In each diagram, abc is a straight line. Find the unknown angles.

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:

Length = 12 m, Width = 8 m

Step-by-step explanation:

Let the width of the rectangle is b.

Length, l = 4+b

The perimeter of the rectangle = 40 m

We know that,

Perimeter of rectangle = 2(l+b)

2(4+b+b) = 40

4+2b = 20

Subtract 2 from boths sides,

2b = 16

b = 8

Width = 8 m

Length = 4+8 = 12 m

Hence, the length and the width of the rectangle is 12 m and 8 m respectively.

Answer:

Slope = 15/4

Step-by-step explanation:

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

Hope this helps:)

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:

(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:

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:

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:

d

Step-by-step explanation:

180-149= 31.

31+ 122= 153

180-153= 27

a= 27

Answer:

54 square inches

Step-by-step explanation:

9 times 12 is 108. That is the area of a rectangle with the same length and width/height. A right triangle is half of that. So 108/2=54

Hi there!  

»»————-　★　————-««

I believe your answer is:  

Option B  

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Area of A Triangle:}}\\\\---------\\\frac{b*h}{2}\\\\\boxed{\text{Key:}}\\\\\text{b - base}\\\text{h - height}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Finding the area of the Triangle:}}\\\\-------------\\\ \frac{9*12}{2}\\\\\rightarrow\frac{108}{2}\\\\\rightarrow \boxed{54}\\\\\text{The area should be 54 square inches.}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

B. (1, 2)

D. (-10, 1)

Step-by-step explanation:

Both points land in the highlighted area.

Hope this helps! :)

Answer:

The correct answer would be

A. (–12, 0) & D. (–10, 1)

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:

step one 1 ×3 = 4

Step-by-step explanation:

how first fo ther

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.

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:

7 lol

Step-by-step explanation:

self explanatory-

but you divide 1 by 7 you get 7

Answer:

x = 13

Step-by-step explanation:

The sum of the exterior angles of a 4 sided polygon is 360

139+ 6x+9x+2x = 360

Combine like terms

139+17x=360

Subtract 139 from each side

17x = 360-139

17x = 221

Divide each side by 17

17x/17 = 221/17

x = 13

Answer:

2 Function B

Step-by-step explanation:

Answer:

Function B is greater

Step-by-step explanation:

The gradient of Function B is of 3 = m

Though the gradient of Function A  is of 1 = m, obviously being of the smaller size

If you didn't know, gradient is the same as the slope

Hope this helps

Answer:

6.n/4

7.3/4time G or 0.75G

Step-by-step explanation:

6.3m+n/12-m-n/4=3m-3m+n+3n=4n/12=n/4

7.G=0.9a/1.2b G=3/4*a/b

Answer:

0.9961

Step-by-step explanation:

Number of options per question = 2

P(success), p = 0.5

q = 1 - p = 0.5

Number of trials, n = 8

P(x ≥ 1) = p(x= 1) + p(x=2) +... + p(x = 8)

P(x = x) = nCx * p^x * q^(n-x)

Using a calculator to save computation time :

p(x ≥ 8) = 0.9961

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:

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).

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:

10%

Step-by-step explanation:

10% of the Male students have blonde hair

Answer:

I am

Step-by-step explanation:

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

9514 1404 393

Answer:

  ∠A ≈ 72°

Step-by-step explanation:

Fill in the given numbers and do the arithmetic.

  cos A = (2.9² +2.5² -3.2²)/(2(2.9)(2.5)) = 4.42/14.5

The inverse cosine function is used to find the angle, given its cosine.

  A = arccos(4.42/14.5)

  ∠A ≈ 72°

9514 1404 393

Answer:

  a) 2π radians

  b) 10π inches

  c) 5/4π inches per minute

Step-by-step explanation:

The formulas are fairly straightforward. Use the given values in each.

a) θ = ωt

  θ = (π/4 radians/min)(8 min) = 2π radians

__

b) s = rθ

  s = (5 in)(2π radians) = 10π in

__

c) v = s/t

  v = (10π in)/(8 min) = 5/4π in/min

Answer:

50

Step-by-step explanation:

6m-n

Let m = 9 and n = 4

6*9-4

Multiply first

54-4

Then subtract

50

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!