Two people enter a whispering gallery and want to know where they should stand so they can hear the other person's whisper. The gallery is 100 feet wide and the vertical distance from their head to the peak of the ceiling is 30 ft.

Answers

Answer 1

Answer:

The two people should stand 40 feet from the center so that they can hear each other whisper

Step-by-step explanation:

From the question

Width of the gallery = 100 feet

Width = 2a

a = Width/2

a = 100/2 = 50 feet

Height of the gallery = b = 30 feet

Hence, the distance is

d² = a² - b²

d = √a² - b²

d = √50² - 30²

d = √2500 - 900

d = √1600

d = 40 feet

Hence, the two people should stand 40 feet from the center so that they can hear each other whisper.


Related Questions

The cost of 3 scarves is $72.75. What is the unit price?

Answers

Answer:

$24,25

Step-by-step explanation:

72.75 ÷ 3 = 24,25

Match the vocabulary word with the correct definition.

Answers

Answer:

1. right triangle - a triangle with one angle that measures 90 degrees

2.radius- a line segment from the center of a circle to any point on the circle

3. ray- a part of a line that has 1 endpoint that goes in one direction forever

4. rotational symmetry- a property that allows a figure to be rotated less than 360 degrees and still look the same

5. regular polygon- a polygon whose sides are all the same lengths and whose angles are the same measure

6. reflection- a transformation in which a figure is flipped across a line to give a mirror image of the original figure

Step-by-step explanation:

guys im so desperate right now please help me

Right triangle ABC is similar to Right triangle XYZ. The value of cosB = 5/13. What is the value of sin Y?

Answers

Answer:

if sin B = sin Y then sin Y = 12/13

Step-by-step explanation:

Triangle ABC is similar to Triangle XYZ

Let angle C be the right angle

Cosine of B is equal to 5/13

Cos B = adjacent/hypotenuse = 5/13

NOTE = below is the lowercase letters that represent the side lengths, not the angles

Adjacent (length of a) = 5 <-- given

Hypotenuse (length of c) = 13 <-- given

Opposide (length of b) = a^2 + b^2 = c^2 --> 5^2 + b^2 = 13^2 --> b = 12

sin B = sin Y

sin B = opp/hyp = 12/13

if sin B = sin Y then sin Y = 12/13

Write the recursive, arithmetic and explicit formula for the nth term of the sequence:
8, 1, -6, -13,... Then find the 10th term

Answers

Recursive Formula

[tex]\begin{cases}a_1 = 8\\a_n = a_{n-1}-7\end{cases}[/tex]

The top row says the first term is 8

The bottom row says that to get the nth term, we subtract 7 from the (n-1)th term. So basically we subtract 7 from each term to get the next term.

Note the subscripts tell us which term we're working with.

======================================================

Arithmetic Formula

We have a = 8 as the first term and d = -7 as the common difference.

a(n) = a + d(n-1)

a(n) = 8 + (-7)(n-1)

a(n) = 8 - 7n + 7

a(n) = -7n+15

The nth term arithmetic formula is a(n) = -7n+15

If you plug in n = 1, you should get a(n) = 8

If you plug in n = 2, you should get a(n) = 1

and so on.

=======================================================

Finding the 10th term

Plug in n = 10 to get

a(n) = -7n+15

a(10) = -7(10)+15

a(10) = -70+15

a(10) = -55

The 10th term is -55

Evaluate: 21x: 8 when x = 4*

Answers

Answer:

10.5

Step-by-step explanation:

21(4) / 8

84 / 8

10.5

Simplify the expression:

3x2 - x + 7 + 5x + 2 - 2x2

Answers

-x+5x + (3x2) + 7 +2 - (2x2)
4x + 6 + 7+ 2 - 4
4x + 11

Answer: yes

Step-by-step explanation:

3 x 2 - x + 7 + 5 x + 2 - 2 x 2

6 - x + 7 + 5x + 2 - 4

6 + 7 + 2 - 4 - x + 5x

13 - 2 + 4x

11 + 4x

3x+y/c = 4 solve for y

Answers

Answer:

Thanks for the points lol

Step-by-step explanation:

how much will a C (76%) bring down my grade if i have 100%/A+ in class?

Answers

Answer:

It’s depends on how much of your grade the assignment was worth

Step-by-step explanation:

Answer: Im pretty sure it will effect your grade by 24% if thats the answer your looking for. It also depends on how much the assignment was actually worth

Find the zero of the function.
f(x) = 4x2 – 12x + 9

The zero of the function is x=

Answers

Answer:

x= 3/2

Step-by-step explanation:

I apologize if it is wrong!

(02.01 LC) Solve:negative 1 over 2 x + 2 = −x + 7 (5 points)??.?.??????

Answers

Answer:

x=10

Step-by-step explanation:

let me know if correct

Answer:

x=10

Step-by-step explanation:

Plsss help mee :,) ill give brainlist

Answers

Answer:

3/5, 1, 8/5, 8

Step-by-step explanation:

Answer:

0, 35, 8/5, 8.  I think

Step-by-step explanation:

hope this helps :3

im sorry if im wrong

1)50% of 60 2) 8 out of 80 is what percent?

Answers

Answer:)

1) 50% of 60 is 30

2) 8 out of 80 is 10%

You're welcome :)

Answer:1. 30

2. 10%

Step-by-step explanation:

HELP ASP!!❤️
WILL GIVE BRAINLIEST!...

Find the slope of the line. Enter your answer in simplest form.

Answers

Answer:

[tex]m=\frac{-4}{3}[/tex]

General Formulas and Concepts:

Order of Operations: BPEMDASSlope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-6, 5)

Point (3, -7)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{-7-5}{3-(-6)}[/tex]Simplify:                        [tex]m=\frac{-7-5}{3+6}[/tex]Subtract/Add:               [tex]m=\frac{-12}{9}[/tex]Simplify:                        [tex]m=\frac{-4}{3}[/tex]

Answer:

the slope is -4/3

Step-by-step explanation:

m=y2-y1/x2-x1

-7-5=(-12)

3-(-6)=9

-12/9

-12/3=(-4)

9/3=3

-4/3

hope this helps :3

if it did pls mark brainliest

You put a frozen pizza in the oven. After 20 minutes,
you take it out. Let T(m) be the temperature of the pizza m
minutes after you place it in the oven. Explain the meaning
of each statement.
I
T(0) = 35
T(15) >T(5)
T(m) = 100

Answers

T(t) = temp at any given time t = time. To = initial temp of the heated object ... A cake removed from the oven has a temperature of 210°F It is left to room that has a temperature of 70°F. After 30 minutes, the temperature of in is 140°F a. Use Newton's Law of Cooling to find a model for the temperatur ... 20 = 1402 -0.02317.

\text{Nine times the difference of 8 and a number.}
Nine times the difference of 8 and a number

Answers

Answer:

9x8=72      72-8=64  64x9=576

Step-by-step explanation:

Answer:

Nine times the difference of 8 and a number = 9(x-8)

Hi guys can you please help me with this problem please ill mark brainiest

Answers

The answer is  y= 23/4

Francis has a large vegetable garden that covers 47 of her backyard. Her patio covers 13 of the yard, and the rest is grass. What portion of Francis’s yard is grass?
If someone can please answer this!!

Answers

You know ...........

1. Natoy's rectangular swimming pool has the length of 3m more than thrice its
width. What are the dimensions of the pool if it has an area of 216m2?
Width (w)
Length (/) = 3w + 3

Answers

Answer:

Step-by-step explanation:

Given

Natoy's rectangular swimming pool has the length of 3m more than thrice its

width.

Width=w

Length =3w+3

So

Area of the rectangular swimming pool=length×width

216=(3w+3)×w

216=3w^2+3w

3w^2+3w-216=0

3(w^2+w-72)=0

W^2+w-72=0

W^2+(9-8)w-72=0

W^2+9w-8w-72=0

W(w+9)-8(w+9)=0

(W+9)(w-8)=0

Sotwo value of w are 8,-9

We take positive value for rectangular swimming so we take w=8m

Width=8m

Length=3×8+3

= 24+3

=27m

is the square root of 3 rational?

Answers

Answer:

1.5

Step-by-step explanation:

Write this statement as a conditional statement in the form “if p, then q.”

A ray divides an angle into two congruent angles. So, the ray is an angle bisector.

Answers

Answer:

if a ray divides an angle into two congruent angles, then the ray is an angle bisector.

Step-by-step explanation:

if p statement is before the comma, called the hypothesis of the conditional statement.

then q statement is after the comma and it is called the conclusion of the conditional statement.

8) What percent of 75 is 60?

Please help

Answers

Answer: 80%

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

70% to 0.70

60*0.70= 42

Anyone know this ?? Please

Answers

Answer:

It is 90 degrees

Step-by-step explanation:

It’s C, it’s been rotated 90° :)

What is the slope??? PLEASE HELP!!!

Answers

Answer:

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.


A van travels 180 miles on 12 gallons of gas. At that rate, how much gas will it need to travel 330 miles

Answers

Answer: 22 gallons of gas.

The amount of gas needed to travel 330 miles will be 36.67 gallons.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The rate is the ratio of the amount of something to the unit.

For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

A van travels 180 miles on 12 gallons of gas. Then the rate is given as,

Rate = 20 / 180

Rate = 0.1111 gallons per mile

At that rate, the amount of gas needed to travel 330 miles will be given as,

⇒ 330 x 0.1111

⇒ 36.67 gallons

The amount of gas needed to travel 330 miles will be 36.67 gallons.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ2

The altitude of an isosceles triangle bisects the base and measures 10ft. If the base of the triangle measures 16ft, calculate: a) the area of the triangle b) and one side of the triangle.

Answers

Answer:

Step-by-step explanation:

the formula for calxulating the area if the isosceles triangle is expressed as;

[tex]A = \frac{1}{2}bh[/tex]

b is the base of the triangle

h is the altitude

Given

b = 16ft

h = 10ft

Substitute

A = 1/2 * 16 * 10

A = 8*10

A = 80ft²

Hence the area of the triangle is 80ft²

b) To get the measure of one side of the triangle, we will use the pythagoras theorem. Let s be the slant side

s² = h²+(b/2)²

s² = 10²+(16/2)²

s² = 10²+(8)²

s² =100+64

s² =164

s = √164

s = 12.8ft

Hence one side of the triangle is 12.8ft

Resolve into factors:- 9x4 + 2x²y²+ y4​

Answers

Answer:

(3x^2+y^2+2xy)(3x^2+y^2-2xy)

Step-by-step explanation:

9x^4+2x^2y^2+y^4

(3x^2+y^2+2xy)(3x^2+y^2-2xy)

Both terms are perfect squares. So you will factor using the difference of squares formula. a^2-b^2=(a+b)(a-b)

Take what the square is for every term.

9x^4. What squared is 9? 3 and take half of the power or 2. That's how you get the 3x^2

2x^2y^2 is the same way. 2xy and 2xy

y^4 is y but dived he powers by 2 to get y^2.

Take one of each and but in () like I have above.

if the measure of 1 = (4x+1) degrees, what is the measure of 6? thank you guys:)

Answers

Answer:

It should be (179 - 4x)

Step-by-step explanation:

Slope from graph Khan academy

Answers

Answer:

Step-by-step explanation: ???

cual es el angulo de inclinacion de la recta de (4,1) y (-1,6)

Answers

Answer:

945678

Step-by-step explanation:

i took the test

HELP NEEDED QUICK I WILL GIVE BRAINLIEST

Marc plans to create a model of the solar system for his school’s science fair. He knows the solar system includes many celestial bodies.

Which statement identifies a possible limitation of this model?

A. The model will be supported with scientific evidence.
B. The model will include all planets of the solar system.
C. The model will be used to predict planet distances and sizes.
D. The model will oversimplify what the solar system looks like.

Answers

Answer:

C) The model will be used to predict planet distances and sizes.

Step-by-step explanation:

A model is used to distort the size and shape of the observed object. Therefore, a model of the solar system will not be accurate when it comes to the planet's distances and sizes. It would take miles upon miles to accurately show the distance between planets.

Answer: D is the answer

Step-by-step explanation:

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