The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle $n^\circ.$ Find $n.$

The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2  - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

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The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10

A quadratic polynomial is a polynomial of the form ax² + bx + c

For any given quadratic polynomial we have

x² - (sum of zeros)x + (products of zeros) = 0

Given that the sum and product of its zeroes respectively 3/2 and 5,

We have that

Substituting the values of the variables into the equation, we have

x² - (sum of zeros)x + (products of zeros) = 0

x² - (3/2)x + (5) = 0

x² - (3/2)x + (5) = 0

Multiplying through by 2, we have

2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2

2x² - 3x + 10 = 0

So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10

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Answer:

[tex]69 = 6x - 8[/tex]

Step-by-step explanation:

All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]

Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.

This leaves you with the one final answer [tex]69 = 6x - 8[/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(h)^2 = (p)^2 + (b)^2

(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (√12)^2 + (√30)^2

→ x^2 = 12 + 30

→ x^2 = 42

→ x = √42

→ x = 6.480...

→ x = 6.5 cm. (approx)

(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√300)^2 = (x)^2 + (√200)^2

→ 300 = x^2 + 200

→ x^2 = 300 – 200

→ x^2 = 100

→ x = √100

→ x= 10 cm.

(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.

→ h^2 = p^2 + b^2

→ (√66)^2 = (x)^2 + (√17)^2

→ 66 = x^2 + 17

→ x^2 = 66 – 17

→ x^2 = 49

→ x = √49

→ x = 7 cm.

(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.

→ h^2 = p^2 + b^2

→ (x)^2 = (2√3)^2 + (5√12)^2

→ x^2 = 12 + 50

→ x^2 = 62

→ x = √62

→ x = 7.874...

→ x = 7.9 cm. (approx)

Answer:

Step-by-step explanation:

hello:

here an solution

The equations of the corresponding circles can be any equation only have to satisfy the  general equation for circle .

The question seems incomplete and complete question given in the image !!!!

A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)

We know that the general equation for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where ( h, k ) is the center and r is the radius.

According to the question

The equation of circle given is [tex]x^2+y^2=1[/tex]

Center at origin

i.e

(h,k) = (0,0)

and radius = 1 unit

Now ,

By changing changing center (h,k) and radius of equation it will give following equations

h                      k                       r                            equation of circle

0                       1                       3                      [tex](x-0)^2+(y-0)^2=3^2[/tex]  

2                       2                       3                       [tex](x-2)^2+(y-2)^2=3^2[/tex]

1                        1                        1                     [tex](x-1)^2+(y-1)^2=1^2[/tex]  

-2                      -1                       2                      [tex](x+2)^2+(y+1)^2=2^2[/tex]

3                       2                       1                        [tex](x-3)^2+(y-2)^2=1^2[/tex]      

-5                      1                        3                       [tex](x+5)^2+(y-1)^2=3^2[/tex]

Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .

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The equivalent expression is:

[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]

Which is the one in option A.

Here we start with the expression:

[tex]m^{5/2}[/tex]

Now, remember that:

[tex]\sqrt{x} = x^{1/2}[/tex]

[tex](x^a)^b = x^{a*b}[/tex]

if we define a = 5 and b = 1/2, we get:

[tex]m^{5/2} = (m^5)^{1/2}[/tex]

Using the first property, we get:

[tex](m^5)^{1/2} = \sqrt{m^5}[/tex]

Then we conclude that the correct option is A.

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Answer:

-31, /~26, -5, 6

Step-by-step explanation:

The Law of sines defines that in a triangle, (Sin A)/a = (Sin B)/b = (Sin C)/c and as per law of sines the length of BC is 24.

The given triangle is ΔABC, we split the given triangle into two right-angled triangle ΔABD and ΔBCD.

In the triangle ΔABD,

sin θ = opposite side/hypotenuse

sin A=BD/AB

BD=(sin A)/AB

And in the triangle ΔBCD,

sin θ = opposite side/hypotenuse

sin B=BD/BC

BD=(sin B)/BC

Hence, BD=(sin A)/AB=(sin B)/BC

Let say, (sin A)/a=(sin B)/b

As per law of sine, (sin A)/a=(sin B)/b

Then,

(sin 46°)/a=(sin 31°)/17

a=(17 × sin 46°)/(sin 31°)

a=23.74

a=24

Hence, the value of BC, rounded to the nearest tenth of a unit is 24.

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Answer:

(f - g)(300) = $1,300 is the profit made from 300 tablets

Step-by-step explanation:

(f - g)(300) is the profit made from 300 tablets

(f - g)(x) = (3 x + 6,000) - (20 x - 400)

- Simplify it

(f - g)(x) = 3 x + 6,000 - 20 x + 400

- Add like terms

(f - g)(x) = -17 x + 6,400

Substitute x by 300

(f - g)(300) = -17(300) + 6,400

(f - g)(300) = -5,100 + 6,400

(f - g)(300) = $1,300

The profit is $1,300

Answer:

12

Step-by-step explanation:

The area of a triangle is calculated with the following formula:

[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))

We can use this formula to find the length of the other leg:

30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction

60 = b*h one of the leg's length is given as 5 so

60 = 5*h divide both sides by 5

12 = h is the length of the missing leg.

Answer:

range of the given set is { 7,2,4,2,1}

Step-by-step explanation:

. Hello !

When the above kind of set is given the second values of each elements belongs to the range or the y whereas, the first values of the elements belongs to the domain or x.

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

This question is incomplete, the missing diagram is uploaded along this answer below.

Area of a rectangle is expressed as; A = l × b

Given that;

A = l × b

180in² = 20in × x

x = 180in² / 20in

x = 9in

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

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See below for the solution to each question

Yes, the graph is a function.

This is because all x values have different y values

This is the set of input values of the graph.

From the graph, we have

x = 0 to x = 17

Hence, the domain is [0, 17]

This is the set of output values of the graph.

From the graph, we have

y = 0 to y = 10

Hence, the range is [0, 10]

This is the maximum point on the graph.

From the graph, we have

Maximum = (12, 10)

This is the minimum point on the graph.

From the graph, we have

Minimum = (0, 0)

These are the intervals where the y values increase as x increase.

From the graph, we have

Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)

These are the intervals where the y values decrease as x increase.

From the graph, we have

Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)

These are the intervals where the y values remain unchanged as x changes.

From the graph, we have

Constant intervals = (5, 7)

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The length of string used to decorate the ceiling = 40.5 meters.

According to the statement

we have given that the hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular ceiling.

And the coordinates of rectangular ceiling is A(5,16), B(17,10), C(14,4), D(2,10).

And we have to find the total length for string is used to decorate the rectangular ceiling.

We know that the Total length of string = Area of the rectangular ceiling.

And area of rectangular ceiling = L*B

So, Length of rectangular ceiling = A+B

Length of rectangular ceiling = (17-5) + (16-10)

Length of rectangular ceiling = (12+6)/2

Length of rectangular ceiling = 9.

So,

Breadth of rectangular ceiling = B+C

Breadth of rectangular ceiling = (17-14)+(10-4)

Breadth of rectangular ceiling = (3+6) /2

Breadth of rectangular ceiling = 4.5

So, the length of string used = 4.5*9

the length of string used = 40.5 meters.

The length of string used to decorate the ceiling = 40.5 meters.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

The hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular celling. A member of the s⊥aff maps the celling on a coordinate grid as shown, where each unit represents . What is the approximate length of string lights the staff needs to decorate the ceiling?

A 20.25 meter

B. 35 meter

C. 40.5 meter

D. 14 meter

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Answer:

D. none

Step-by-step explanation:

we only know about the right angle at the bottom right.

that is not enough information.

we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.

like the other answer options would indicate :

SAS : side - angle - side.

2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.

SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.

HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).

since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.

Answer:

See below

Step-by-step explanation:

Go across the 'x' axis to '6'....then go UP to the graph to find y = 60

 after 6 minutes he has rowed 60 meters

The function can be solved as follows:

f(x) = 3x - 5

Therefore, the function can be solved as follows:

f(6 + 4) = f(10) = 3(10) - 5 = 25

f(6) + f(4) = 3(6) - 5 + (3(4) - 5)

f(6) - f(4) = 13 + 7

f(6) - f(4) = 20

f(6 - 4) = f(2) = 3(2) - 5 = 6 - 5 = 1

f(6) - f(4) = 3(6) - 5 - (3(4) - 5)

f(6) - f(4) = 18 - 5  - (12 - 5)

f(6) - f(4) = 13 - 7

f(6) - f(4) = 6

f(6.4) = f(24) = 3(24) - 5 = 72 - 5 = 67

f(6) . f(4) = (3(6) - 5 ) (3(4) - 5)

f(6) . f(4) = (18 - 5)(12 - 5)

f(6) . f(4) = (13)(7) = 91

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Answer:

AP = 12, and FQ = 8

Step-by-step explanation:

The proportion between AB:FG and AP:FQ is the same.

--> 9:6 = AP:FQ

I'll say that FQ is x and AP is x+4 (since AP is 4 longer than FQ)

--> 9:6 = x+4:x

--> 6(x+4) = 9x

--> 6x + 24 = 9x

--> 24 = 3x

--> x = 8

Since AP= x+4 and FQ= x. AP becomes 12 and FQ becomes 8.

The length of side VW is 7.5 cm

The given parameters are:

DE is 6 cm, EF is 7.5 cm, and DF is 5 cm

Since the two triangles are congruent, then it means that:

So, we have:

VW= EF

The side EF is

EF = 7.5 cm

So, we have:

VW = 7.5 cm

Hence, the length of side VW is 7.5 cm

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The lower bound of the 90% confidence interval for the gift basket's average shipping weight is 55.605.

Given mean weight of 57 ounces ,sample size 70 ,confidence level 90% and standard deviation of 7.1 ounces.

We have to find the lower bound of the confidence interval for the gift's basket's avrage shipping weight.

We can easily find the confidence interval and its lower bound through theformula of margin of error.

Margin of error is the difference between real values and calculated values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the critical value of confidence level

σ is standard deviation,

n is the sample size

We have to first find the z value for 90% confidence level which is 1.645.

Margin of error=1.645*7.1/[tex]\sqrt{70}[/tex]

=11.6795/8.3666

=1.395

Lower bound of the confidence interval = Mean - margin of error

=57-1.395

=55.605.

Hence the lower bound of the confidence interval for the gift basket's average shipping weight is 55.605.

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Answer:

  (c)  f(x) = 3(x -3)(x -7)

Step-by-step explanation:

The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.

The graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...

  (x -3)(x -7) . . . . . . . . eliminates choices A and D

The vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.

Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)

Putting these observations together, we have determined the equation of the function to be ...

  f(x) = 3(x -3)(x -7) . . . . . . matches choice C

[tex]\textbf{Heya !}[/tex]

✏[tex]\bigstar\textsf{Given:-}[/tex]✏

✏[tex]\bigstar\textsf{To\quad find:-}[/tex]✏

▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪

✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex]✏

First, subtract both sides by 7:-

[tex]\sf{-\cfrac{y}{4} > -1-7}}[/tex]

[tex]\sf{-\cfrac{y}{4} > -8}[/tex]

Now multiply both sides by 4:-

[tex]\sf{-y > -8*4}[/tex]

[tex]\sf{-y > -32}[/tex]

last step:-

[tex]\sf{y < 32}[/tex]

`hope it was helpful to u ~

[tex] \implies \: \sf{ - \dfrac{y}{4} \: + \: 7 \: > \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 7 \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 8} \\ \\ \implies \: \sf{ \cancel- \: \dfrac{y}{4} \: > \: \cancel- \: 8} \\ \\ \implies \: \sf{ \dfrac{y}{4} \: < \: 8} \\ \\

\implies \: \sf{ y \: < \: 8 \times 4} \\ \\ \implies \: \bf{ y \: < \: 32}[/tex]

The domain of the function will therefore be 0≤x<∞

Domain of a function are the independent value for which a function exists. Given the function below;

f(x) = [tex]\sqrt[4]{x}[/tex]

Since the value in the root cannot be negative hence the domain of the function will be all positive real numbers.

The domain of the function will therefore be 0≤x<∞

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Answer:

x - 3 > 15

Step-by-step explanation:

Your question is incomplete. please read below for the missing content

y = -3/4x + 14 is the answer.

y = 4/3x+ 7...slope here is 4/3. A perpendicular will have a negative reciprocal slope. All that means is to flip the slope and change the sign.

4/3....flip it....3/4....change the sign....-3/4. So our perpendicular equation has to have a slope of -3/4

y = mx + b

slope(m) = -3/4

(4,11)...x = 4 and y = 11

now we sub and find b, the y int

11 = -3/4(4) + b

11 = - 3 + b

11 + 3 = b

14 = b

so ur line is : y = -3/4x + 14

The perpendicular line has the opposite slope of the reciprocal, so the slope of the line you want to find is 1/2. Inserting the given points into the equation y = 1 / 2x + b and solving b yields b = 6. Therefore, the linear equation is y = ½x + 6. When relocated, it becomes –x / 2+. y = 6.

Q)  What is the equation of the line that passes through the point (4,11) and is perpendicular to the line with the following equation y = 4/3x + 7

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The number of gallons of the 35% acid solution eli should add is; 0.125 gallons

From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

where g is number of gallons

Now,  for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

⇒ 0.05 + 0.35g = 0.15g + 0.075

⇒ 0.35g - 0.15g = 0.075 - 0.005

⇒ 0.2g = 0.025

g = 0.025/0.2

g = 0.125 g

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Answer:

10^4 =  10 × 10 × 10 × 10
       =  10000

Answer:

A

Step-by-step explanation:

By using greatest common factor you are able to take a 2 out of all the numbers

The system of equation have an infinite solution.

6x   = -6y - 30

-3x -3y = 15

Therefore, let's rearrange the system of equations.

6x + 6y = -30

-3x - 3y = 15

multiply equation(ii) by 2

6x + 6y = -30

-6x - 6y = 30

add the equations

0 = 0

Since 0 = 0 for any value of x, the system of equations has infinite solutions.

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