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adell
6 days ago
9

A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3

seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?
Mathematics
2 answers:
babunello [10.3K]6 days ago
8 0

Result: 15.5

Step-by-step breakdown:

PIT_PIT [11.1K]6 days ago
5 0

Since the ball achieves a peak height of 18 meters at 1 second, it will begin descending thereafter. Therefore, we anticipate that the height will drop below 18 m after 1.5 sec.

f(x) = –10x2 + 20x + 8
f(x) = –10(1.5^2) + 20(1.5) + 8
f(x) = 15.5 m

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a falling object travels a distance given by the formula d=5t + 16t^2 ft, where t is measured in seconds. how long will it take
zzz [11052]

It is provided that

d=5t+16t^{2}

We need to determine t when d equals 74

Thus, 74=5t+16t^{2} or

16t^{2}+5t-74 = 0

16t^{2}+37t-32t-74 = 0

t(16t + 37) - 2(16t + 37) = 0

(t - 2)(16t + 37) = 0

t - 2 = 0 or 16t + 37 = 0

t cannot be negative.

Thus, t equals 2

Therefore, it will require 2 seconds for the object to cover 74 feet.










8 0
1 month ago
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Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartF
Leona [11225]

Answer:

(B) There is a single solution: x = 0.

Step-by-step explanation:

The equation that Kate is attempting to solve is: \dfrac{2}{3} (6x-3)=\dfrac{1}{2}(6x-4)

\dfrac{2(6x-3)}{3}=\dfrac{(6x-4)}{2}\\\dfrac{2*3(2x-1)}{3}=\dfrac{2(3x-2)}{2}\\4x-2=3x-2\\$Adding two both sides$\\4x=3x\\4x-3x=0\\x=0

Consequently, this equation results in one solution: x = 0.

4 0
1 month ago
You have a stack of pennies without counting the pennies, how can you know if there is a odd or even number of them
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Imagine having a pile of pennies and you want to determine if the count is odd or even without tallying them one by one. You can separate them into pairs by placing one coin in the left pile and one in the right.

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8 0
1 month ago
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Rename 120,000 = ten thousands
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29 days ago
An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount o
PIT_PIT [11128]

During an archaeological excavation, an ancient campfire is uncovered. The charcoal is determined to have significantly less than 1/1000 of the standard amount of ^{14}\text{C} ​. Calculate the minimal age of the charcoal, taking into account that 2^{10} = 1024

Response:

57300 years

Step-by-step breakdown:

Using the relationship of half-life time against fraction, which can be expressed as:

\dfrac{N}{N_o} = (\dfrac{1}{2})^{\frac{t}{t_{1/2}}

In this context,

N indicates the current atom

represents the initial atomN_o

t signifies the time

denotes the half-lifet_{1/2}

Since the charcoal was found to contain less than 1/1000 of the typical amount of ^{14}\text{C} ​.

Thus;

\dfrac{N}{N_o} = \dfrac{1}{1000}

However; the objective is to estimate the minimum age of the charcoal while noting  2^{10} = 1024

this means 2^{10} = 1024, then:

\dfrac{1}{1000}> \dfrac{1}{1024}

\dfrac{1}{1000}> \dfrac{1}{2^{10}}

\dfrac{1}{1000}> (\dfrac{1}{2})^{10}

If

\dfrac{N}{N_o} = \dfrac{1}{1000}

Then

\dfrac{N}{N_o} > (\dfrac{1}{2})^{10}

Consequently, it can be estimated that the minimum time elapsed is 10 half-lives.

For ^{14}\text{C}, the standard half-life time is 5730 years

Thus, the estimation of the minimum age of the charcoal is  5730 years × 10

= 57300 years

5 0
10 days ago
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