8. A megaphone is formed by taking a cone with radius of 18 centimeters and an edge length of 60 centimeters from tip to base
and cutting off the tip. The
cut is made 12 centimeters along the edge from the tip and is parallel to the base. The cut produces
a new radius of 4 centimeters. Round your answers to the nearest tenth.
Hint: A megaphone is hollow, so do not include the base.
a. What is the surface area of the whole cone?
b. What is the surface area of the tip that is removed?
카
cone
megaphone
whole cone
C.
What is the surface area of only the megaphone?

Answer:

A.  Complementary and Adjacent

B.  ∠KLM = 22°  and  ∠MLN = 68°

Step-by-step explanation:

Question A

As ∠KLN is a right angle, ∠KLN = 90°

⇒ ∠KLM + ∠MLN = 90°

When the sum of two angles is 90°, they are called complementary angles.

∠KLM and ∠MLN have a common side of ML and a common vertex (corner point) L.

When two angles have a common side and a common vertex but do not overlap in any way, the are called adjacent angles.

Question B

First find n:

∠KLM + ∠MLN = ∠KLN

⇒ 2n + (6n + 2) = 90

⇒ 2n + 6n + 2 = 90

Combine like terms:

⇒ 8n + 2 = 90

Subtract 2 from both sides:

⇒ 8n = 88

Divide both sides by 8:

⇒ n = 11

Now substitute the found value of n into the expressions for the two angles:

⇒ ∠KLM = 2(11) = 22°

⇒ ∠MLN = 6(11) + 2 = 68°

Answer:

e) 36x² - 32y³ = (4)(9x² - 8y³)

f) 45a⁴ - 54a³ = (9a³)(5a - 6)

Step-by-step explanation:

e) 36x² - 32y³ = (4)(9x² - 8y³) becuase 4*9 = 36 and 4*8 = 32

f) 45a⁴ - 54a³ = (9a³)(5a - 6) becuase 9*5 = 45 and 9*6 = 54 and when a is multiplied by a³ you get a⁴

(the exponent are added)

PLEASE RATE!! I hope this helps!!
If you have any questions comment below

Answer:

135 degrees

Step-by-step explanation:

The image shows how i had my answer please

Answer:

(-∞,∞)

Step-by-step explanation:

Answer:

41, 243, 2

Step-by-step explanation:

40 + (1 + 2) - 2

=41

3[16 - (2 + 5)]^2

=243

100-50/100-3(2+3)^2

=2

Answer:$740

Step-by-step explanation: subtract 750 - 10 and there’s your answer look where it says “The money is taken from his bank account” that’s how you know you should subtract by the word take. Hope this helps

Answer:

The opposite sides in a rectangle are equal.

Step-by-step explanation:

If all sides were equal, you would have a square.

If the opposite sides were not parallel, you would not have 4 sides that meet at 90 degrees.

All angles in a rectangle are 90 degrees.

Answer:

The opposite sides in a rectangle are equal.

Step-by-step explanation:

hope this helps  hope you get it correct

Answer:

[tex]\frac{3\sqrt{2}+2\sqrt{3}}{6}[/tex] or [tex]\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}[/tex]

Step-by-step explanation:

[tex]\sin\frac{3\pi}{4}-\tan\frac{5\pi}{6}\\\\\sin\frac{3\pi}{4}-\frac{\sin\frac{5\pi}{6}}{\cos\frac{5\pi}{6}}\\ \\\frac{\sqrt{2}}{2}-\frac{\frac{1}{2} }{-\frac{\sqrt{3}}{2}}\\ \\\frac{\sqrt{2}}{2}+\frac{1}{\sqrt{3}}\\ \\\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{3}\\ \\\frac{3\sqrt{2}}{6}+\frac{2\sqrt{3}}{6}\\ \\\frac{3\sqrt{2}+2\sqrt{3}}{6}[/tex]

Answer:

[tex]\bf C)\: -\cfrac{1}{32}[/tex]

Step-by-step explanation:

[tex]\tt \cfrac{1}{2^{-2}x^{-3}y^5}[/tex]

[tex]\tt x=2\\y=-4[/tex]

~

Substitute ''x'' with '2' & 'y' with "-4":-

[tex]\tt \cfrac{1}{2^{-2}\times \:2^{-3}\left(-4\right)^5}[/tex]

First let's solve [tex]\tt 2^{-2}\times \:\:2^{-3}\left(-4\right)^5[/tex]

[tex]\tt 2^{-2}\times \:2^{-3}=\boxed{\cfrac{1}{32} }[/tex]

[tex]\tt \cfrac{1}{32}\left(-4\right)^5[/tex]

Calculate exponents:- -4^5= -1024

[tex]\tt \cfrac{1}{32}\left(-1024\right)[/tex]

Remove parentheses, apply rule:- [tex]\tt a\left(-b\right)=-ab[/tex]

[tex]\tt-\frac{1}{32}\times \:1024[/tex]

[tex]\tt \cfrac{1}{32}\times \cfrac{1024}{1}[/tex]

Apply fraction rule:-

[tex]\tt -\cfrac{1\times \:1024}{32\times \:1}[/tex]

[tex]\tt \cfrac{1024}{32}[/tex]

Divide numbers:-

[tex]\tt -32[/tex]

Now that we're done factoring the denominator let's bring down the numerator which is ' 1 ':-

[tex]\tt -\cfrac{1}{32}\;\; \bf Answer[/tex]

☆-------☆-------☆-------☆

[tex]\dfrac 1{2^{-2}\cdot x^{-3}\cdot y^5}\\\\=\dfrac 1{2^{-2} \cdot2^{-3} \cdot (-4)^5}\\\\=-\dfrac 1{2^{-2} \cdot 2^{-3} \cdot (2^2)^5}\\\\=-\dfrac{1}{2^{-2} \cdot 2^{-3} \cdot 2^{10}}\\\\=-\dfrac{1}{2^{-2-3+10}}\\\\=-\dfrac 1{2^{5}}\\\\=-\dfrac 1{32}[/tex]

Answer:

the answer is

[tex] \frac{12 {c}^{8} }{ {d}^{2} } [/tex]

Step-by-step explanation:

[tex] \frac{12}{ {c}^{ - 8} {d}^{2} } [/tex]

Answer:

$37.5+$3r

Step-by-step explanation:

We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).

We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.

Then, you can add it which is $37.5+$3r

Answer:

D

Step-by-step explanation:

sub in the x value and if its equal to -2 its on that line

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Here's the solution~

Standard equation of a circle is represented as :

[tex]\qquad \sf  \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]

where,

Now, let's plug in the values to find the required equation of circle ~

[tex]\qquad \sf  \dashrightarrow \:(x - 8) {}^{2} + (y - ( - 10)) {}^{2} = (4\sqrt{3} ) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 8) {}^{2} + (y + 10) {}^{2} = 16 \times 3[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 8) {}^{2} + (y + 10) {}^{2} = 48[/tex]

The equation of given circle with centre C ( 8 , - 10 ) and diameter ( 8√3 ) is x² + y² - 16x + 20y + 116 = 0

[tex]\quad\rule{300pt}{1pt}\quad [/tex]

The standard equation of Circle is given by :

[tex] {\pmb{\sf {\longrightarrow r^2 = (x-h)^2 +( y-k)^2}} }[/tex]

This is the standard form of the equation. Thus if we know the coordinates of center of the circle and it's radius, we can easily find its equation

Here, in this question we are given that the centre C is ( 8 , -10 ) and diameter 8√3.

[tex] \longrightarrow[/tex]h = 8

[tex] \longrightarrow[/tex] k = - 10

[tex] \longrightarrow[/tex] r = [tex] \sf{\dfrac{diameter}{2}}[/tex]

[tex] \longrightarrow[/tex]‎ r = [tex] \sf 4\sqrt{3}[/tex]

[tex] \qquad\qquad\rule{250pt}{1pt}\qquad[/tex]

On putting the values in the formula :

[tex] \sf{:\implies \qquad r^2 = (x-h)^2+ ( y-k)^2 }[/tex]

[tex] \sf{:\implies \qquad (4\sqrt{3})^2 = ( x-8)^2 +(y-(-10))^2 }[/tex]

[tex] \sf{:\implies \qquad (4)^2.(\sqrt{3})^2=(x-8)^2+(y+10)^2}[/tex]

[tex] \sf{:\implies \qquad 16\times 3 =( x^2 + 8^2 -2\times x \times 8 ) + ( y^2 + 10^2 + 2\times y \times 10 )}[/tex]

[tex] \sf{:\implies \qquad 48 = x^2 + y^2 - 16x + y^2 + 100 + 20y }[/tex]

[tex] \sf{:\implies \qquad 48 = x^2 + y^2 -16 x + 20y + 100 + 64 }[/tex]

[tex] \sf{:\implies \qquad 48 = x^2 +y^2 -16x +20y +164}[/tex]

[tex] \sf{:\implies \qquad x^2 + y^2 -16x +20y +164 - 48 = 0}[/tex]

[tex] \sf{:\implies \qquad{\boxed{ \sf x^2 + y^2 -16x + 20y +116 = 0 }}}[/tex]

‎ㅤ‎ㅤ‎ㅤ‎ㅤ~Hence, the required equation of Circle is x² + y² - 10x + 20y + 116 = 0

Using the mean concept, it is found that the correct option regarding the sample mean is given by:

b. can be smaller, larger, or equal to the population mean.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

No matter the population mean, the sample mean is calculated as stated above, having no restrictions about it's value, hence option b is correct.

More can be learned about the mean concept at https://brainly.com/question/24628525

#SPJ1

{11, 17, 27}

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

Explanation:

Let's go through the answer choices.

Now return back to choice C. Notice how adding any two sides leads to a sum larger than the third side

The three conditions of the triangle inequality theorem are met, so a triangle is possible for choice C.

Answer: B and C

Step-by-step explanation:

404 + 50 + 50 = 504

you are buying  144 magazines total

504/144 = cost of one magazine

cost of one = 3.50

you are paying $60 a year for 12 years

60 x 12 = 720

720/144 = 5

5 - 3.50 = 1.50

2.

120x + 180x = 1080

300x = 1080

x = 1080/300

x = 3.6

3.6 x 60 = 216

Answer:

above 84°/. of the vehicles have a gas mileage greater then 24 mpg

Answer:

The answer is D

Step-by-step explanation:

(7/x² × x²)+(1/3×x²)+(x+2/x × x²)

(7 + x/3 + x²+2x) times 3 to eliminate the 3 under x/3

so u will get 21+x+3x²+6x

Final answer = 3x²+7x+21

Answer:

sorry the image isnt clear

Answer:

Can you post it again but clearer

Answer: 907.46

Step-by-step explanation:

Answer:

c. 3/5

Step-by-step explanation:

Answer:

Hope the picture will help you!!

un punto en un gráfico de líneas es un valor específico que normalmente es un valor de entrada y salida (x)

Ray is [tex]x[/tex] years old.

Ron is [tex]y[/tex] years old.

In 2 years, Ron will be two years older than now, so [tex]x+y+2[/tex] years old.

Answer:

39

Step-by-step explanation:

all angles of a triangle equal to 180, so you just have to subtract those two known angles from 180, and you will get the answer.

Find the value of angle x .

The concept of this question belongs to angles of triangle . We know that the sum of all the three angles of triangle is 180°.

As we know that all the angles of triangle is equal to 180° . So :

Therefore , angle x is of 39° .

Answer:

Step-by-step explanation:

General form of the linear differential equation can be written as:

[tex]\frac{dy}{dx}+P(x)y=Q(x)[/tex]

For this case, we can rewrite the equation as:

[tex]\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}[/tex]

Here [tex]P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}[/tex]

To find the solution (y(x)), we can use the integration factor method:

[tex]Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx[/tex]

Then [tex]F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}[/tex]

So, we can find:

[tex]y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C[/tex]

Suppose that [tex]x\in \double R[/tex], then [tex]\sqrt{|x|}=\sqrt{x}[/tex] , and we find:

[tex]y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}[/tex]

To check our solution is right or not, put your y(x) back to the ODE:

[tex]y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}[/tex]

[tex]2xy'=\frac{x-C}{\sqrt{x}}[/tex]

[tex]2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}[/tex]

(it means your solution is right)