A capsule is in the form of a hollow cylinder surmounted by a hemispherical bowl of the same diameter, 12 cm on both ends. The total height of the capsule is 16 cm. Find the surface area of the capsule. п cm?

Answers

Answer 1

The surface area of the capsule is calculated by adding the surface area of the cylinder and the surface area of the hemispherical bowl.

What is the hemispherical bowl?

A hemispherical bowl is a type of bowl with a rounded bottom that is shaped like half of a sphere. It is often used in laboratories, kitchens, and dining rooms. The bowl’s curved surface prevents the contents from spilling, which makes it an ideal choice for mixing, swirling, and scooping. Additionally, the bowl’s shape makes it look aesthetically pleasing, so it can be used as a decorative piece as well.

The surface area of the cylinder = 2πr2 + 2πrh

Where r is the radius of the cylinder and h is the height of the cylinder.

The radius of the cylinder = 12 cm

The height of the cylinder = 16 cm

Therefore, the surface area of the cylinder = 2π(12)2 + 2π(12)(16) = 1536π cm2

The surface area of the hemispherical bowl = 2πr2

Where r is the radius of the hemispherical bowl.

The radius of the hemispherical bowl = 12 cm

Therefore, the surface area of the hemispherical bowl = 2π(12)2 = 144π cm2

The total surface area of the capsule = 1536π cm2 + 144π cm2 = 1680π cm2

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Related Questions

Find three points on the parabola.
x^2−6x−4y+5=0

Answers

Answer:

(0,1.25), (1,0), (-1,3)

Step-by-step explanation:

Find the perimeter of the figure. Round to the nearest tenth.
answer.
3 ft
3 ft
20 ft
5 ft
14 ft
Perimeter
feet

Answers

Answer:

Step-by-step explanation:

Add the sides together:

3+3+20+5+14=45

Find the H.C.E of 108 and 72.

Answers

Answer:

36 is the HCF of 108 and 72

Answer:

36.

Step-by-step explanation:

HCF of 108 and 72

108 = 2 * 2 * 3 * 3 * 3

72 = 2 * 2 * 2 * 3 * 3

So picking out the common factors we have

HCF = 2 * 2 & 3 * 3

= 4 * 9

= 36.

Write an equation that shows the relationship 40% of 140 is x

Answers

Answer:

x=140times0.4

Step-by-step explanation:

then subtract your anser from 140

Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 13)(0,13) and (3, 832)(3,832).

Answers

Answer: Down Below

Step-by-step explanation: y=ab%5Ex

that goes through points (0, 10) and (2, 490)

y=ab%5Ex.......plug in (0, 10)

10=ab%5E0

10=a%2A1

a=10

so far

y=10b%5Ex......plug in (2, 490)

490=10b%5E2

b%5E2=490%2F10

b%5E2=49

b=sqrt%2849%29

b=7

your function is:+y=10%2A7%5Ex

A function assigns the values. The exponential function that goes through (0, 13) and (3, 832) is y=13(4)ˣ.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given the exponential eqation is y=abˣ, substitute any one of the point in equation we will get,

13 = ab⁰

13 = a ₓ 1

a = 13

Therefore, the function can be written as y=13bˣ.

Substitute other point in the equation,

832 = 13 (b³)

b³ = 832/13

b³ = 64

b = 4

Hence, the exponential function that goes through (0, 13) and (3, 832) is y=13(4)ˣ.

Learn more about Function:

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First, by the Complex Root Theorem, if 1 + i is a zero, then 1 - i must also be a zero.

Therefore:

[tex]f(x)=1(x-(0))(x-(1))(x-(1+i))(x-(1-i))[/tex]

Simplify:

[tex]f(x)=x(x-1)(x-(1+i))(x-(1-i))[/tex]

Expand the third and fourth factors:

[tex](x-(1+i))(x-(1-i))=(x-(1+i))(x)-(x-(1+i))(1-i)[/tex]

Distribute:

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

Expand:

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

Therefore:

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

Hence, our polynomial function is:

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

The regular price of an item at a store is $2,000. If the sale price is $1,120, what percent is the discount?

Answers

Answer:

$3,120

Step-by-step explanation:

$2,000

+$1,120

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

$3,120

Hence, the percent is the discount is $ [tex]3120[/tex].

What is the percentage?

A percentage is a number or ratio expressed as a fraction of [tex]100[/tex]. It is often denoted using the percent sign, "%".

Here given that,

The regular price of an item at a store is $[tex]2,000[/tex]. If the sale price is $[tex]1,120[/tex].

So,

[tex]2,000+1120=3120[/tex] $

Hence, the percent is the discount is $ [tex]3120[/tex].

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Determine if the following function is even, odd or neither.
f(x) = 4x2 – 8x + 5

Answers

9514 1404 393

Answer:

neither

Step-by-step explanation:

A polynomial consisting of even-degree terms only is even.

A polynomial consisting of odd-degree terms only is odd.

The given f(x) polynomial has both even- and odd-degree terms, so is neither.

A line segment has an endpoint at (-7, 11) and (-6, 4), what is the length of
the segment?

Answers

Answer:

d = 5√2 units

Step-by-step explanation:

Let's use the distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Plug in the values with your endpoints.

d = √[(-6 - (-7))² + (4 - 11)²]

Solve within the parentheses.

d = √[(1)² + (-7)²]

Solve the exponents.

d = √[1 + 49]

Solve within the brackets.

d = √50

Simplify the square root.

25 • 2 = 50

√25 • √2 = √50

5 • √2 = √50

d = 5√2 units

Hope this helps!

Find the value of x. I WILL GIVE 100 POINTS ANSWER QUICK!

Answers

Answer:0.714 not sure exactly if i need to simplify, mullitiply, or divide.

Step-by-step explanation:

the answer is 0.714 ! hope this helped clarify

Directions: Find the missing term in each pair of equivalent ratios.
1. 3:4 = 21:n
2. 1:5 = n : 40
3. 2 : n = 8 : 12
4. n = 2
42 7

5. 4 = 20
9 n

Answers

Step-by-step explanation:

1 multiplied by 7

3;4=21:28

2) multiplied by 8

1:5= 8:40

3)divided by 4

2:3= 8:12

4) multiplied by 6

12/42= 2/7

5) multiplied by 5

4/9= 20/45

22×(4.5×4.5×4.5+9)=

what is the answer?

Answers

2202.75 is the answer

Answer:

2202.75

Step-by-step explanation:

calculator

Which is the inverse of the function f (x) = 1/4x + 1/2

Answers

Answer:

f⁻¹(x) = 4x - 2

Step-by-step explanation:

To find the inverse of a function, switch the places of x and y (or f(x)).

f(x) = 1/4x + 1/2 → y = 1/4x + 1/2

Switch the variables.

x = 1/4y + 1/2

Now you want to convert the equation back into y = mx + b form.

x = 1/4y + 1/2

Subtract 1/2 from both sides.

x - 1/2 = 1/4y

Now, you want to isolate y further by dividing both sides by 1/4 (or multiplying by 4).

4(x - 1/2) = y

Distribute the 4.

4x - 2 = y → y = 4x - 2 → f⁻¹(x) = 4x - 2

This is the inverse of your given function.

Translate this sentence into an equation.

64 is the product of Goran’s height and 4

Use the variable g to represent Goran’s Height

Answers

Answer:

g×4=64

product means multiply

so that would mean Gorans height times 4 and that would all equal 64

hope this helped

if the measure of angle a is 109, what is the measure of angle b

Answers

Answer:

Step-by-step explanation:

Those are supplementary angles meaning they add up to 180 degrees

180 - 109 = 71

That would make b 71 degrees

Answer:

71 degrees !!

Step-by-step explanation:

Since the angles A and B both are next to each other, they form a linear pair. Since they are a linear pair, they both add up to 180 degrees (same as a straight angle!) So, if A is 109, you would simply subtract that from 180, and you'd get 71 !!

180-109= 71 !!

I hope this helps... have a great day !

At lunch time, Benjamin often borrows money from his friends to buy snacks in the school cafeteria. Benjamin borrowed $0.75 from his friend Clyde five days last week to buy chips. Represent the amount Benjamin borrowed as the product of two rational numbers; then, determine how much Benjamin owed his friend last week.

Answers

Answer:

3.75

Step-by-step explanation:

x/(x-2)*(x+2)*(x-1) into partial fraction
no matter how many times i redo it my answers just not matching with that of my books. can we have different answers?

Answers

Answer:

((-1 + x) (2 + x) X)/(-2 + x)

Step-by-step explanation:

1 (x^(2)x)/(x-2)+(xx)/(x-2)-(2x)/(x-2)

2 (x(x+1)-2)x)/(x-2)

3 (x(xx+x)-2x)/(x-2)

4(x^(2)x+xx-2x)/(x-2)

5 (-2 + x + x^2) X)/(-2 + x)

Root

X = 0 , X-2=0

Roots

X=-2

X=1

Michael and Imani go out to eat for lunch.

Part A: If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill?

Part B: If Michael and Imani add an 18% tip to the bill, what does their lunch cost in total?

Answers

Answer:

Step-by-step explanation:

part=A

So, we must find out what the total bill cost is such that we begin by multiplying the price with the tax such that $25.30(0.08) = $2.024.

Then we add the tax to the price such that

$25.30+2.024 = $27.32

In the case of adding an 18% tip,

So continuing on from the above post, $27.32 is the total after taxes. Then we add an 18% tip which is

$27.32 (.18) = $4.92..........Then, we add it to the $27.32 to get

$27.32 + $4.92 = $32.24 in total!

Find the value of x.

Answers

Answer:

I think the answer is x=120

PLEASE HELP!
4x + 2y = 6
-2x + 2y = 18
There combined answer please!
SHOW YA WORK

Answers

Step-by-step explanation:

From the given information;

The null hypothesis & alternative hypothesis:

[tex]\mathbf{H_o:\mu = 2} \\ \\ \mathbf{H_1 : \mu \ne 2}[/tex]

The test statistics can be computed as:

[tex]Z = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \dfrac{2.025- 2}{\dfrac{0.07}{\sqrt{35}}}[/tex]

[tex]Z = \dfrac{0.025}{\dfrac{0.07}{\sqrt{35}}}[/tex]

[tex]Z =2.11[/tex]

The p-value = 2(Z > 2.11) since this is a two-tailed test

The p-value = 2( 1 - Z < 2.11)

The p-value = 2 (1 -0.9826)

The p-value = 2 (0.0174)

The p-value = 0.0348

Decision Rule: To reject the [tex]\mathbf{H_o}[/tex] if the p-value is less than [tex]\mathbf{H_o}[/tex]

Conclusion: We fail to reject [tex]\mathbf{H_o}[/tex] and conclude that the population mean = 2, thus the machine is properly adjusted.

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