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2 years ago

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The height of a flare fired from a 32-foot high platform can be modeled by the function h= -16t^2 + 16t + 32, where h is the hei

ght in feet above the ground and t is the time in seconds. Find the time it takes the flare to reach the ground

1 answer:

Amanda [17]2 years ago

4 0

Answer:

Time, t = 2 seconds

Step-by-step explanation:

The height of a flare fired from a 32-foot high platform can be modeled by the function :

$h= -16t^2 + 16t + 32$

Here, h is the height in feet above the ground and t is the time in seconds.

It is required to find the time taken by the flare to reach the ground. When its reaches ground, height covered by it equals 0 such that,

h = 0

$-16t^2 + 16t + 32=0\\\\t=\dfrac{-16+\sqrt{16^2-4\times (-16)(32)} }{2(-16)}, \dfrac{-16-\sqrt{16^2-4\times (-16)(32)} }{2(-16)}\\\\t=-1\ s, 2\ s$

Neglecting t = -1 seconds, the time taken by the flare to reach the ground is 2 seconds.

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Does 23y+50+27y=50y+50 have one solution, no solution, or infinite solutions

stellarik [79]

The answer is infinite solutions.

subtract 50 from each side to get
23y+27y=50y

ad 23y and 27y to get 50y
50y=50y
and no matter what number you put in place you get the correct answer

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3 years ago

Read 2 more answers

The following picture shows two gears meshed together with the arrows lined up. Gear A has 48 teeth, while gear B has 28 teeth.

spin [16.1K]

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<u>Step-by-step explanation:</u>

The LCM of 48 and 28 is 336

It would take 336 ÷ 28 = 12 revolutions of gear B

and 336 ÷ 48 = 7 revolutions of gear A

to match up the arrows.

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3 years ago

Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!

Over [174]

Step-by-step explanation:

initial speed = 272 ft/s

h = -16t² + 272t

a. 1120 = -16t² + 272t we change a bit into

16t² - 272t + 1120 = 0 then divide all with factor 16

t² - 17t + 70 = 0

(t - 10)(t - 7) = 0

t = 10 and t = 7

7 s when it goes up and 10 sec when the rocket goes down.

b. 1152 = -16t² + 272t we change a bit into

16t² - 272t + 1152 = 0 then divide all with factor 16

t² - 17t + 72 = 0

(t - 9)(t - 8) = 0

t = 9 and t = 8 sec

c. since the answer of a and b is:

7 sec and 8 sec the rocket goes up but at 9 sec and 10 sec the rocket goes down then we can take conclusion that the maximum height is reached at 8.5 s

so how long the rocket in the air?

goes up : 8.5 sec

goes down : 8.5 sec

total = 17 sec

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3 years ago

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Step-by-step explanation:

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2 years ago

At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

$p_1 = \frac{20}{100} = 0.2$

$s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04$

p2 -> 1997

10 out of 100, so:

$p_2 = \frac{10}{100} = 0.1$

$s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03$

Distribution of p1 – p2:

$p = p_1 - p_2 = 0.2 - 0.1 = 0.1$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05$

Confidence interval:

$p \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower bound of the interval is:

$p - zs = 0.1 - 1.645*0.05 = 0.01775
$

The upper bound of the interval is:

$p + zs = 0.1 + 1.645*0.05 = 0.18225
$

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

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3 years ago