The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modelled by the function h = -5t2 + 15t + 20 What was the maximum height of the flare?

Answers

Answer 1

Answer:

31.25 metres at t=1.5 seconds.

Step-by-step explanation:

The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modeled by the function

[tex]h=-5t^2+15t+20[/tex]

We need to find the maximum height of the flare.

In the given quadratic function, the leading coefficient is negative it means the function represents the downward parabola.

Vertex of a downward parabola is the point of maxima.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then

[tex]Vertex=\left(-\dfrac{b}{2a}, f(-\dfrac{b}{2a})\right)[/tex]

In the given function, a=-5, b=15, c=20. So,

[tex]-\dfrac{b}{2a}=-\dfrac{15}{2(-5)}=\dfrac{15}{10}=1.5[/tex]

Put x=1.5 in the given function.

[tex]h=-5(1.5)^2+15(1.5)+20[/tex]

[tex]h=31.25[/tex]

Therefore, the maximum height of the flare is 31.25 metres and t=1.5 seconds.


Related Questions


14. What is the percent decrease on a DVD recorder that is marked down from $400 to $350?

1. 87.5%

2. 20%

3. 12.5%

5. 14.29%​

Answers

Answer:

12.5%

Step-by-step explanation:

Percent decrease is calculated as

[tex]\frac{decrease}{original}[/tex] × 100%

Decrease = $400 - $350 = $50 , thus

percent decrease = [tex]\frac{50}{400}[/tex] × 100% = [tex]\frac{50(100)}{400}[/tex] = 12.5%

The percent decrease on a DVD recorder that is 12.5%. The correct option is 3

What is the percentage?

A percentage is a minimum number or ratio that is measured by a fraction of 100.

let the value of which a thing is represented in percentage is "a'

let the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), therefore we will first divide the whole part in 100 parts and then we multiply it with b so that we can get b items per 100 items(that is exactly what b per cent means).

Hence, that thing in number is

(a/100)x b

Percent decrease is calculated as;

Decreased in price/original price × 100%

Decrease = $400 - $350 = $50 , thus

Therefore, percent decrease = 50/400 × 100%  

= 12.5%

Learn more about percentages;

brainly.com/question/24159063

#SPJ6

What are the zeros of f(x) = x2 - 8x+ 15?​

Answers

Answer:

x=5   x=3

Step-by-step explanation:

f(x) = x^2 - 8x+ 15

Factor

What two numbers multiply to 15 and add to -8

-5*-3 = 15

-5+-3 = -8

f(x) = (x-5) (x-3)

Setting equal to 0

0= (x-5) (x-3)

Using the zero product property

x-5 =0     x-3=0

x=5   x=3

An A-frame cabin is 26.23 feet high at the center and the angle the floor makes with the base is 53. How
wide is the base?

Answers

Answer:

60.84 feet

solution,

[tex]tan \: theta = \frac{perpendicular}{base} \\ tan \: (53) = \frac{bc}{ac} \\ tan \: (53) = \frac{26.23}{ac} \\ ac = \frac{26.23}{0.4311} \\ ac = 60.84 \: feet[/tex]

Hope this helps...

Good luck on your assignment..

This table shows values that represent a quadratic function.
x
0
1
2
3
4
5
6
y
--1
-2
5
-10
-17
-26
-37
What is the average rate of change for this quadratic function for the interval
from x = 3 to x = 5?
A. 8
B. 16
O C. -16
c
D. 8

Answers

Answer:

D

Step-by-step explanation:

The y values change by -26 - (-10) = -16 in the interval and the x values change by 5 - 3 = 2 so the average rate of change is -16 / 2 = -8.

Answer:

D. -8

Step-by-step explanation:

Risked it all for my grades.

expand the following 8 (3x-y)

Answers

Answer:

24x-8y

Step-by-step explanation:

8(3x-y) - distributive property

24x-8y

Answer:

24x - 8y.

Step-by-step explanation:

8(3x - y) = 8 * 3x - 8 * y = 24x - 8y

Hope this helps!

how can knowledge of circles apply to daily life??

Answers

Answer:

sdgsdgsdgsdgsdgsd

Step-by-step explanation:

gsdgsdgsdgsdgsd

Eva sees a dolphin 3.23.23, point, 2 meters below sea level and a bird \dfrac{47}{10} 10 47 ​ start fraction, 47, divided by, 10, end fraction meters above sea level. Which of the expression represents the vertical distance between the dolphin and the bird?

Answers

This question is not that clear, so let me rewrite it here -

Eva sees a dolphin 3.2 meters below sea level and a bird [tex]47/10[/tex] meters above sea level. Which of the expressions represents the vertical distance between the dolphin and the bird?

Now we are given that Eva sees the dolphin at a distance 3.2 meters below sea level, respectively she sees a bird at [tex]47/10[/tex] meters above sea level. The vertical distance between the dolphin and the bird should thus be the distance dolphin is below sea level + distance of bird above sea level -

[tex]y = 3.2 + 47 / 10,\\y = 3.2 + 4.7,\\y = 7.9 meters\\-------------\\Solution = 7.9 ( meters )[/tex]

The expression that represents the vertical distance between the dolphin and bird should be 3.2 + 47 / 10.

4 friends evenly divided up an n-slice pizza. One of the friends, Harris, ate 1 fewer slice than he received. How many slices of pizza did Harris eat? Write your answer as an expression.

Answers

Answer:

m-2times 4

Step-by-step explanation:

Answer:

n/4 -1

Step-by-step explanation:

i got it from khan

What is the measure of ∠x angles are not necessarily drawn to scale.

Answers

Answer:

58 degrees

Step-by-step explanation:

The other two angles are 56 and 66 degrees and you know that all the angles add up to 180 degrees.

So just subtract:

180-56-66= 58 degrees

it works because the lines are parallel in the picture.

Evaluate. 8−2⋅3+7 Enter your answer in the box

Answers

Answer:

9

Step-by-step explanation:

8−2⋅3+7

PEMDAS

Multiply and divide first

8−6+7

Then add and subtract

2+7

9

Answer:

9

Step-by-step explanation:

Remember to follow the order of operations, PEMDAS.  Note that PEMDAS =

Parenthesis

Exponent (& Roots)

Multiplication

Division

Addition

Subtraction

First, multiply -2 with 3:

-2 * 3 = -6

Next, follow the left -> right rule. First subtract, then add:

8 - 6 = 2

2 + 7 = 9

9 is your answer.

~

34.9 was rounded to 1 decimal place. What is the upper bound?

Answers

Answer:  34.95

=======================================================

Explanation:

The upper boundary, or upper bound, is a fence of sorts.

Note how the following values all round to 34.9, when rounding to one decimal place

34.9434.94534.94934.949934.9499934.94999934.949999934.94999999

We can keep going with the pattern of 9s at the end and whatever value you form will still round to 34.9; so you can see that there is no largest value we can reach that will round to 34.9

All of those values are slowly approaching 34.95, which is the upper fence I mentioned. We can get closer and closer to this value, but we can't actually reach it. Otherwise, 34.95 will round to 35.0

One advantage to using your debit card is: A:You don’t have to subtract it from your checking account balance B: It is convenient C:You can spend as much as you want D:You can give your friend the PIN number in case you forget it. Plz help me

Answers

Answer:

B.

Step-by-step explanation:

First, you never want to give out your banking information to anyone, so D is incorrect. A is incorrect because a debit card withdraws money from your checking account to pay for items you purchase. C is also incorrect because you can only spend the same amount of money in your checking account.

Identify the parts relating to CircleA. What is Line F G? Secant What is Line segment D B? Tangent What is Line segment D H? Secant What is AC? Radius

Answers

Answer:

Line FG  secant

Line segment DH   secant

Line segment DB  tangent

Line segment AC  radius

Step-by-step explanation:

A Secant is a line that passes through the two points on a circle.It cuts the circle on two points.

Line FG is a secant as it passes through two pints.

Line segment DH is also a  secant as it passes through two points.

A tangent is a line that passes through only one point on a circle. It is outside the circle. It is perpendicular to the radius at the point where it touches the circle.

Line segment DB is  a  tangent as it passes through only one point.

Radius is the line segment joining the center of the circle and any point on the circumference of the circle. It is half of the diameter.

Line segment AC is  a radius as it joins the center of the circle with the circumference.

Answer:

1) FG -- Secant

2) DB -- Tangent

3) DH -- Secant

4) AC -- Radius

Step-by-step explanation:

(not a joke question) 81 1/4 is equal to 2. true or false and please explain why!

Answers

Answer:

Fasle

Step-by-step explanation:

81 1/4s would be 81/4 which would be 20 and 1/4

What is the volume of the sphere shown below?

O A. 69127 units
O B. 23047 units
O C. 1927 units
O D. 57677 units

Answers

Answer:

Step-by-step explanation:

r = 12

V = 4*pi * r^3 / 3

V = 4 * 3.14 * 12^3 /3

V = 4 * 3.14 * 1728 / 3

V = 4 * 5425.92 /3

V = 21703.68/3

V = 7234.56

None of the answers look correct.

Suppose the manager agrees to pay each employee a​ $50 bonus if they meet a certain goal. On a typical​ Saturday, the​ oil-change facility will perform 4545 oil changes between 10 A.M. and 12 P.M. Treating this as a random​ sample, at what mean​ oil-change time would there be a​ 10% chance of being at or​ below? This will be the goal established by the manager. There would be a​ 10% chance of being at or below nothing minutes. ​(Round to one decimal place as​ needed.)

Answers

Answer:

The answer is given below

Step-by-step explanation:

The mean (μ) = 21.2 minutes and the standard deviation σ = 3.5 minutes.

the​ oil-change facility will perform 45 oil changes between 10 A.M. and 12 P.M, therefore the sample size n = 45

there be a​ 10% chance of being at or​ below. From the normal distribution table, The z score corresponding to a probability of 10% (= 0.1)  is -1.28.

z = -1.28

To calculate the mean​ oil-change time, we use the formula:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }\\\\ Substituting \ values:\\-1.28=\frac{x-21.2}{\frac{3.5}{\sqrt{45} } }\\\\x-21.2=-0.6678\\\\x=-0/6678+21.2\\\\x=20.5[/tex]

Mariah is completing a language arts review sheet she estimates that it takes her one minute to complete each multiple-choice question and six minutes to complete each essay question this equation represents the total time it takes her to complete X multiple choice question and y essay question X plus 6Y equals 36 select the correct answer from each drop down menu

Answers

Answer:

The answer is below

Step-by-step explanation:

Given the time taken to answer each multiple choice question as one minute, the time taken to x multiple choice question = 1 minute/question × x questions = x minutes

Given the time taken to answer each essay question as six minute, the time taken to y essay question = 6 minute/question × y questions = 6y minutes

Therefore the total time taken to complete X multiple choice question and y essay questions = the time taken to x multiple choice question + the time taken to y essay question = x + 6y

Answer:  

directly off of edmentum                                                  

47:PLEASE HELP Find the y-intercept of -x +2y=20

Answers

Answer:

(0,10)

Step-by-step explanation:

-x + 2y = 20

2y = x +20

y = 1/2x + 10

This is slope-intercept form. The y-intercept is 10.

(0,10)

Answer:

(0, 10)

Step-by-step explanation:

Can be simplified to

2y = x+20 by adding x to both sides

then divide by 2 to get to slope intercept form: y = ax+b

b is the y-intercept

y = 1/2x + 10

so the answer is 10

Please answer this in two minutes

Answers

Answer:

Tan(x) = 1/[tex]\sqrt{3}[/tex]

We know that Tan 30 = 1/[tex]\sqrt{3}[/tex]

Therefore, x = 30 degrees

X would be 30 degrees, hope this helps

Classify the number -61.
1. Integer, rational, real
2. Rational, real
3. Whole, integer, rational, real
4. Natural, whole, integer, rational, real

Answers

Answer:

1. Integer, rational, and real

Step-by-step explanation:

Remember:

(This is how my teacher taught it; yours may have done it differently)

Real numbers are numbers that can be plotted on a number line.

Rational numbers can be represented as a fraction (if they can't be represented as such they are irrational).

Integers are natural numbers, the opposite of natural numbers, and zero.

Whole numbers are natural numbers and zero.

Natural numbers are numbers you can count with.

-61 fits under real numbers, rational numbers, and integers. Assuming you want to be as specific as possible, the answer will be 1. Integer, rational, and real.

Help is much appreciated. It is easy but, for me I am just confused.

Answers

What do you need help on ?
What is the question that you’re confused on or the thing?

Latisha worked for six hours and 45 minutes how should she write that on her time card

Answers

Answer:

Hey there!

6 hrs 45 mins =  405 mins, or 6.75 hours.

Hope this helps :)

The zeroes of the function are . of the zeroes have a multiplicity of 2.

Answers

Answer:

The three roots have a multiplicity of 2

Step-by-step explanation:

The zeros of the function refers to those points on the x-axis on which the curve passes through

These are the points -2,0 and 4

Now we want to determine which of these points has a multiplicity of 2?

The correct answer is that all have a multiplicity of 2 since 2 can be factored out

2(-1) , 2(0) and 2(2)

Answer:

the answer is A. none

13. Fill in this diagram so that each of the rows, columns and
diagonals adds to 18.
What is the sum of all the corner numbers?
(A) 20
(B) 22
(C) 23
(D) 24
(E) 25​

Answers

Answer:

D. 24

Step-by-step explanation:

Let's name the diagram

Row 1: a1, a2, a3

Row 2: b1, b2, b3

Row 3: c1, c2, c3

From the diagram,

b2 and c2 have been given

All rows, columns and diagonal must sum up to 18

If b2=6 and c2=4

a2=18-(6+4)

=18-10

=8

a2=8

Assume a1=4

Diagonals a1+b3+c3=18

4+6+c3=18

10+c3=18

c3=18-10

=8

Assume a3=6

Diagonals a3+b2+c1=18

6+6+c1=18

12+c1=18

c1=18-12

=6

So b1=18-(6+4)

=18-10

=8

b1=8

b3=18-(6+8)

=18-14

=4

b3=4

Input all the numbers into the boxes

We have,

4 8 6

8 6 4

6 4 8

Corner numbers are a1,a3,c1,c3

=4,6,6,8

Sum of all the corner numbers=4+6+6+8

=24

D. 24

Explain how to solve for the rate in a simple interest equation if you are given the interest amount, the principal, and the time.

Answers

Answer:

divide the interest amount by the product of the principal and time

Step-by-step explanation:

The simple interest formula is I = prt where I is the interest, p is the principal, r is the rate and t is the time (in years). Rewriting this formula so that r is the subject we get r = I / pt. Therefore the answer is divide the interest amount by the product of the principal and time.

write an equation to represent the cost of printing photos (C) in terms of the number photos printed (P)

(use picture for the information)

PLEASE answer asap! it will be appreciated.

Answers

Answer: C=0.20p

Step-by-step explanation:

As you could see if you print 10 photos you will have to pay 2 dollars which means if you print 1 photo you will have to pay 20 cents.

Solve the system of equations using substitution.
X = 2
4 = 2y - 6x

Answers

Answer:

-2y=-6(2)-4

-2y=-12-4

-2y/-2=-16/-2

y=8

In the figure, angle A measures 45° and angle E measures 15°.
The measurement of angle C is___
The measurement of angle D is___

Answers

Answer:

m<C = 45

m<D = 30

Step-by-step explanation:

m<A + m<B + m<C = 180

45 + 90 + m<C = 180

m<C = 45

m<E + m<A = 60

60 + 90 + m<D = 180

m<D = 30

PLS HELP ME IVE BEEN TRYING

Answers

Answer:

try and let me know is it correct or not line A-4 lineB-8

Step-by-step explanation:

i also use mathswatch

The figure is not trying to scale. PQ and MN are straight lines. Find X

Answers

Answer:
45°
Explanation:
AngleMR is 90° which means Angle MP and angle X have to be equivalent and all three angles add up to 180°, making angle X equal to 45°
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