The coordinates of B

A television screen's width is 1.778 times its height. If its

Nana76 [90]

Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

a^2+b^2=c^2 becomes (9b/16)^2 + b^2 = c^2

Squaring the nominator and the denominator of the fraction yields

81b^2/256 + b^2 = c^2

To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

81b^2/256 + 256b^2/256 = c^2

Adding fractions with the same denominators is now easy and produces

337b^2/256 = c^2

Cross multiply to get

337b^2 = 256c^2

Divide both sides by 337 to get b^2

b^2=256c^2/337

Take the square root of both sides to get b

b = sqrt(256c^2/337)

Lots of complicated Pythagorean responses. This is much simpler to answer with Trigonometry.

TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

w = diag x 0.872 + 2 x bw

h = diag x 0.49 + 2 x bw

(Where diag is the diagonal size of the screen and bw is the bezel width)

Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

Next, calculate the ratio of the height relative to the hypotenuse (the diagonal length) using arc-sine, which yields the relative proportion of opposite length over the hypotenuse for a given angle:

h = asin(0.512)

The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

6 0

3 years ago

A jewellery shop sells 240 items in a month, 180 was sold online the rest were sold in store. Work out the ratio of online sales

cricket20 [7]

Answer:

3 : 1

Step-by-step explanation:

180 out of 240 sold online so (240 - 18) sold in store

180 : 60

18 : 6

3 : 1

5 0

3 years ago

A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation x^2/500 - y^2

Reil [10]

Answer:

100m

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard devia

Anna35 [415]

With 10 integers available, $X$ has PMF

$\mathbb P(X=x)=\begin{cases}\dfrac1{10}&\text{for }0\le x\le9,x\in\mathbb Z\\\\0&\text{otherwise}\end{cases}$

We're interested in the statistics of the new random variable $Y=5X$ . To do this, we need to know the PMF for $Y$ . This isn't too hard to find.

$\mathbb P(Y=y)=\mathbb P(5X=y)=\mathbb P\left(X=\dfrac y5\right)$

Since the PMF for $X$ gives a value of $\dfrac1{10}$ whenever $x$ is an integer between 0 and 9, it follows that $\dfrac y5$ must also be an integer for the PMF to give the identical value of $\dfrac1{10}$ . This means

$\mathbb P(Y=y)=\begin{cases}\dfrac1{10}&\text{for }y\in\{0,5,\ldots,45\}\\\\0&\text{otherwise}\end{cases}$

Now the mean (expectation) is

$\mathbb E(Y)=\displaystyle\sum_yy\mathbb P(Y=y)=\frac1{10}\sum_{y\in\{0,\ldots,45\}}y$
$\mathbb E(Y)=\dfrac{225}{10}=22.5$

The variance would be

$\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb V(X)=\displaystyle\sum_yy^2\mathbb P(Y=y)-\mathbb E(Y)^2$
$\mathbb V(X)=\displaystyle\frac1{10}\sum_{y\in\{0,\ldots,45\}}y^2-\left(\frac{225}{10}\right)^2$
$\mathbb V(X)=\dfrac{7125}{10}-\dfrac{50625}{100}=206.25$

The standard deviation is the square root of the variance, so you have

$\sqrt{\mathbb V(X)}=\sqrt{206.25}\approx14.3614$

8 0

3 years ago

The equation of line a is y=−14x+3. If line b runs perpendicular to line a and passes through (2, 6), what would be the equation

AysviL [449]

Hint : The product of the slopes of two lines perpendicular to each other is - 1 .

______________________________

In slope-intercept ( y = ax + b ) from of the linear equations the coefficient of x is the slope of the line.

Thus :

Slope of line a = - 14

______________________________

Suppose that the slope of line b is x according to the Hint we have :

- 14 × x = - 1

negatives simplify

14x = 1

Divide both side by 14

14x ÷ 14 = 1 ÷ 14

x = 1/14

So the slope of line b is 1/14

_____________________________

Now let's find the equation of line b by point-slope formula using the point question have us ( 2 , 6 ) :

y - y( given point ) = Slope × ( x - x ( g p ) )

y - 6 = 1/14 × ( x - 2 )

y - 6 = 1/14 x - 2/14

y - 6 = 1/14 x - 1/7

Add both sides 6

y - 6 + 6 = 1/14 x - 1/7 + 6

y = 1/14 x - 1/7 + 42/7

y = 1/14 x + 41/7

And we're done ...

6 0

3 years ago