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Ad libitum [116K]
2 years ago
8

Bill uses mirrors to augment the “laser experience” at a laser show. At one show he places three mirrors, A, B, C, in a right tr

iangular form. If the distance between A and B is 24m more than the distance between A and C, and the distance between B and C is 24m less than the distance between A and C, what is the distance between mirror A and mirror C?
Mathematics
1 answer:
USPshnik [31]2 years ago
5 0

The distance between mirror A and mirror C is,: AC = 96, BC=72, AB =120.

<h3>Distance</h3>

AC = x

BC = x- 24

AB = x + 24

<h3>Pythagorean theorem</h3>

AB2  = AC2 +   BC2

or ( x + 24 )²= x² + ( x - 24 )²

x² + 48 x + 576 = x² + x² - 48x + 576

96 x = x²

x (96 - x ) = 0

x= 96

Hence,

AC = 96

BC = 96-24=72

AB = 96+24=120

Therefore the distance between mirror A and mirror C is,: AC = 96, BC=72, AB =120.

Learn more about distance here:brainly.com/question/23848540

#SPJ1

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The Law of Large Numbers states that as the number of trials of an experiment increases, the experimental probability of an even
Lena [83]

The law of large number states that , if number of trials increases in an experiment , in a fair trial where each outcome has same chance of occurring or having equal probabilities,when total number of trials  goes higher and higher the probabilities of each single outcome becomes approximately equal.→→In case of Experimental Probability

The Coin Possessed by Jake is a Magic coin.

Now Outcomes received by jake when he tosses the coin certain number of times.He flipped it 100 times, and found that it came up heads 64% of the time. He flipped it another 500 times, and it came up heads 57% of the time. He then flipped it 1000 times, and it came up heads 58% of the time. Then, he flipped it 1500 times, and it came up heads 62% of the time.

Based on the information provided , it appears that coin is not fair . It is  Unbiased.So , if we apply law of large numbers here after number of trials will go higher and higher , the chances of coming head will be more than tail i.e theoretical probability of the magic coin coming up heads is> 50%.

To test my hypothesis i have used the information provided by Jake, which shows that coin is not fair. The probability of head has more than tail i.e by 14%, 7%,8% and 12%.


8 0
4 years ago
Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u
soldier1979 [14.2K]

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

8 0
3 years ago
will the opposite of a number always,sometimes,or never be greater than the number itself??????? can someone do an example and a
weeeeeb [17]

When the number is positive, its opposite is less than the number.

9 ==> -9 . . . . . . less
72 ==> -72 . . . . less
324 ==> -324 . . less


When the number is negative, its opposite is greater than the number.

-8 ==> 8 . . . . . . greater
-3/4 ==> 3/4 . . . greater
-429 ==> 429 . . greater .

We've seen that the opposite can be less, and it can also be greater.
I guess that means that it's sometimes greater.

8 0
3 years ago
Read 2 more answers
Help with these 2 Please
tensa zangetsu [6.8K]

The employees that drive to work is 380

The total number of employees that drive to work is 660

<h3>How many employees drive to work?</h3>

A fraction is a non integer that is made up of a numerator and a denominator. A fraction is used to express the ratio or the relationship between two or more quantities. An example of a fraction is 1/2.

The number of employees that drive to work can be determined by multiplying the fraction of the employees that drive to work by the total number of employees.

Employees that drive to work = 2/3 X 570 = 380

In order to determine the employees that drive to work, take the following steps:

Determine the total number of employees : 3 x 330 = 990

The total number of employees that drive to work: 2/3 x 990 = = 660

To learn more about multiplication of fractions, please check: brainly.com/question/1114498

#SPJ1

8 0
1 year ago
Find the measure of angle C.<br> B (110°<br> 30°<br> A
Oksana_A [137]

Explanation is in the file

tinyurl.com/wpazsebu

6 0
3 years ago
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