What is the measure of angle ABC

a disc is thrown into the air with an upward velocity of 62 ft/s.its height h in feet after t seconds is given by the function h

Korolek [52]

Given that the height of the disc is modeled by the function:
h=-16t^2+20t+6
a] The maximum height will be as follows:
At maximum height:
h'(t)=0
from h(t)
h'(t)=-32t+20=0
thus
t=20/32
t=5/8 sec
thus the maximum height will be:
h(5/8)=-16(5/8)^2+20(5/8)+6
=12.25 ft

b] <span>How long will it take the disc to reach the maximum height?
</span>time taken to reach maximum height will be:
from h(t)
h'(t)=-32t+20=0
thus
t=20/32
t=5/8 sec
thus time taken to reach maximum height is t=5/8 sec

c]<span>How long does it take for the disc to be caught 3 feet off the ground?
</span>h(t)=-16t^2+20t+6
but
h(t)=3
thus
3=-16t^2+20t+6
solving for t we get:
0=-16t^2+20t+3
factoring the above we get:
t=5/8-/+√37/8
t=-1.5256 or 2.776
since there is no negative time we pick t=2.776
Hence time taken for the disc to be caught 3 ft from the ground is 2.776 ft

3 0

3 years ago

Select the correct answer. Rational function h is continuous, with a horizontal asymptote at y = 1. Which function could be func

Troyanec [42]

Answer:

Can i see an picture plz????? I think C but I can't be sure there has to be a picture with this. I think C.

8 0

2 years ago

I need help with this ASAP!

earnstyle [38]

Answer and Step-by-step explanation:

1) If you graph the lines, you will get the lines in the first attachment. You will see that the intersection point is (3, 5), which is the solution to that system.

2) First, let's convert both of these into slope-intercept form so that they're easier to graph.

x - 3y = 2

x = 3y + 2

3y = x - 2

y = $\frac{1}{3}x-\frac{2}{3}$

AND

-3x + 9y = -6

9y = 3x - 6

y = $\frac{3}{9} x-\frac{6}{9} =\frac{1}{3} x-\frac{2}{3}$

We see that these two lines are exactly the same, which means that no matter what coordinate works for one, it will work for the other. In other words, there are infinitely many solutions.

And, if you graph these lines, you will get the graph in the second attachment, where they are the same line.

Hope this helps!

5 0

4 years ago

Read 2 more answers

A population of plastic chairs in a factory has a weight's mean of 1.5 kg and a standard deviation of 0.1 kg . Suppose a sample

Firlakuza [10]

Answer:

0.9544 = 95.44% probability that the sample mean will be within +0.02 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

$\mu = 1.5, \sigma = 0.1, n = 100, s = \frac{0.1}{\sqrt{100}} = 0.01$

What is the probability that the sample mean will be within +0.02 of the population mean?

Sample mean between 1.5 - 0.02 = 1.48 kg and 1.5 + 0.02 = 1.52 kg, which is the pvalue of Z when X = 1.52 subtracted by the pvalue of Z when X = 1.48. So

X = 1.52

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$