frac{3-9-11+5}{4}\\=\frac{-12}{4}\\=-3[/tex]

Total number of values is 4

So,

[tex]Average = \frac{Sum}{Values}\\= \frac{-3}{4}[/tex]

Hence,

The average change in water level is: -3/4

The real answer pls this is a test that’s already late

Answers

Answer:

Divide 150 by 3 to find the number of pears (50 pears)

Step-by-step explanation:

Answer:

Divide 150 by 3 to find the number of pears 50 pears

Step-by-step explanation:

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Riemann hypothesis, explain please.

Answers

Answer:

The Riemann Hypothesis states that all non trivial zeros of the Riemann zeta function have a real part equal to 0.5. ... The Riemann Zeta function has some zeros that are easy to find which are of little interest but there are some other ones that are harder to find which is why the are called non-trivial.

Step-by-step explanation:

I need help on this plz!!!

Answers

Answer:

x-intercept = -2

Step-by-step explanation:

*Note = x-intercept is when y is 0*

y + 2 = 2(x + 3)

0 + 2 = 2(x + 3)

2 = 2x + 6

2 - 6 = 2x

-4 = 2x

-4/2 = 2x/2

-2 = x

To check, we find the Slope intercept Form and Graph it.

y + 2 = 2(x + 3)

y + 2 = 2x + 6

y = 2x + 6 - 2

y = 2x + 4

5(10k + 1) + 2(2+8k)

Answers

Answer:

5(10k + 1) + 2(2+8k)

Use distributive property

5(10k)+5(1)+2(2)+2(8k)

50k+5+4+16k

combine like terms (50k and 16k are alike as well as 5 and 4)

50k+16k and 5+4

66k+9 is the answer


Which table made this graph ?

Answers

Answer:

I

Step-by-step explanation:

Just because. Just get it right.

Norma's retirement party will cost $24 if she invites 12 guests. If there are 13 guests, how much will Norma's retirement party cost? Solve using unit rates.

Answers

Answer:

If there are 13 guests, it would cost Norma $26

Step-by-step explanation:

Since 12 guest equals 24 dollars all you have to do is divide 24/12 which would give you 2dollars. this means that she has to pay 2 dollars per guest. Multiply 13 becuase you want to know how much money it would cost with 13 guests and you get 26 dollars. Hope this helps.

Answer:

It'll cost $26 !

Step-by-step explanation:

if you set it up like this;

[tex]\frac{13}{x}= \frac{12}{24}[/tex]

you can see a few ways of solving this !

one way is cross multiplication .

13 x 24 = 312

312 / 12 = 26

1. Rajeev is is convinced that he and Catarina have the same amount of plants in their
homes. Rajeev has four cacti, 12 zucchini plants, and 10 air plants. Catarina has 12
cacti, 9 air plants, and 4 daisy plants. Is Rajeev correct? Write an equation or
inequality to show your thinking,

Answers

4 + 12 + 10 = 12 + 9 + 4
26 = 25
No Rajeev is wrong since he has one more plant than Catarina

Answer:

Rajeev is incorrect.

Step-by-step explanation:

Rajeev has 26 (4+12+10) plants in his home. Catarina has 25 (12+9+4) plants in her home.

From this, we get:

4+12+10 > 12+9+4

because:

26>25

So, Rajeev has more plants than Catarina, rather than the same amount.

You could use the bolded inequality to show your thinking.

What the range of 80,84,86,87,90,91,92,94,100

Answers

Answer:

20

pls mark brainliest if possible

Step-by-step explanation:

the range is the difference between the values of the largest and smallest values. You can figure this out with subtraction.

Largest number: 100

Smallest number: 80

Range: 20

Which equation could be used to find the value of x in the triangle below?
1x + 12
28-29
X + 5
O A
4x - 12 = 180
4x = 12
2x + 17 = 180
D
x + 12 = 3x - 24

Answers

Answer:

4x - 12 = 180

Step-by-step explanation:

Sum of the angles of triangle equals 180

x + 12 + 2x - 29 + x + 5 = 180

Simplified

4x - 12 = 180

Please help!
Rewrite the rational exponent as a radical. (2 points)

Answers

Answer:

Answer: 3) [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Radical Form and Exponent Form

A radical can be expressed as a rational exponent following the identity:

[tex]\displaystyle \sqrt[m]{x^n}=x^\frac{n}{m}[/tex]

We should also recall that:

[tex](x^n)^m=x^{nm}[/tex]

We are given the expression:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}[/tex]

Applying the power of power:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\left(5^{\frac{3}{4}\cdot \frac{2}{3}}\right)[/tex]

Simplifying:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=5^{\frac{1}{2}}[/tex]

Converting to radical form:

[tex]\displaystyle \left(5^{\frac{3}{4}}\right)^\frac{2}{3}=\sqrt{5}[/tex]

Answer: 3) [tex]\sqrt{5}[/tex]

(pg. 282) #2b A farm lets you pick 3 pints of raspberries for $12.00. How many
pints do you get per dollar?

Answers

Answer: Unit price is $4 for 1 pint

Check if ur question was stated right

Step-by-step explanation:

$12 ÷ 3 pints = 4

What is lighter, 1 kg of feather or 1 kg of iron?

Answers

Answer:

none they are both 1 kg

Step-by-step explanation:

Answer:

Both weight the same. 1kg of feathers weights the same as 1kg of iron.

Step-by-step explanation:

Since both are 1kg, they weight the same. It doesn't matter that one is feathers and one is iron.

jim uses 3 cups of peaches to yield 4 jars of peach jam 4 jars of jam. He also makes strawberry-peach jam. He uses equal amounts of strawberries and peaches. How many cups of strawberries does Jim need to yield 10 jars of strawberry-peach jam? The answer is 3 and 3/4, but how do you get 3 and 3/4?

Answers

Jim will probably need 6 cups of strawberries to yeild 10 jars

What formula should be entered to calculate the total budget?

Answers

Answer:

The tatal budget of what, there's no budget the budget down so I can do the problem.

There’s no picture pls show it pls

Which value of x is a solution of the inequality?
​3x+5≤14​

A. x = 3

B. x = 4

C. x = 5

D. x = 6

Answers

Answer:

A

Step-by-step explanation:

3*3+5=14 which is the only solution betwen ABCD

Find the solution(s) of the following equation.
c^2 = 121c
2
=121c, squared, equals, 121
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
c = 11c=11c, equals, 11

(Choice B)
B
c = -11c=−11c, equals, minus, 11

(Choice C)
C
c = 13c=13c, equals, 13

(Choice D)
D
c = -13c=−13c, equals, minus, 13

(Choice E)
E
None of the above

Answers

Answer:

A and B

Step-by-step explanation:

11 x 11 = 121

-11 x -11 = 121

Find the value of x that would prove u is parallel to v

Answers

Answer:

4

Step-by-step explanation:

If u is parallel to v, so:

(24x - 1) + (20x +5) = 180

24x - 1 + 20x + 5 = 180

24x + 20x - 1 + 5 =180

44x - 1 + 5 = 180

44x + 4 = 180

44x = 180 - 4

44x = 176

44x / 44 = 176 / 44

x = 4

A recipe requires 1 cup of milk for every 4 cups of flour. Choose a linear equation that describes the proportional relationship?
A- y=4x
B- y=4x+1/4
C-y=1/4x+4
D-y=1/4x

Answers

Answer:

A

Step-by-step explanation:

For every 4 cups of flour, there is one cup of milk, therefore, the first equation describes the relationship.

i will mark you has brainliest if you answer this question ​

Answers

Answer:

Y=X+74

Step-by-step explanation:

75=m+b......*

76=2m+b.........**,b=76-2m

then substitute b=76-2m

on the first equation

75=m+76-2m

m=1

b=74

Y=X+74 is the answer

5u+u–u please tell me !

Answers

Answer: = UwU

Step-by-step explanation:

Answer:

5u

Step-by-step explanation:

Simplifying

5u + -1u = u + 15

Combine like terms: 5u + -1u = 4u

4u = u + 15

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-1u' to each side of the equation.

4u + -1u = 15 + u + -1u

Combine like terms: 4u + -1u = 3u

3u = 15 + u + -1u

Combine like terms: u + -1u = 0

3u = 15 + 0

3u = 15

Divide each side by '3'.

u = 5

Simplifying

u = 5

6x − 5y = 5
3x + 5y = 4

Answers

6x - 5y = 5
3x + 5y = 4
9x = 9
9 x 1 = 9
x = 1

Write the equation of the line that is parallel to y = -x – 5 and has a y-intercept at (0, 11).

Answers

Answer:

[tex]y=-x+11[/tex]

Step-by-step explanation:

We know that the new equation must be parallel to [tex]y=-x-5[/tex].

Therefore, since they are parallel, the slope of the new equation must be the same as the old.

The slope of the original equation is -1.

Therefore, the slope of our new equation is also -1.

We also know that it has a y-intercept at (0, 11).

And as determined earlier, it has a slope of -1.

So, we can use the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We will substitute -1 for m and 11 for b. Thus, our equation is:

[tex]y=-x+11[/tex]

Complete the square to write the equation, 4x2 + 24x – y + 43 = 0, in standard form.

Answers

Answer:

y=4

x=3

7

Step-by-step explanation:

Edg2021

Slide 1: Intro Slide

Slide 2: A then B

Slide 3: A, C, D

Slide 4: B then A

Slide 5: B

Slide 6: h = -3, k = 1, a = 3, b = 2, Center: (-3,1), Slope of Asymptote = 2/3

Slide 7: 4, 3, 7

Slide 8: C

Slide 9: C

Slide 10: B

Slide 11: D

Thank me later, brainliest, and you're welcome. Have a nice day and good luck on the quiz! :]

Write the slope- intercept form of the equation of each line.​

Answers

Answer:

y=8x-6

Step-by-step explanation:

Dominic is cutting a rectangular hole in his paper, from top left corner to the bottom right corner. The rectangle will be 4.5 cm long and 3.5 cm wide. which of the following is closest to the distance between the corners of the rectangle?

Answers

Answer:

Step-by-step explanation:

So initially you have a square piece of metal, 15" x 15". You cut out squares from the corners of each side with side length x.

 

So you'll have a sheet that looks something like this now (assuming the formatting works):

 

   _____

__|       |__

|               |

|__        __|

   |____|

 

Your original side length was 15, but it has now been reduced by x on each side, so you're now going to have a new side length of 15 - 2x

 

When you fold the box up, the box will have a height of just x.

 

So you have a base with lengths (15 - 2x) and (15 - 2x), and a height which is just x.

 

V = l*w*h

 

So

 

V = (15 - 2x)(15 - 2x)(x)

 

= 225x - 60x^2 + 4x^3

 

Hope this helps

Please help me out!​

Answers

Answer:

11. B      12. B, C, and D

Step-by-step explanation:

A = Rational numbers

B = Integers

C = Whole numbers

D = Natural numbers

E = Irrational numbers

11.  B

60/15 is a natural number because it equals 4 and is a positive integer

12. B, C, and D

An integer is a whole number meaning that because B. 42/6 = 7, C. 2√100 = 10, and D. 8 are all not fractions or decimals, they are integers.

10 5 5 10 5 5 1. What is the perimeter of this figure, to the nearest unit ?! ​

Answers

Step-by-step explanation:

IIIIIIIIIIIIisjsbsbszzvsbshsgsvsbdhdhd dbdhhdbd 5 dbdhdbdbdbsgs s dbshsbd dbshsvssbs sjhdd. dhd

PLEASE ANSWER THIS ASAP !!!!

Answers

Answer:

Step-by-step explanation:

hmmmmmmmmmmmm???

]

it’s -15 i hope this helped

Please answer thiss!!! I need ASAP!

Answers

Answer:

Need to distribute negative sign between groups.

Step-by-step explanation:

- (3x - x^2 + 1) =

-3x + x^2 - 1

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