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

Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. Which equation explains the relationship between segment AB and segment A double prime B double prime? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3 segment A double prime B double prime = segment AB over 2 segment AB = segment A double prime B double prime over 2 segment AB over segment A double prime B double prime = one half segment A double prime B double prime over segment AB = 2

Answers

Answer:

A. segment A double prime B double prime = segment AB over 2

Step-by-step explanation:

Triangle ABC with coordinates of:

A = (-3, 3), B = (1, -3), C = (-3, -3)

Translation (x + 2, y + 0), coordinates will be:

A' = (-1, 3), B = ( 3, -3), C = (-1, -3)

Dilation by a scale factor of 1/2 from the origin, coordinates will be:

A'' = (-0.5, 1.5), B'' = (1.5, -1.5), C= (-0.5, -1.5)

Let's find the length of AB and A''B'' using distance formula

d = √(x2-x1)² + (y2 - y1)²AB = √(1-(-3))² + (-3 -3)² = √4²+6² = √16+36 = √52 = 2√13A''B'' = √(1.5 - (-0.5)) + (-1.5 - 1.5)² = √2²+3² = √13

We see that

AB = 2A''B''

Now the answer options:

A. segment A double prime B double prime = segment AB over 2

Correct

B. segment AB = segment A double prime B double prime over 2

Incorrect. Should be AB = A''B''*2

C. segment AB over segment A double prime B double prime = one half

Incorrect. Should be AB/A''B'' = 2

D. segment A double prime B double prime over segment AB = 2

Incorrect. Should be A''B''/AB = 1/2

Answer:

A. segment A double prime B double prime = segment AB over 2

Step-by-step explanation:

The speed of sound in hydrogen is about 3.9 times its speed in air. If its speed in
hydrogen is almost 1287 m/s, what is its speed in air?

Answers

Answer:

330

Step-by-step explanation:

Answer:

330 m/s

Step-by-step explanation:

Divide 1287 m/s by 3.9 to get the speed of sound in air as given that the speed of sound in hydrogen is 3.9 times it's speed in hydrogen.

Hope this makes sense.

Good luck!!

If Kayla buys 50 apples for $20 what is the unit rate?

Answers

Answer:

2.50 dollars an apple.

Step-by-step explanation:

Divide 50/20

Answer:

2.5 per apple

Step-by-step explanation:

50 ÷ 20=2.5

Write the reciprocal of -2/7

Answers

Answer:

answer is -7/2

Step-by-step explanation:


Evaluate the function.
f(x) = -x^2 + 6
Find f(-3)

Answers

What uhhhhhh 12 I geuss

Hello! Did anyone took the isat ( International student admission test) ?? Please let me know !

Answers

Answer:

No, I haven't taken the isat.

Step-by-step explanation:

Answer:

No, what is it for?

Step-by-step explanation:

Unit 4 Test, Part 2: Congruence and Constructions
Help with my math please

Answers

Answer/Step-by-sep explanation:

1. Given:

∆NMK ≅ ∆TRP

[tex] \overline{NM} = 20 [/tex]

[tex] \overline{MK} = 15 [/tex]

[tex] \overline{KN} = 25 [/tex]

[tex] \overline{TR} = 3x - 1 [/tex]

a. To complete the congruent statement, thus: ∆MNK ≅ ∆RTP

b. The side that is congruent to [tex] \overline{TR} [/tex] is [tex] \overline{NM} [/tex]. Thus:

[tex] \overline{TR} [/tex] ≅ [tex] \overline{NM} [/tex]

c. Since [tex] \overline{TR} [/tex] ≅ [tex] \overline{NM} [/tex], therefore:

[tex] \overline{TR} = \overline{NM} [/tex]

[tex] 3x - 1 = 20 [/tex] (substitution)

Add 1 to both sides

[tex] 3x = 20 + 1 [/tex]

[tex] 3x = 21 [/tex]

Divide both sides by 3

[tex] x = \frac{21}{3} [/tex]

[tex] x = 7 [/tex]

2. a. Slope of LK = [tex] \frac{rise}{run} = \frac{4}{3} [/tex]

Slope of LM = [tex] \frac{rise}{run} = -\frac{3}{5} [/tex]

b. ✍️Length of LK is the distance between L(-7, 4) and (-4, 8):

[tex] Lk = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] Lk = \sqrt{(-4 -(-7))^2 + (8 - 4)^2} [/tex]

[tex] Lk = \sqrt{(3)^2 + (4)^2} [/tex]

[tex] Lk = \sqrt{9 + 16} [/tex]

[tex] Lk = \sqrt{25} [/tex]

[tex] Lk = 5 [/tex]

✍️Length of LM is the distance between L(-7, 4) and (-2, 1):

[tex] LM = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] LM = \sqrt{(-2 -(-7))^2 + (1 - 4)^2} [/tex]

[tex] LM = \sqrt{(5)^2 + (-3)^2} [/tex]

[tex] LM = \sqrt{25 + 9} [/tex]

[tex] LM = \sqrt{34} [/tex]

[tex] LM = 5.8 [/tex] (nearest tenth)

∆KLM is not an isosceles ∆ because it does not has two equal side lengths. This we can see because LK and LM are not equal.

Therefore, Anthony is incorrect. Am isosceles ∆ has two equal sides.

what is the slope- intercept form of x+4y=16

Answers

Answer:

Y= -1/4x +4

Step-by-step explanation:

Slope intercept form is y=Mx+b

4y=16-x

Y= -1/4x +4

what is distributive property?

Answers

Answer:

To distribute means to divide something or give a share or part of something. For example, for the problem 4(6+2), you would use the distributive property and distribute the 4. Making the end result, 24+8.

Answer:

The distributive property tells us how to solve equations in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division. Normally when we see an equation like this … 4(8+3) distributive property format 4(8+3) -> 4(11) -> 44 we just evaluate what’s in the parentheses first, then solve it: 4(8+3)=4x8 + 4x3=44 These are the 2 methods

Step-by-step explanation:

A set of average city temperatures in October are normally distributed with a mean of
20.
6

C
20.6

C20, point, 6, degrees, start text, C, end text and a standard deviation of
2

C
2

C2, degrees, start text, C, end text.
What proportion of temperatures are between
1
8

C
18

C18, degrees, start text, C, end text and
20.
6

C
20.6

C20, point, 6, degrees, start text, C, end text?

Answers

Answer:

0.4032

Step-by-step explanation:

completely factor 1-100x^2​

Answers

Answer:

Since both terms are perfect squares, factor using the difference of squares formula,  a 2 − b2 = ( a + b ) (a − b )  where  a= 1  and  b = 10 x . ( 1 + 10 x ( 1 − 10 x )

Step-by-step explanation:

CONVERT 1.3333........ into p/q form​

Answers

Answer:

4/3In short form, it is x is equal tox= 12/9

The function p is defined as p(x) = x2 – 3x. If the
function q is defined as q(x) = p(x) – 4, what is the
value of q(10) ?
A) -30
B) 6
C)
66
D) 70

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]q(x) = {x}^{2} - 3x - 4[/tex]

[tex]q(10) = ( {10})^{2} - (3 \times 10) - 4 [/tex]

[tex]q(10) = 100 - 30 - 4[/tex]

[tex]q(10) = 70 - 4[/tex]

[tex]q(10) = 66[/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Thus the correct answer is (( C )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

which triangle is the most similar to triangle ABC? ​

Answers

Using the process of elimination,

Answer J is the answer, it is the only answer that has a ratio between the given shape of 1:2, the dilation is 1/2 or x2 if you're going from object J to ABC.

if you spun the spinner 100 times would you expect it to land on red

Answers

How many colors are there in total?

What is the median?
-2 -3 8 -6 -9

Answers

Answer:

-3

Step-by-step explanation:

its the middle number so you put them in order and get the ndeswer just whatevers in the midde

-9 -6 -3 -2 8

Answer:

The median is -3

Step-by-step explanation:

-9 -6 -3 -2 8 (least to greatest)

What should we subtract from 50/29 to get 24

Answers

Answer:

-22.28

Step-by-step explanation:

Let the number to be subtracted from 50/29 to get 24 to be x

So this can be written as : 50/29 - x =24 ----collect like terms as

50/29 - 24 = x

1.72 -24 = x

-22.28 = x

So to check the answer;

50/29 -{x} = 24

50/29 - {- 22.28} = 24

1.72+ 22.28 = 24 ---correct.

does this graph show a function? explain how you know

Answers

the answer is A i believe. there is a function but there are never y values with more than one x value.

Answer:

B

Step-by-step explanation:

if you drew a line on top of any part of the parabola, you will only touch the line once.

(when drawing a line, they are always vertical, not horizontal)


C.
tan(450)
Help please!

Answers

Answer:

The answer is 0

Step-by-step explanation:

16x² +8-7x-3x2 - 13x

Answers

Answer:

[tex]13x^{2}[/tex]-20x+8

Step-by-step explanation:

Step 1: rearrange the equation

16x^2 - 3x^2 - 7x - 13x +8

Step 2: solve the equation

16x^2 - 3x^2 = 13x^2

-7x - 13x = -20x

(the +8 will stay the same)

so when we put it all together it gives us

13x^2 - 20x + 8

What is the boiling point of salty ocean water?

Answers

Answer: approximately 105.7°C

Step-by-step explanation:

Seawater of 35 psu has a specific heat of 0.932 compared with 1.000 for pure water. Pure water freezes at 0 °C and boils at 100 °C (212 °F) under normal pressure conditions. When salt is added, the freezing point is lowered and the boiling point is raised. Therefore, we can tell that salt increases the boiling temperature, but not by very much. If you add 3 grams of salt to 100 grams (or mL) of water, instead of boiling at 100° C, it'll boil at 100.5° C.

And I'm not sure about the ocean water because the expected range is too wide and various, so maybe I guess the boiling point of salty ocean water would be about 105.7°C?

THIS IS URGENT, IM ABOUT TO START CRYING!!!
The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −5
0 −1
1 3
g(x)

g(x) = 4x + 3



Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points)

(10 points)

Answers

PART A:

Finding the slope of the function f(x)

Choose any two pairs of coordinate from the table; (-1, -15) and (0, -10)

Let (-1, -15) be (x₁, y₁) and (0, -10) be (x₂, y₂)

Slope =

Slope of f(x) = 5

The function g(x) is given in the straight line equation form

Where,  is the slope and  is the y-intercept

Slope of g(x) = 2

-----------------------------------------------------------------------------------------------------------

g(x) = 2x + 8

Where, the slope (m) = 2 and the y-intercept (c) = 8

The y-intercept of g(x)  is 8

for f(x), we can read the y-intercept when x = 0.

From the table, when x = 0, y = -10

The y-intercept of f(x) is -10

Function g(x) has higher y-intercept

4 ice cream cones cost $6. At this rate, how much do 7 ice cream cones cost?
this is a test for middle schoolers but anyone is free to answer​

Answers

Answer:

$42

Step-by-step explanation:

Equation: y = 6x

x = number of ice cream cones

y = 6(7) = 42

Hi! I believe your answer is $10.50. If it's $6 for 4 ice cream cones, divide 6 by 4 and you'll get 1.5, or $1.50 per ice cream cone. For 7 ice cream cones, multiply the unit rate ($1.50 per ice cream cone) by 7. The total cost is $10.50. I hope this helps you! Good luck and have a great day. ❤️✨

0,1,-1,undefined ......

Answers

The answer is -1
You substitute the given value into the function and then evaluate.
Hope this helped :)

100 points---> true or false. my name is grace, my favorite sports are football and softball, and I'm a left handed utility player

Answers

Answer:

true

Step-by-step explanation:

I haven't a clue on what is going on here but I will act like I do

Answer:

I will say true

Step-by-step explanation:

Thanks for free points

The value of $\sqrt{73}$ is between two positive, consecutive integers. What is the product of these two integers?

Answers

Answer:

Step-by-step explanation:

What are the two closest square numbers to 73?

64 and 81

[tex]\sqrt{64} \leq \sqrt{73} \leq \sqrt{81}\\8\leq \sqrt{73} \leq 9\\8*9 = 72[/tex]

Answer:

72

Step-by-step explanation:

Since $73$ is between $64=8^{2}$ and $81=9^{2}$, we know that $\sqrt{73}$ is between $8$ and $9.$ Our answer is $8\cdot9=\boxed{72}.$

38. By the commutative property, 3(w +9) is
equivalent to which expression?
A. 3w + 9
B. 3w + 27
C.
D. 3(9+ w)

Answers

Answer:

B

Step-by-step explanation:

3 ( w + 9 )

3 × w + 3 × 9

3w + 27

Hope this helps

plz mark as brainliest!!!!!!!

I think it’s d, but if not then the other answer says b.

Also I don’t see an answer for c.

PLEASE HELP ME!!! Point Q is located at (-4, 6) Point R is located at (8, 6)
what is the distance from point Q to point R?

Answers

Q = (-4, 6)
R = (8, 6)

You can work out the distance between the points by doing the following formula:


√(x₂ - x₁)² + (y₂ - y₁)²

Factor in our points:

√(8 - -4)² + (6 - 6)²

Solve the brackets (remember a negative and a negative make a positive):

√(12)² + (0)²

= √144 + 0

= √144

Solve this expression to get your final answer of the distance between two points:

√144 = 12

I hope this helps. If it does then a Thanks or a Brainliest would mean a lot! :)

If I pay $600 in interest for my simple interest loan for $10,000 at an
interest rate of 3%, how long did I have the loan for?

Answers

Answer:

2 periods

Step-by-step explanation:

Simple interest is compounded one time, usually annually, although it could be less time or longer. Thus I answer 2 periods. If your choices include 2 years, that is most likely the answer.

To find the answer,

$10,000 x .03 = $300.

$600 / $300 = 2 periods.

Hope this helps.

Good luck

How many of the numbers between 8 and 65 are a multiple of 7?
A) 5
B) 6
C) 7
D) 8

Answers

Answer:

8 is the answer.

8 numbers between 8 and 65 are a multiple of 7

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