A rock is thrown upward from the top of a high cliff overlooking the ocean at a speed of 96 feet per second . The rock's height above ocean can be modeled by the equation H(t) = - 16t ^ 2 + 96t + 112 . How long will it take seconds for the rock to hit the ocean? Do not include units in your answer.

Answers

Answer 1

Answer:

7

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

The height of the rock after t seconds is given by the following equation:

[tex]H(t) = -16t^2 + 96t + 112[/tex]

How long will it take in seconds for the rock to hit the ocean?

This is t for which:

[tex]H(t) = 0[/tex]

So

[tex]-16t^2 + 96t + 112 = 0[/tex]

Simplifying by -16

[tex]t^2 - 6t - 7 = 0[/tex]

So a quadratic equation with [tex]a = 1, b = -6, c = -7[/tex]

[tex]\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64[/tex]

[tex]t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7[/tex]

[tex]t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1[/tex]

Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.


Related Questions

22. According to ghost hunters, large cities have, on average, 9 haunted houses each. As far as we know, it is unpredictable which houses will be haunted; and just because one house is haunted, that does not mean any of its neighbors will or will not be haunted. a) What is the standard deviation of the number of haunted houses in a large city

Answers

Answer:

The standard deviation of the number of haunted houses in a large city is 3.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval, which is the same as the variance.

According to ghost hunters, large cities have, on average, 9 haunted houses each.

This means that [tex]\mu = 9[/tex]

a) What is the standard deviation of the number of haunted houses in a large city?

Square root of the variance, so:

[tex]\sqrt{9} = 3[/tex]

The standard deviation of the number of haunted houses in a large city is 3.

find the measure of the angle pic added

Answers

the answer is 165° :))
165 degreeeeeeeeeeeee

A pet store sold 12 siamese cats. If the ratio of siamese cats to house cats sold was 2 : 1, what is the combined amount of cats sold?

Answers

Answer:

32 cats in total

Step-by-step explanation:

so 18 siamese

the ratio was9:7=siameese:house

18=9 units

divide 9

2=1 unit

house=7 units

7 times 2=14

14 house cats

combined=siameese+house=18+14=32

so 18 siamese
the ratio was9:7=siameese:house
18=9 units
divide 9
2=1 unit
house=7 units
7 times 2=14
14 house cats

combined=siameese+house=18+14=32

for brainliest!!!! please help :)

Answers

Answer:

area = 572.3 m²

Step-by-step explanation:

area = PiR²

r = 27/2

area = (3.14)(13.5²)

area = 572.3 m²

SOMEONE ANSWER MY FREAKING QUESTIONS!!!!!!



please

Answers

Answer: i dont know trie asking linder0917

Step-by-step explanation:

ok

Write 2 9/10 as an improper fraction.

pls hurry!
and pls explain how to do it

Answers

Answer:

29/10

Step-by-step explanation:

Answer:

[tex] \frac{29}{10} [/tex]

Step-by-step explanation:

[tex]2 \frac{9}{10} \\ \frac{2 \times 10 + 9}{10} [/tex]

A stamp collector has 55 stamps from the United States, 30 stamps from Canada, and 15 from Mexico. If he were to close his eyes and randomly select 20 from his collection, about how many would you expect to be from Mexico?

Answers

6% chance I think but I’m not sure

Which of the following is true for a circle that has an area of approximately 113 square feet?

a
The diameter is 6 feet and the circumference is 38 square feet.
b
The radius is 6 feet and the circumference is 38 square feet.
c
The diameter is 6 feet and the circumference is 38 feet.
d
The radius is 6 feet and the circumference is 38 feet.

Answers

Answer:

radius is 6, diameter is 12, circumference is 38

Step-by-step explanation:

The area of a circle hs the following formula:

A = π*r², where r is the circle radius (distance from center to edge of circle)

So, we have A = 113 = π*r²

Divide both sides by π:      113/π = r²

Approximately:                 35.97 = r²

Square-root both sides:   5.997 = r

                                           So, the radius is about 6 feet

The circumference of a circle has the following formula:

C = π * D, where D is the diameter of the circle (distance from one side of circle to opposite side, through the center)

But the length of a diameter is just that of two radiuses. (This is obvious when the 2 radii are collinear.)

Since r = 6 feet, D = 12 feet, and the circumference C = 12 * π = 37.699, about 38 feet.

*** So the radius is about 6 feet, the diameter is about 12 feet, and the circumference is about 38 feet,

It lloks like b and d are identical. Typo. maybe?

Please help please thank

Answers

Answer:

3/4 of an hour

Step-by-step explanation:

the longest is 1 hour. the shortest is 1/4 of an hour. 1 minus 1/4 is 3/4

f(x)=2x + 2
g(x)= x – 5
Find f(x) + g(x)

I need help understanding how to do a problem like this
Thank you

Answers

Answer:

3x - 3

Step-by-step explanation:

f(x) + g(x)

(2x + 2) + (x - 5)

3x - 3

What is the distance between - 10
and 2 on the number line?
12 units
-8 units
5 units
8 units

Answers

Answer:

12 units

Step-by-step explanation:

Draw a number line and mark x = -10 and x = 2.  You can readily see that the distance from -10 to the origin is 10 units, and from the origin to 2 is 2 units, in both cases measured from left to right.  Adding these two positive quantities together, we get 10 + 2, or 12.

The distance from -10 to 2 on the number line is 12 units.

Is the association between x and y positive or negative?
A. none B.positive C, negative

Answers

Answer:

A.non at all so, please choose the right answer

Answer:

A.non at all so, please choose the right answer

Jerry buys a new cell phone and signs up for a yearly cell phone plan. The cell phone costs $329 and the yearly plan costs 490 per year for every year he uses the cell phone. The only costs associated with the cell phone are the purchase price and the cost of the yearly cell phone plan.

a) Describe the annual cost of the cell phone per year as a function of the number of years he uses the cell phone.

b) What happens to the average price per year the longer Jerry holds onto this plan and explain why?

Answers

Answer:

(329 + 490X) / X = Cost

Thus, the average annual price decreases as the cell phone is used for more years, because the fixed cost (the cost of the value of the cell phone) is divided each time by a greater number of years.

Step-by-step explanation:

Since Jerry bought a new cell phone and signed up for a yearly cell phone plan, and the cell phone costed $ 329 and the yearly plan costs $ 490 per year for every year he uses the cell phone, to determine the annual cost of the cell phone per year as a function of the number of years he uses the cell phone, the following mathematical reasoning must be performed:

(329 + 490X) / X = Cost

So, for example, if the cell phone was used for 3 years, the function would apply as follows:

(329 + 490x3) / 3 = X

(329 + 1470) / 3 = X

1,799 / 3 = X

599.66 = X

Thus, the average annual price decreases as the cell phone is used for more years, because the fixed cost (the cost of the value of the cell phone) is divided each time by a greater number of years.

Can somebody help please #asap help w number 8

Answers

Answer:

y=4x bc each one is 4 so for one box it cost $4

Answer:

The expression will be y = 4x.

Step-by-step explanation:

First, we have to form expressions for number of boxes and total amount she earn :

Let x be the number of boxes,

Let y be the total amount,

Given that the costs of each box is $4 so in order to find the total amount, you have to multiply the number of boxes by 4 :

y = 4x

Help me please......

Answers

Answer:  46

Step-by-step explanation:

Let the 3 consecutive even numbers be x, (x-2) and (x+2) respectively.

According to the question,

x + (x - 2) + (x + 2) = 132

or, x + x - 2 + x + 2 = 132

or, 3x = 132

or, x = 132 ÷ 3

or, x = 44

So, first even number = 44

Required third number = 44 + 2

= 46

23rd term of -11,-7,-3 in arithmetic sequence

Answers

Answer:

The 23rd term for the sequence is -99

Step-by-step explanation:

We can use an explicit rule to find the 23rd term.

Given Info:

=> Sequence: -11,-7,-3

=> f(1) = -11

=> Common difference (d) = -4

Explicit rule: f(1) + d(n-1)

So,

-11 -4 (n-1)

Substitute 23 for n

=> -11 - 4(23-1)

=> -11 - 4(22)

=> -11 - 88

=> -99

hope this helps and is right :)

p.s. i really need brainliest

que expresision algebraica es P (x)=3x - 5x +6?

Answers

33 is the answer bye

Solve for x.
X -8 = -11
PLZ HELP I NEED ANSWER ASAP

Answers

Answer:

x= -3

Step-by-step explanation:

Solve the solution of this inequality
9−4d≥−3

Answers

Answer: d

3

Step-by-step explanation: that’s the answer buddy

Answer: X is less than or equal to 3.

I am 100% sure it's right.

Step-by-step explanation:

What is the answer for this?

Answers

Answer:

Proved

Step-by-step explanation:

Given

[tex](2 * 10^2) * (3 * 10^5) = 3.5 * 10^7 + 2.5 * 10^7[/tex]

Required

Prove

On the right hand side, we have:

[tex]2 * 10^2 * 3 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]

Rewrite:

[tex]2 * 3* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]

[tex]6* 10^2 * 10^5 = 3.5 * 10^7 + 2.5 * 10^7[/tex]

Apply law of indices

[tex]6* 10^{2+5} = 3.5 * 10^7 + 2.5 * 10^7[/tex]

[tex]6* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]

Express 6 as 3.5 + 2.5

[tex](3.5 + 2.5)* 10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]

Open bracket

[tex]3.5 *10^7+ 2.5*10^7 = 3.5 * 10^7 + 2.5 * 10^7[/tex]

Proved

Using the provided measures determine the measure of angle K.

A)30.5°
B)34.90
C)41.2°
D)58.0°

Answers

Answer:

B. 34.90°

Step-by-step explanation:

✔️First, find GF using Trigonometric function:

Reference angle = 58°

Adjacent length = GF

Hypotenuse = 6 cm

Apply CAH, thus:

Cos 58 = Adj/Hyp

Cos 58 = GF/6

GF = 6*Cos 58

GF = 3.17951558 ≈ 3.18 cm

✔️Find angle K using the Sine Rule:

[tex] \frac{sin(K)}{GF} = \frac{sin(G)}{KF} [/tex]

Substitute

[tex] \frac{sin(K)}{3.18} = \frac{sin(64)}{5} [/tex]

Multiply both sides by 3.18

[tex] sin(K) = \frac{sin(64)}{5}*3.18 [/tex]

[tex] sin(K) = 0.5716 [/tex]

[tex] K = sin^{-1}(0.5716) [/tex]

K = 34.8618741° ≈ 34.90°

Compare and contrast how to graph: x = 5 and y = 3.

Answers

x=3+y x=5+y i think sorry if it is wrong

-2(x+2)=1/4(-8x-16) how many solutions does it have

Answers

Answer:

infinite

Step-by-step explanation:

Please help and show work

Answers

The answer should be X= 3.60m

what is the area of triangle ABC?? i need this asap

Answers

Answer:

A)  36√3

Step-by-step explanation:

First, figure out the height.  Since it's an equilateral triangle, it would be

6²+B²=12²

36+B²=144

B²=144-36

B²=108

B=√108

B=√36x√3

B=6√3

Now we can get the area.

1/2(6√3)(12) = 36√3

Watch help video
Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = 2x(x - 3)
Answer:
Submit Answer

Answers

The answer is x1=0,x2=3

Find the value of x.
А.
6
B
5
y
x = V[?]

Answers

Answer:

I thought this was going to be easy been sitting here for 20min

4x - 8 = 32
?!!!! please help me plss

Answers

Answer:

The answer is X=10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

4x - 8 = 32

4x = 40

x = 10

Solve for x...............

Answers

Answer:

x = 12 degrees

Step-by-step explanation:

They all have to add up to 360, so:

[tex]5x + 4 + 4x+9+7x+4+9x-6+4x+1=360\\29x + 12 = 360\\29x = 348\\x = 12[/tex]

After a discount of 40%, the sale price of a ride pass at a fun park is $30. What is the original
price?

Answers

Answer:

30 divided by 0.40 = 75

The original price was $75

Step-by-step explanation:

30 divided by 0.40 = 75

The original price was $75

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