All categories

3 years ago

A lighting designer is finalizing the lighting plan

Mathematics

1 answer:

kykrilka [37]3 years ago

6 0

Answer:

Step-by-step explanation:

It depends on the shape of the stage, generally, the stage is cuboidal or cubical in shape, so assuming the stage is cuboidal.

Here, the spotlight has top cover the minimum angle of 90° (for a corner position of the spotlight.

Now, compute how much angles the spotlight can cover.

From its central position, the spotlight can rotate 25° to the left or right, so, angle covered due to rotation is 25°+25°=50°.

As the beam of light from the spotlight can spread 22°.

So, the total angle covered by spotlight= 50° + 22°=72°, which is less than the minimum angle required to cover the entire stage.

Hence, the designer can't use the spotlight to light each of the objects on the stage.

You might be interested in

Let Y be a random variable with a density function given by

Neporo4naja [7]

From the given density function we find the distribution function,

$F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y$

(a)

$F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)$

$\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1$

$\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}$

(b)

$F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y$

$\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2$

$\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}$

(c)

$F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})$

$\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3$

$\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}$

5 0

2 years ago

What is the product of 2X plus 3 and 4X squared minus 5X plus 6

Tju [1.3M]

The product of something means multiplying the terms together.

(2x+3) (4x^2-5x+6)

Secondly you need to distribute the terms to each other (Think of problems like FOIL)

2x * 4x^2 + 2x(-5x) + 2x * 6 + 3 * 4x^2 + 3(-5x) + 3 * 6

Then you must take into account that some of the numbers are negative. (minus-plus rules!)

2x * 4x^2 - 2x * 5x + 2x * 6 + 3 * 4x^2 - 3 * 5x + 3 * 6

Now is the tricky part of simplifying everything.

2x * 4x^2 = 8x^3

2x * 5x = 10x^2

2x * 6 = 12x

3 * 4x^2 = 12x^2

3 * 5x = 15x

3 * 6 = 18

8x^3 - 10x^2 + 12x + 12x^2 - 15x + 18

Then you group like terms.

8x^3 - 10x^2 + 12x^2 - 3x + 18

8x^2 + 2x^2 - 3x + 18

The trickiest part of this is distributing all of the terms within the parentheses, once you've done that, it's smooth sailing!

5 0

3 years ago

What is the slope of the line

lidiya [134]

Answer:

c is the correct answer

Step-by-step explanation:

because i worked it out

8 0

2 years ago

Read 2 more answers

A jar of natural peanut butter normally cost four dollars today it's on sale for $3.60 what is the percentage of the discount

kakasveta [241]

$4 is the original price of the jar consisting of peanut butter so therefor it = 100%. It's for sale at $3.60, so we divide $4 by 100% so we get the percentage for each cent and then we times it by 3.60 to get the percentage for $3.60 which is 90%. Now we subtract 90% from 100% to get the discounted percentage for 40cents :)

5 0

3 years ago

In a study, a group of 10-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they

Yakvenalex [24]

The amount of weight gained

7 0

2 years ago

Read 2 more answers