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Answer:

I. Radius, r = 2.90 cm

II. Height, h = 4.10 cm

Step-by-step explanation:

Given the following data;

Volume of cone = 24 cm³

To find the height and radius of the cup that will use the smallest amount of paper;

Mathematically, the volume of a cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]  ......equation 1

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the formula, we have;

[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]

Multiplying both sides by 3, we have;

[tex] 108 = \pi r^{2}h[/tex]

Making radius, r the subject of formula, we have;

[tex] r^{2} = \frac {108}{ \pi h} [/tex]

Taking the square root of both sides, we have;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

Mathematically, the lateral surface area of a cone is given by the formula;

[tex] LSA = \pi rl [/tex]  ......equation 2

Where;

r is the radius of a cone

l is the slant height of a cone.

To find the slant height, we would apply the Pythagorean' theorem;

[tex] l = \sqrt {r^{2} + h^{2}} [/tex]

Substituting r into the above equation, we have;

[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Substituting the values of r and l into eqn 2, we have;

[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]

Simplifying further, we have;

[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]

[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]

Next, to find the value of h, we differentiate the above mathematical equation with respect to h;

[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]

Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;

[tex] \frac {dS}{dh} = 0 [/tex]

[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]

Rearranging the equation, we have;

[tex] \pi = \frac {216}{h^{3}} [/tex]

We know that π = 3.142

[tex] 3.142 = \frac {216}{h^{3}} [/tex]

Cross-multiplying, we have;

[tex] 3.142h^{3} = 216 [/tex]

[tex] h^{3} = \frac {216}{3.142} [/tex]

[tex] h^{3} = 68.75 [/tex]

Taking the cube root of both sides, we have;

Height, h = 4.10 cm

Lastly, we find the value of r;

[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]

[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]

[tex] r = \sqrt { \frac {108}{12.88}} [/tex]

[tex] r = \sqrt {8.39} [/tex]

Radius, r = 2.90 cm

The height and radius of the cup that will use the smallest amount of paper is;

Radius = 2.52 cm

Radius = 2.52 cmHeight = 3.58 cm

Let us first state some relevant formulas;

Volume of a cone is;

V = ⅓πr²h

Surface area of a cone is;

S = πrL

Where L is Slant height and has a formula;

L = √(h² + r²)

We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³

24 = ⅓πr²h

πr²h = 72

r = √(72/πh)

Putting √(72/πh) for r in the Slant height equation gives;

L = √(h² + (72/πh))

Thus;

S = π × √(72/πh) × √(h² + (72/πh))

Differentiating with respect to h gives;

dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)

At dS/dh = 0,we will have;

(π - 144/h³) = 0

Thus;

h³ = 144/π

h = 3.58 cm

Thus, from r = √(72/πh);

r = √(72/(π × 3.58))

r = 2.52 cm

Read more at; https://brainly.com/question/4405937

Answer:

(a) The time to complete 1 cycle and return is 16/3

(b) The minimum height is 30 inches and the maximum is 54 inches

Step-by-step explanation:

Given

[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]

Solving (a): Time to complete 1 cycle and return

This implies that we calculate the period.

This is calculated using:

[tex]T = \frac{2\pi}{w}[/tex]

Where:

[tex]w = \frac{3\pi}{8}[/tex]

So, we have:

[tex]T = \frac{2\pi}{3\pi/8}[/tex]

Rewrite as:

[tex]T = \frac{8*2\pi}{3\pi}[/tex]

[tex]T = \frac{16}{3}[/tex]

Solving (b): The maximum and the minimum height

To do this, we have:

[tex]-1 \le \sin(\theta) \le 1[/tex]

Which means:

[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]

So, the maximum and the minimum of [tex]\sin(\frac{3\pi}{8})[/tex] are:

[tex]\sin(\frac{3\pi}{8}) = -1[/tex] --- minimum

[tex]\sin(\frac{3\pi}{8}) = 1[/tex] --- maximum

Given that:

[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]

So, the minimum height is:

[tex]h_{min} = 12 * -1 + 42 = 30[/tex]

The maximum is:

[tex]h_{max} = 12 * 1 + 42 = 54[/tex]

Answer: 18 cm

Step-by-step explanation: 9 feet x 2

Answer:

Last one (x + 4, y - 1).

Step-by-step explanation:

From the point, you go right 4 (going right on a graph is positive).

From there, you go down 1 (going down on a graph is negative).

192 because if you put 24 into 8 groups there are 192

Answer:

[tex]Mean=79[/tex]

[tex]\sigma=30.3951.[/tex]

Step-by-step explanation:

From the question we are told that:

[tex]Age Bracket :19-20[/tex]

[tex]5th\ percentile = 42[/tex]  

[tex]50th\ percentile = 79[/tex]  

[tex]95th\ percentile = 142.[/tex]

Generally the mean Median and mode of the 50th percentile is are all equal

[tex]Mean=Median=Mode[/tex]

Therefore

[tex]Mean=79[/tex]

Generally for Normal distribution

[tex]5th\ percentile\ = mean - 1.645*\sigma[/tex]  

[tex]95th\ percentile\ = mean + 1.645*\sigma[/tex]

Therefore

[tex](95th\ percentile\ - 5th\ percentile) = 2*(1.645*SD).[/tex]

[tex]\sigma=(95th\ percentile\ - 5th\ percentile)/3.29[/tex]

[tex]\sigma=\frac{142-42}{3.29}[/tex]

[tex]\sigma=30.3951.[/tex]

Answer: the required sample size =1658944

Step-by-step explanation:

When the prior population proportion for the study is unknown , then the formula for sample size is [tex]Sample \ size = 0.25(\dfrac{z^*}{Margin\ of \ error})^2[/tex]

z-value for 99% confidence = 2.576

[tex]Sample \ size = 0.25(\dfrac{2.576}{0.001})^2\\\\=0.25(2576)^2\\\\=1658944[/tex]

Hence, the required sample size =1658944

Answer:

-4/3

Step-by-step explanation:

2(-2/3)

= -4/3

Answer:

[tex]( \frac{x}{y} ) \times t \\ \frac{ - 2}{3} \times 2 \\ = \frac{ - 4}{3} [/tex]

Answer:

Slope = 15/4

Step-by-step explanation:

Use the slope formula and you'll get the same answer.

Hope this helps:)

Answer:

I am

Step-by-step explanation:

Answer:

4cp^2 ( 4c^3+5p

Step-by-step explanation:

See image below:)

The factored form of the expression will be [tex]4cp^2 (4c^3+5p)[/tex]

Given the expression  16c^4p^2+20cp^3​

Get the factor for each term

From the factors, you can see that 4cp^2 is common to both terms. Hence the factored form of the expression will be:

[tex]4cp^2 (4c^3+5p)[/tex]

Learn more on factored form here: https://brainly.com/question/25948667

Answer:

Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the most positive and the most negative comments to evaluate the airlines will not be an accurate measure of the airline because these are not a good enough sample. The opinions of those who fall in-between the most positive and negative should also be included as they could have some vital details as well.

Also, in order to be completely accurate, all the comments of the airline should have been posted because this would represent the entire population of comments and so would give the best assessment.

9514 1404 393

Answer:

  1 to 5

Step-by-step explanation:

20 cm to 1 m = 20 cm to 100 cm = 20 to 100 = 1 to 5

Answer:

A

Step-by-step explanation:

Hi there!

The given equation of the line is in slope-point form, which is y-y1=m(x-x1), where (x1,y1) is a point and m is the slope

the given equation is y-5=-3(x - 17)

-3 is in the place of where m is, so -3 is the slope. Remember that the sign is part of the slope, so it can't be B (3). Therefore, the answer is A

Hope this helps!

Answer:

10%

Step-by-step explanation:

10% of the Male students have blonde hair

Answer:

D

Step-by-step explanation:

Base perimeter = side x 5 = 8 x 5 = 40 cm

LA = (base perimeter x slant height)/2 = (40 x 9)/2 = 180 cm^2

SA  = base area + lateral area = 110.1 + 180 = 290.1 cm^2

Answer:

The answer is 23

Step-by-step explanation:

Answer:

the answer of the question is 23

Answer:

30 and 60

Step-by-step explanation:

Let x represent the first angle

(x) the sum of the first angle plus twice of the second angle 2(90 - x)

x + 180 - 2x = 150

180 - 150 = 2x - x (we export like terms to the same side of the equation)

30 = x is the measure of the first angle and since the second angle is complementary to this the measure of the second angle is 90 - 30 = 60

Answer:

8.8

Step-by-step explanation:

Akhtar's bonus = 20% × £70 = £14

karl's bonus = 20% × £26 = £5.2

Difference = £14 - £5.2 = 8.8

**I'm not sure about the answer sorry, please get it checked.

Answer: Hello the system of equations and other data required are missing attached below are the missing data

answer :

attached below

Step-by-step explanation:

1st system of equations ( top left ) = Image number 8

system of equation ( Image 10 ) = Image 4

system of equation ( Image 9 ) = Image 6

system of equations ( Image 7 ) = Image 2

attached below is a pictorial representation of the solution

Answer:

The y-intercept of function a is greater than the y intercept of function b

Step-by-step explanation:

function a:

y = 4x + 2

function b:

y = 2x + 1

Answer:

(B) part is the answer which means he shook hands with 2.

Step-by-step explanation:

Since Dora shook hands four time with: Alan, Bella, Claire, Erik. Then Erik shook hands only with Dora. Claire shook hands three times with Bella, Claire and Dora. Then Bella shook hands with two people Claire and Dora. Now Erik would shook hands only with those who shook hands with him. 2 people Claire and Dora

The required handshake Erika had is given as 2. Option B is correct.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
According to the question,

Dora shake hands 4 times,
So Dora shakes hands with Anna, Bella, Claire, and Erika.

Anna shake hands 1 time,
From the above combination.
Dora shakes hands with Anna,
Implies Anna does not shake hands with Erika,

Clair shakes hands 3 times,
So Clair shakes hands with Bella, Claire, and Erika.

Bella shake hands 2 times,
So Bella shakes hands with Bella and Claire.

From the above reasoning, Erika shakes hands with Dora and Clair.

Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2

Answer:

x =3702.5

Step-by-step explanation:

Given data

(120+2x)+(70+2x)=15,000

Let us open the bracket

120+2x+70+2x=15,000

Collect like terms

120+70+2x+2x=15,000

190+4x=15000

4x=15000-190

4x= 14810

Divide both sides by 4

x=14810/4

x= 3702.5

Hence the value of x =3702.5

Answer:

7 lol

Step-by-step explanation:

self explanatory-

but you divide 1 by 7 you get 7

Answer:

Step-by-step explanation:

This is really super super simple as long as you know the rules for finding a perpedicular slope from a given line. The perpendicular slope of a line is the opposite reciprocal of the given slope. Our given slope is 3/5, therefore, the perpendicular slope is -5/3. There's only one line with that exact slope, so the choice is the last one. (BTW, check the coordinate you gave. It should be

(15, -5), not (15, 5)!)

Answer:

Figure D. (A)

When you flip the figure across like a mirror, it remains the same shape as the other side. An easy way to determine this is by cutting a line down the middle.

Reflectional symmetry states that if there exists at least one line that divides a figure into two halves such that one-half is the mirror image of the other half.

Edit: Typo!

Answer:

4

Step-by-step explanation:

in y=mx+b, the "b" is the y-intercept

Answer:

4

it's in y = mx + b form, where b is the y-intercept

Answer:

The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.

Step-by-step explanation:

Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:

5X + 7 x (X + 8.50) = 245.50

5X + 7X + 59.50 = 245.50

12X + 59.50 = 245.50

12X = 245.50 - 59.50

12X = 186

X = 186/12

X = 15.50

Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.