Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.

Answers

Answer 1
The function would be h(t)=-16t²+v₀t+0, where v₀ is the initial velocity of the firework.

0 is the initial height, since you cannot hold one in your hand and safely set it off.

This will have a maximum; the firework will reach a highest point and fall back down.  This is also evident from the equation; the negative in front of t² flips the parabola upside down, which gives it a maximum.

Related Questions

Compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?

Answers

Answer:

a statement that your prediction was less than or greater than the actual count

a statement about how you would change your estimation process

Step-by-step explanation:

Choose any of these two.. There both correct btw

The statements that is true about your prediction of the total pennies on rows 1-4 are statement (b) and (d).

A predictive function is one of mathematical function that helps us to know about future events based on past events. There are many types of functions that can be classified as predictive functions.

The prediction was off by greater than 1,000,000 of the actual total. After seeing the result for rows 1-4, you would indeed change your prediction for the total because it indicates a significant deviation.

Complete question

Check every statement that is true about your prediction of the total pennies on rows 1-4.

a) Your prediction was off by less than or equal to 1,000,000 of the actual total.

b) Your prediction was off by greater than 1,000,000 of the actual total.

c) After seeing the result for rows 1-4, you would change your prediction for the total.

d After seeing the results for rows 1-4, you would not change your prediction for the total.

A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?

Answers

For the answer to the question above,The tangent line from the horizon to the radius of the earth is perpendicular between the tangent point and the center. So, therefore, we can use Pythagorean's theorem to write an equation:

x² + r² = (r+h)²
x² + 3959² = (3959 + 3.7)²
x² = 3962.7² - 3959²
x = 171.2 miles
I hope this helps

A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?

Answers

To solve this you can multiply the white paint by [tex] \frac{2}{7} [/tex] to find the amount of red paint to add which is 32/7 oz or roughly 4.5 oz

Answer:

4.5 oz

Step-by-step explanation:

Find the sum of the series

Answers

The sum of the function will be as follows:
(3*2+1)+(3*3+1)+(3*4+1)
=(6+1)+(9+1)+(12+1)
=7+10+13
=30
Thus the sum of the series is:
30

True or False: A rectangular equation that is not a function may be a function in the polar coordinate system

Answers

I think it should be true but if im wrong sorry its my best educated guess

The given statement is true.

The given statement is a rectangular equation that is not a function that may be a function in the polar coordinate system.

What is a rectangular equation?

A rectangular equation or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane.

Polar equations indeed can describe graphs as functions, even when the equations in the rectangular coordinate system are not one of the functions. Polar equations can be graphed accurately using hands by using the Polar Coordinate System.

Therefore, the given statement is true.

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Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)

Answers

The volume of the ball is given by:
 V = (4/3) πr ^ 3
 Deriving we have:
 V '= (3) (4/3) (π) (r ^ 2) (r')
 Clearing r 'we have:
 r '= V' / ((3) (4/3) (π) (r ^ 2))
 Substituting values:
 r '= 4 / ((3) (4/3) (π) ((24) ^ 2))
 r '= 0.000552621 c / min
 Then, the surface area is:
 A = 4πr2
 Deriving we have:
 A '= 8πrr'
 Substituting values:
 A '= 8π (24) (0.000552621)
 A '= 0.33 cm ^ 2 / min
 Answer:
 
The surface area of the balloon is shrinking at:
 
A '= 0.33 cm ^ 2 / min

What is the perimeter of rectangle that is 92 feet long and 46 feet wide?

Answers

Final answer:

The perimeter of a rectangle that is 92 feet long and 46 feet wide is calculated using the formula P = 2l + 2w, resulting in a perimeter of 276 feet.

Explanation:

The question asks for the perimeter of a rectangle with specific dimensions. To calculate the perimeter of a rectangle, we use the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. Given that the rectangle is 92 feet long and 46 feet wide, we substitute these values into the formula to get the perimeter: P = 2(92) + 2(46) = 184 + 92 = 276 feet.

Therefore, the perimeter of the rectangle is 276 feet.

Factor the trinomial below.

9x2 + 6x + 1

A. (9x + 1)(x – 1)
B. (9x + 1)(x + 1)
C. (3x + 1)(3x + 1)
D. (3x + 1)(3x – 1)

Answers

Option C is your answer. 

9x² + 6x + 1
9x² + 3x + 3x + 1
3x(3x + 1) + 1(3x + 1)

(3x + 1)(3x + 1)

In the diagram, the radius of the outer circle is 5cm and the area of the shaded region is 16π cm^2. What is the radius or the inner circle?

Answers

you divided your diameter by 2

By using the area of the ring we will see that the radius of the inner circle is 3cm.

What is the radius of the inner circle?

I assume that we have some kind of ring. To get the area of the ring, we need to take the area of the circle defined by the outer radius of the ring, and subtract the area defined by the circle with the inner radius of the ring.

Remember that the area of a circle of radius R is:

A = pi*R^2

We know that:

The radius of the outer circle is 5cm, so its area is:

A = pi*(5cm)^2 = pi*25cm^2

And the area of the ring is pi*16 cm^2

Then the area of the inner circle should be such that:

pi*25cm^2 - A' = pi*16cm^2

Then, solving for A'

A' = pi*25cm^2 - pi*16cm^2 = pi*9cm^2 = pi*(3cm)^2

So the radius of the inner circle is 3cm.

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When darcy's school bus travels at 30 miles per hour, it gets from her home to school in 12 minutes. what is the speed of darcy's bus if it makes the same trip in 18 minutes?

Answers

we know that
speed=distance/time------> distance=speed*time

step 1
find the distance with
speed=30 miles/hour-----> 30 miles/60 minutes-----> 0.5 miles/minute
time=12 minutes
distance=speed*time------> distance=0.5/12----> distance=6 miles

the distance from home to school is 6 miles

step 2
find the speed with
distance=6 miles
time=18 minutes
speed=6/18----> 0.33 miles/minute-----> *60----> 20 miles/hour

the answer is
20 miles/hour  or 0.33 miles/minutes

The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.

Answers

Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
 x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
 Therefore, the coefficients of the expansion are given by:
 1, 6, 15, 20, 15, 6, 1
 Answer:
 
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1

Answer:

1, 6, 15, 20, 15, 6, 1

Step-by-step explanation:

A right triangle has sides if length 4,12 and 13 what is its perimeter

Answers

Answer:

  29

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  4 + 12 + 13 = 29

The perimeter of the triangle is 29. (It is not a right triangle.)

___

A right triangle with side lengths 12 and 13 will have a short side of 5. Its perimeter is 30.

The shortest side of a right triangle measures 88 m. the lengths of the other two sides are consecutive odd integersodd integers. find the lengths of the other two sides.

Answers

x - one side
x+2 - the side, that has value of consecutive odd integer of x
x+2  is the longest side, so it is a hypotenuse
(x+2)² = x²+88²
x²+4x+4 = x² + 7744
4x=7740
x= 1935 
x+2=1935+2=1937

Check
1937²=1935²+88²
3751969=3751969


-9 > -2 -3/4v solve.

Answers

[tex]-9 > -2-\dfrac{3}{4}v\ \ \ |+2\\\\-7 > -\dfrac{3}{4}v\ \ \ |change\ both\ sides\\\\\dfrac{3}{4}v > 7\ \ \ \ |\cdot\dfrac{4}{3}\\\\v > \dfrac{28}{3}\to v\in\left(9\frac{1}{3};\ \infty\right)[/tex]

Geo: Topic 3- Parallelograms 1pt A rhombus is a parallelogram with all four sides of equal length. One way to determine if a given parallelogram is a rhombus is to test whether its diagonals are perpendicular. The vertices of a parallelogram are M(−1,2), N(9,2), P(3,−6), and Q(−7,−6). Determine whether the parallelogram is a rhombus by checking to see if the diagonals are perpendicular. What is the slope of MP¯¯¯¯¯¯? What is the slope of NQ¯¯¯¯¯¯? Are diagonals MP¯¯¯¯¯¯ and NQ¯¯¯¯¯¯ perpendicular? Is the parallelogram a rhombus?

Answers

it would be 5,1 over 2

The population of a city has increased by 26 % since it was last measured. If the current population is 44,100 , what was the previous population?

Answers

The previous population of the city was 35000.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Assume the previous population to be [x].

Then, we can write -

x + 26% of x = 44100

x + 26x/100 = 44100

x + 13x/50 = 44100

(50x + 13x)/50 = 44100

63x = 44100 x 50

63x = 2205000

x = 35000

Therefore, the previous population of the city was 35000.

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Final answer:

The previous population of the city was 35,000 before experiencing a 26% increase to the current population of 44,100.

Explanation:

To calculate the previous population of a city that has experienced a 26% increase to its current population of 44,100, we need to reverse the percentage increase. The formula for this is:

Previous population = Current population / (1 + Percentage increase)

In this case, the percentage increase is 26%, or 0.26 in decimal form. The calculation is:

Previous population = 44,100 / (1 + 0.26) = 44,100 / 1.26

This gives us:

Previous population = 35,000 (rounded to the nearest whole number)

Hence, the previous population of the city was approximately 35,000 before the 26% increase to the current 44,100.

Write the quadratic function in vertex form: f(x) = 4x2 + 2x -5

A)f(x) = 4(x + 14)2 - 214B)f(x) = 4(x + 116)2 - 214C)f(x) = 4(x + 14)2 - 194D)f(x) = 4(x + 116)2 - 194


Answers

Please use " ^ " to denote exponentiation:  f(x) = 4x^2 + 2x -5.  To find the vertex form of this equation, complete the square:

f(x) = 4x^2 + 2x                                           - 5
      = 4(x^2 + (2/4)x)                                         - 5
      =  4(x^2 + (1/2)x )                                  -5
      = 4(x^2 + (1/2)x + 1/16  ) - 4/16 - 5
      = 4(x+1/4) - 21/4    <= in vertex form

Here h= -1/4 and k = -21/4.  The vertex is at (-1/4, -21/4)

Answer:its B

Step-by-step explanation:

f(x) = -4 (x + 1/4)² - 15/4

In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.

If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?
-1/8
-1/2
-2/3
-3/4



Answers

1/8 because if I choose a black one first then put it back there isn't a 50% chance

Choose the best answer.

The most expensive type of life insurance is:

term insurance
whole-life insurance
endowment life insurance
limited-payment life insurance

Answers

The most expensive is life insurance because it covers your whole life

Answer:

Endowment life insurance

Step-by-step explanation:

got it right on odyssey

A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?

Answers

There are 10 deciliters in 1 liter (deci means 10).

Divide 5.25 by 10 to find how many liters are needed.

5.25/10 = 0.525

0.525 liters of milk are needed for the cake.

Help please !!!!!!!!!!!

Answers

I think the answer is D.
the answer would be the second or third one as you need to add on the minus seven, i think the third is correct but i’m not 100% sure on what the addition property of equality is or what the commutative property of addition

Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. How much will Vivian pay for her surgery if it costs $9600?
2320
2420
2820
after doing the math and writing it out. it has to be one of these three answers but i do beleive that its the second answer but i need reassurance

Answers

We have been given that Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. We have been given that her surgery costs $9600 and we need to find how much will Vivian have to pay for her surgery.

Since we know that the insurance company will pay any amount after Vivian has paid $500. Therefore, the remaining amount after Vivian pays $500 as deductibles will be $9600 - $500 = $9100.

Now we know that Vivian's insurance company will pay 80% of this amount, therefore, Vivian will have to pay the 20% of $9100 in addition to the $500 she already paid.

20% of $9100 is [tex]9100\cdot \frac{20}{100} = \$1820[/tex]

Therefore, the total amount that Vivian pays for surgery is $500 + $1820 = $2320.

Therefore, the first choice given is the right answer.

which of the following parametric equations are equivalent to the polar equation r=3 cos theta

Answers

To solve the problem you must know that to change from Cartesian to polar coordinates you must write:
 x = rcos (θ)
 Where "r" is the radius
 Likewise y = rsin (θ)
 Therefore, in the expression r = 3cos (θ) one can write r as:
 r = x / cos (θ)
 So:
 x / cos (θ) = 3cos (θ)
 x = 3cos ^ 2 (θ)
 The same for y ...
 y = rsin (θ)
 y = 3cos (θ) sin (θ).

  Finally the correct answer is option 2.
 x = 3cos ^ 2 (θ) y = 3cos (θ) sin (θ).

Answer:

B

Step-by-step explanation:

exactly 2/5 of the unversity students live off campus. Of those students, 3/10 of them live at home. what fraction of the univesity's students live at home? Reduce your answer to lowest terms

Answers

To find the answer, we multiply these two fractions
2/5 * 3/10
6/50
3/25 of the students live at home

YO!!!!!!WILL GIVE 100 POINTS!!!!!!!!!!!BRAIN!!!!!!!!!!!!

Answers

For this case we have the following function:
 f (x) = ((x + 2) ^ 2) * (x-4) * (x + 1) ^ 3
 The roots are given by:
 ((x + 2) ^ 2) * (x-4) * (x + 1) ^ 3 = 0
 x + 2 = 0
 x = -2 (multiplicity 2)
 x-4 = 0
 x = 4 (multiplicity 1)
 x + 1 = 0
 x = -1 (multiplicity 3)
 Answer:
 
option A

Answer:

Following function:

 f (x) = {(x + 2)²} × (x-4) × (x + 1)³

 The roots are given by:

 {(x + 2)²} × (x-4) × (x + 1)³ = 0

 x + 2 = 0

 x = -2

 x-4 = 0

 x = 4

 x + 1 = 0

 x = -1

 Answer:

 option A

Step-by-step explanation:

solve the equation 4(-x+4)=12

Answers

4(-x+4)=12     distribute 4 to the parentheses
-4x-16=12       add 16 to both sides
-4x=28            divide by -4
x=-7

The answer is x=-7

Rewrite with only sin x and cos x.
sin 2x - cos 2x

Select one:
a. 2 sin2x - 2 sin x cos x + 1
b. 2 sin x
c. 2 sin2x + 2 sin x cos x - 1

Answers

I may be wrong but I think it is C.

Find the average value have of the function h on the given interval. h(u) = (15 − 10u)−1, [−1, 1]

Answers

-20 is the correct answer

The average value have of the function h(u) = (15 − 10u)−1 on the given interval  [−1, 1] is -5.

What is average value of the function?

The average value of a function is given by the formula:

[tex]fav = \frac{1}{b - a} \int\limits^b_a f({x}) \, dx[/tex]

Now the given function is,

h(u) = (15 − 10u) − 1

or, h(u) = 15 − 10u − 1

or, h(u) = 14 − 10u

So, the average value on the given interval [−1, 1] is given as:

[tex]fav = \frac{1}{1 - (-1)} \int\limits^1_{-1} h({u}) \, du[/tex]

Thus, putting the value of h(u) we get,

[tex]fav = \frac{1}{(1 + 1)} \int\limits^1_{-1} (14 - 10u) \, du[/tex]

Thus integrating we get,

fav = (1/2) { [14u] - [10u²/2]

⇒ fav = (1/2) { [14u] - [5u²]

Applying the limits we get, -1 to 1,

⇒ fav = (1/2) { 14[-1 + 1] - [5{-1² + 1²}]

Solving we get,

⇒ fav = (1/2) { 14[0] - [5{1 + 1}]

⇒ fav = (1/2) {- [5{2}]

⇒ fav = -5

Thus, the average value have of the function h(u) = (15 − 10u)−1 on the given interval  [−1, 1] is -5.

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Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

A) 17 miles

B) 32 miles

C) 37 miles

D) 40 miles

Answers

Answer:

D) 40 miles

Step-by-step explanation:

First we must find the distance between the mall and the house.  The figure formed is a right triangle.  The length of the side from the mall to the house forms the hypotenuse of the triangle.  We can use the Pythagorean theorem to find the length:

a² + b² = c²

The two legs of the triangle, a and b, are 15 and 8:

15² + 8² = c²

225 + 64 = c²

289 = c²

Take the square root of each side:

√289 = √(c²)

17 = c

This makes the total distance

15+8+17= 40 miles

Hey! Pretty easy once you get the hang of these problems.

So you start off with the Pythagorean Theorem. Which is : a^2 + b^2 = c^2

Then just fill it in :

15^2 + 8^2 = c^2

225 + 64 = c2

289 = c^2

17 = c

And last :

15 + 8 + 17 = 40 MILES

hoped this helped!! :))

The rectangular prism shown has a volume of 140 m3. This prism is enlarged using a scale factor of 2. What is the volume of the enlarged prism?

Answers

1120m3 is correct hope this helps :)
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