A particle is moving along a projectile path at an initial height of 96 feet with an initial speed of 16 feet per second. This can be represented by the function H(t) = −16t2 + 16t + 96. What is the maximum height of the particle?

Answers

Answer 1

Answer:

The maximum height the projectile reaches is 100 feet

Step-by-step explanation:

Notice that the given equation representing the height of the projectile is a quadratic equation which negative leading coefficient (-16). Such type of equations would have a parabola that branches downwards as its graph.

therefore, what we need to find is the coordinates of the top vertex of that parabola. We can use for such the typical formula for the x-position of the vertex of a parabola with standard equation:

[tex]f(x)=ax^2+bx+c[/tex]

with x-position of the vertex given by:

[tex]x_v=\frac{-b}{2a}[/tex]

Then in our case  ([tex]H(t)=-16t^2+16t+96[/tex])  we have:

Horizontal position of the vertex given by:

[tex]t_{vertex}=\frac{-16}{2(-16)} =\frac{1}{2}[/tex]

and now we can find the maximum height plugging this value into the height expression:

[tex]H(t)=-16(\frac{1}{2}) ^2+16\,(\frac{1}{2})+96=-4+8+96=100\,\,ft[/tex]


Related Questions

Which expression has the greatest value?
(1 + 2)3
(15 - 1)0
(5-2) 2
(2 x 4)1

Answers

The first one because it has the greatest value of 9

Answer:

(1+2)3

Step-by-step explanation: it equals 9 the the other expressions  equal 8 0 and 6 so option one is the greatest value.

What is a regular Polygon? Name all the types of polygon.(HELP ASAP)

Answers

Answer:

A regular polygon is a polygon with sides of equal length. Some examples include, a equilateral triangle, square, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon, regular decagon...

so 90/7 divided by 1 and three-fourths i keep trying but i keep getting a different answer what would be the best estimate

Answers

Answer:

see below

Step-by-step explanation:

90/7  ÷ 1 3/4

Change to an improper fraction

90/7 ÷ (4*1+3)/4

90/7 ÷7/4

Copy dot flip

90/7 * 4/7

360 /49

The exact answer is 7 17/49

To estimate I would round 49 to 50 and 360 to 350

350/50 is approximately 7 and since I rounded the numerator down and the denominator up,  the answer would be a little higher

What is the length of BC in the right below?

Answers

Answer:

B. 17

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

We have a and b, so:

8² + 15² = c²

c = √(8² + 15²)

c = 17

And we have our final answer!

Answer:

To find the length of BC we use Pythagoras theorem.

BC² = AB² + AC²

AB = 8 AC = 15

BC² = 8² + 15²

BC = √64 + 225

BC = √ 289

BC = 17

BC is 17

Hope this helps.

quick plz....When √98- √128 is simplified it is equal to:

A,15√2

B, -√30

C. -√2

D. 10√3

Answers

It’s C thank me later

Answer:

[tex]-\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{98} -\sqrt{128}[/tex]

[tex]\sqrt{49 \times 2} -\sqrt{64 \times 2}[/tex]

[tex]\sqrt{49} \sqrt{2} -\sqrt{64} \sqrt{2}[/tex]

[tex]7\sqrt{2}-8\sqrt{2}[/tex]

[tex]=-\sqrt{2}[/tex]

3x2 + 2x - 5 and -4 + 7x2

Answers

Answer:

3×2+2x-5

6-5+2x

1+2x

-4+7×2

-4+14

10

Which statement is true for the numbers 2.5 and -2.5? A. On the horizontal number line, 2.5 and -2.5 are equal and are located on the same point. B. On the horizontal number line, -2.5 is located to the left of zero and 2.5 is located to the right of zero. C. On the horizontal number line, 2.5 and -2.5 are both located to the right of zero. D. On the horizontal number line, 2.5 is located to the left of zero and -2.5 is located to the right of zero.

Answers

Answer:B

Step-by-step explanation: because when u draw the number line all the negative numbers is written at the left side of the zero and all positive numbers are found at the right side of the zero

Answer: I believe it’s B

Step-by-step explanation:

A school allots £1500 to spend on a trip to the theatre. Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off A train ticket for the day will cost £15 each. If 2 teachers and the maximum number of students attend, how much money will the school have left over?

Answers

Answer:

Step-by-step explanation:

School allots £1500 to spend on a trip to the theatre.

Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off

therefore 4/5*35 = 28 for the tickets

:

A train ticket for the day will cost £15 each.

therefore total cost for each: 28 + 15 = 43 pounds each

:

If 2 teachers and the maximum number of students attend, how much money will the school have left over?

:

let s = no. of students

43(s+2) =< 1500

43s + 86 =< 1500

43s =< 1500 - 86

43s =< 1414

s =< 1414/43

s =< 32.88, 32 students max

:

find how much left over. plus 2 teachers = 34 people

1500 - 43(34) =

1500 - 1462 = 38 pounds left over

Simon makes 30 cakes He gives 1/5 of the cakes to sali He gives 10% of the cake to Jane What fraction of 30 does he have left

Answers

Answer:

7/10 or 0.7 or 70% left.

Step-by-step explanation:

Since he gives 1/5 of the cake to Sali, he gave 1/5 * 30 = 6 cakes away to Sali. Since 10% is 1/10, he gave away 1/10 * 30 = 3 cakes away to Jane. He has a total of 30 - 3 - 6 = 21 cakes left. 21/30 = 7/10, or 0.7, or 70% left.

Answer: 21/30

Explanation this is because 1/5of 30 is 6 and 10 percent of 30 is 3

6+3=9

30-9=21

Therefore Simon has 21/30 cakes left

I hope it helps

Evaluate the following expression

Answers

Answer:

Hope this is correct

Step-by-step explanation:

HAVE A GOOD DAY!

Sound waves are emitted from a fishing boat. Some of the sound waves are reflected by fish and detected back at the boat.The shortest time between the sound waves being emitted and detected is 0.26 s. The speed of sound in water is 1500 m/s.A) Calculate the distance between the boat and the nearest fish.

Answers

Answer:

195 m.

Step-by-step explanation:

The time for the  sound waves to reach the fish is 0.26/2 = 0.13 seconds.

Distance = speed * time

= 1500 * 0.13

= 195 m.

find the sum 12x^2+3x+6

Answers

Answer:

[tex]3(8x ^{2} + x + 2)[/tex]

factor out 3 polynomial 8xsqurd +x+2 not factored as it doesn't have any rational roots

Answer:

This cannot be simplified any further.

Step-by-step explanation:

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by , where is the number of hours since 10 AM, .

Answers

Complete Question:

Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour is given by [tex]x(t) = -4t^2 + 20t + 60[/tex], where is the number of hours since 10 AM:

a) Find an expression for the revenue per hour as a function of x, R(x)

b) Find and simplify, R(x(t))

Answer:

a) R(x) = 2x

b) [tex]R(x(t)) = -8t^2 + 40t + 120[/tex]

Step-by-step explanation:

a) This is a very trivial exercise.

[tex]x(t) = -4t^2 + 20t + 60[/tex]

The number of hot dogs sold per hour is given by x

Charge per hot dog = $2

An expression of revenue per hour,R, as a function of the number of hot dogs sold per hour, x, is therefore: R(x) = 2x

b) [tex]x(t) = -4t^2 + 20t + 60[/tex]

R(x(t)) = 2(x(t))

[tex]R(x(t)) = 2(-4t^2 + 20t + 60)\\R(x(t)) = -8t^2 + 40t + 120[/tex]



11. The formula for finding a number that's the square root of the sum of another number n and 6 is



A. x = √n + 6.

B. x = √n + 6.

C. x = √n + √6.

D. x = √n6.

Answers

Answer:

x = [tex]\sqrt{x+6}[/tex]

Step-by-step explanation:

The question states that it is the square root of the sum of both n and 6. That means n and 6 are added first before square rooted. Between B and C, choose the answer that has the parenthesis around x and 6, like (x + 6).

Josie is a travel agent who loves to analyze data about the vacation destinations she books for her clients. She believes that the
more she knows about a destination, the better she can educate and prepare her clients to get the most enjoyment out of
their trips. She's recently been investigating the climate of Paradise Island, where one of her biggest clients, Jack, is planning to
visit. Her research of the temperature history of Paradise Island is vital to Jack's travel plans, as he has an ideal temperature
that he prefers for vacationing. In this task, you'll use technology and regression techniques to help Josie plan Jack's ideal
vacation to Paradise Island.
Part A
Josie has collected data that shows the average daily high temperature for several months over the last year. In her table
of data, month 1 can be interpreted as January, month 2 as February, and so on.
Month, x
Average Daily High Temperature, y
(°F)
50
56
1
2
3
67
5
84
6
89
7
98
92
84
9
10
12
58
button to insert a screenshot of your scatter plot in the

Answers

Answer:

The scatter plot for the data is attached below.

Step-by-step explanation:

The data collected by Joise for the average daily high temperature for several months over the last year is as follows:

Month              X      Average Daily High Temperature, Y (°F)

January            1                                   50

February          2                                  56

March               3                                  67

May                  5                                  84

June                 6                                  89

July                   7                                  98

September       9                                  92

October           10                                  84

December       12                                  58

The scatter plot for the data is attached below.

How long is 139.5 minutes

Answers

Answer:

[tex]\mathrm{2.325 \: hours}[/tex]

Step-by-step explanation:

[tex]\frac{139.5}{60}=2.325[/tex]

[tex]\mathrm{2 \: hours\: 19.5 \: minutes}[/tex]

(25 POINTS) Write the inequality of the following graph?

Answers

Answer:

f(x) > -x + 2

Step-by-step explanation:

First I found the equation of the line.

The y intercept is at 2 so I know to add 2 at the end

The slope is -1 since it is going downwards

Since the top side is shaded, that represents greater than, if it was shaded downwards, it would be less than

Putting all that together, the equation is f(x) > -x + 2

Which equation is an example of the commutative property of multiplication?
O (4 + 21) = (21 + 4)
O (4 + 21)(3-51) = (3-51)(4 + 21)
(4 + 21(3-51) = (4 + 21)(3-51(1)
(4 + 21) = (4 + 21 + 0)

Answers

Answer:

the answer is (4 + 21)(3-51) = (3-51)(4+ 21)

The equation is an example of the commutative property of multiplication is 4 + 21)(3-51) = (3-51)(4 + 21).

What is Commutative Property?

The commutative property is a mathematical statement that states that the order in which numbers are multiplied has no effect on the product.

According to the commutative property of multiplication, if we multiply two integers, the result will remain the same even if the positions of the integers are swapped.

Let A and B be the two integers, then;

A × B = B × A

As, we know commutative Property supports multiplication and Addition.

First,  (4 + 21) = (21 + 4)

This is Commutative Property of Addition.

Second,  (4 + 21)(3-51) = (3-51)(4 + 21)

This is Commutative Property of Multiplication

Third, (4 + 21(3-51) = (4 + 21)(3-51(1)

No property can be applied.

Fourth, (4 + 21) = (4 + 21 + 0)

This is expansion.

Learn more about Commutative Property here:

https://brainly.com/question/778086

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The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog Three-fifths milligram of the medicine, which equation relates the weight, w, and the dosage, d? d = StartFraction 1 Over 50 EndFraction w d = three-fifths w d = 18 w d = 50 w

Answers

Answer:

Step-by-step explanation:

A direct variation equation is of the form

y = kx,

where, in words, it reads "y varies directly with x" or "y varies directly as x". In order to use this as a model, we have to have enough information to solve for k, the constant of variation. The constant of variation is kind of like the slope in a straight line. It rises or falls at a steady level; it is the rate of change.

We have that a vet gives a dose of three-fifths mg to a 30 pound dog. If the dose varies directly with the weight of the dog, then our equation is

d = kw and we need to find k in order to have the model for dosing the animals.

[tex]\frac{3}{5} =k(30)[/tex]

Divide both sides by 1/30 to get k alone.

[tex](\frac{1}{30})(\frac{3}{5})=k[/tex] and

[tex]k=\frac{1}{50}[/tex]

Our model then is

[tex]d=\frac{1}{50}w[/tex]

This means that for every pound of weight, the dog will get one-fiftieth of a mg of medicine.

Answer:

A

Step-by-step explanation:

Find 310% of 150. a number blank

Answers

Answer:

465

Step-by-step explanation:

Of means multiply

310% * 150

Change to decimal form

3.10 * 150

465

Answer:

465

Step-by-step explanation:

1 percent of 150 is 1.5.

Multiply 1.5 by 310 to 465

Alhondro wants to determine the average shoe size of all of male students in his school

Answers

We need the rest of the question

the radius of wheel of a bicycle is 40 cm. taking pie =3.14, a)find tthe circumference of the wheel.b) find the distance covered by the bicycle in 200 complete revolution of the wheel.please ans this question. i beg you

Answers

Answer:

a)=251.2 cm    b)=50240 cm

Step-by-step explanation:

a) The formula for calculating the circumference of a circle is c=d*pie, where D is the diameter of the circle.

Therefore, C = 2 * 40 * 3.14 = 251.2 cm

b) The distance covered by 200 revolutions of the wheel is 200 times the circumference, 200*251.2=50240 cm.So to think about this we can assume that there is a point A on the wheel, the distance that point A travels when it rotates 200 times.

Which of the graphs below would result if you made the leading term of the following function negative? f(x)=2x^4+2x+2

Answers

If we change the sign of the leading coefficient of the polynomial, the graph of the new polynomial will open downwards. The graphs can be seen at the end.

Which graph do we get when the leading coefficient is negative?

Here we start with the polynomial:

[tex]f(x) = 2x^4 + 2x + 2[/tex]

The leading coefficient is one that multiplies the term with the largest exponent. In this case, is 2.

Changing its sign will cause the polynomial's arms now will open downwards (instead of upwards, as in the original polynomial).

The graphs of both functions can be seen below. The green is the original one, and the blue is the changed one.

If you want to learn more about polynomials:

https://brainly.com/question/4142886

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Abcd is a rectangle.​

Answers

It’s within reach. .. ..

please answer very quickly

Answers

Answer:

ABD

Step-by-step explanation:

Need help people pls

Answers

Answer : 0.75
Cause it is

Mr. Mole left his burrow and started digging his way down.
A represents Mr. Mole's altitude relative to the ground (in meters) after t minutes.
A= -2.3t – 7
How fast did Mr. Mole descend?

Answers

Answer:

He's descending at a pace of 2.3 meters per minute.

Step-by-step explanation:

This is because the equation shows us the slope or the speed he's going at.

A= -2.3t - 7

A= Altitude

-2.3 = Slope

- 7 is his starting altitude in meters

But every minute, t, he is going down 2.3 meters. It's easier to think about if you consider, A = y, and, t = x. Now you have the equation, y = -2.3x - 7.

And you graph it to see the progression in slope.

Can somebody help me with this ?? :)

Answers

Answer:

A.

Step-by-step explanation:

We have AC = DF, ∠A =∠D, so

we need AB = DE.

We get SAS congruence.

For the following geometric sequence find the explicit formula: {-1, 3, -9,...}

Answers

multiplies by -3 every time

Answer:

[tex]a_{n}[/tex] = - 1 [tex](-3)^{n-1}[/tex]

Step-by-step explanation:

The explicit formula for a geometric sequence is

[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = - 1 and r = 3 ÷ - 1 = - 3 , thus explicit formula is

[tex]a_{n}[/tex] = - 1 [tex](-3)^{n-1}[/tex]

Which linear inequality is graphed with y > –x – 2 to create the given solution set? y > x + 1 y x – 1 y < x + 1

Answers

Answer:

D

Step-by-step explanation:

I took the test, dont listen to the person above me:)

Answer:

y<x+1

Step-by-step explanation:

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