A cubical block of side 14 cm is surmounted by a hemisphere . what is the greatest radius that the hemisphere can have?

Answers

Answer 1

Answer:

9.9cm

Step-by-step explanation:

The hemisphere will have its greatest radius along the diagonal of the cube it was surmounted on. The base of the cubical block will be square in nature. Since a cube has all its sides equal, we can find the length of its diagonal using pythagoras theorem as shown.

[tex]hyp^{2} = adj^{2} +opp^{2}[/tex]

Note that the diagonal will be the hypotenuse of the square face which is the longest sides.

Given adjacent = 14cm and opposite = 14cm

[tex]hyp^{2} = 14^{2} +14^{2}\\hyp = \sqrt{196+196} \\hyp = \sqrt{392} \\hyp = 19.8cm[/tex]

The diagonal of the base of the cube is 19.8cm which is equivalent to the greatest diameter of the sphere.

The greatest radius that the hemisphere can have = 19.8/2 = 9.9cm

Answer 2
General Formulas and Concepts:Geometry

Drawing diagrams

Circles

Radius rDiameter dRelationship between r and d:
[tex]\displaystyle r = \frac{d}{2}[/tex]

Cubes

Length lWidth wHeight h

Application:

Let's draw a figure to supplement a visual image to further understand what we need to find. Please refer to the attached image for reference. Please excuse the poor handwriting/drawing. It is also not to scale.

We know that there is a cubical block w/ side measurements of 14 cm. "Surrmounted" means on top. So a hemisphere (half of a sphere) is on top of our block.

If we take a look at our geometrical shape from the top-down angle, we can see that the top would just look like a circle within a square, as depicted in blue.

Labeling our measurements, we can see that the length, width, and height of our cubical block are equal to 14 cm due to the definition of a cube. This extends to the definition of a square as well, so the length and width of our square are also equal to 14 cm.

With the side of the square equal to 14 cm, we know that this is equal to the circle's diameter. So d = 14 cm. We can solve for the radius of the circle/hemisphere by substituting it into the radius formula:

[tex]\begin{aligned}r & = \frac{d}{2} \\& = \frac{14 \ \text{cm}}{2} \\& = \boxed{ 7 \ \text{cm}} \\\end{aligned}[/tex]

Answer:

∴ the greatest radius that the hemisphere can have is equal to 7 cm. Any r > 7 cm would result in the hemisphere being over the edge of the cube.

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Learn more about Geometry: https://brainly.com/question/27732359

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Topic: Geometry

Unit: Composition of Geometrical Shapes

A Cubical Block Of Side 14 Cm Is Surmounted By A Hemisphere . What Is The Greatest Radius That The Hemisphere

Related Questions


On a separate sheet of paper, graph 3x+6y=18 In the box below, enter the y value when x = 2.

Answers

Answer:

y=2 when x=2

Step-by-step explanation:

3(2)=6

6+6y=18

6y=18-6

6y = 12

6y/6 = 12/6

y=2

Answer:

y=2 when x=2

Step-by-step explanation:

Did it on edge


Can someone help me with this geometry question I don’t understand it

Answers

when answering questions like these, it helps to draw arrows,, the variable will always be on top, so in this situation you would draw an arrow from the a to the 10 and an arrow from the 38 to the 12 making them both fractions, you would then cross multiply, after cross multiplying you would get 12a=380 then you would divide by 12 equaling 31.6

6x – 5 = 13 – 3х solve

Answers

Answer:

x=2

Step-by-step explanation:

6x−5=13−3x

Step 1: Simplify both sides of the equation.

6x−5=13−3x

6x+−5=13+−3x

6x−5=−3x+13

Step 2: Add 3x to both sides.

6x−5+3x=−3x+13+3x

9x−5=13

Step 3: Add 5 to both sides.

9x−5+5=13+5

9x=18

Step 4: Divide both sides by 9.

[tex]\frac{9x}{9}[/tex]= [tex]\frac{18}{9}[/tex]

x = 2

Answer: x=2

Step-by-step explanation:

Start by adding 3x to 6x, this eliminates the variables on the right side of the equation and leave you with 9x-5=13. From here, add five to both sides of the equation, which cancels out on the left side and leads you to have 18 on the right side. Remember that you want to have a lone variable, so you take the current equation of 9x=18 and divide both sides by 9, which cancels out on the left side and leaves the right side as 2. Therefore, x=2.

A cylindrical container of five rubber balls has a height of 30 centimeters and a diameter of 6 centimeters. Each ball in the container has a radius of 3 centimeters. Find the amount of space in the container that is not occupied by rubber balls. Round your answer to the nearest whole number.

Answers

Answer:

There is 170 cm³ free space in the container.

Step-by-step explanation:

Cylindrical container: height = 18 cm ; diameter = 6 cm.

3 balls each have a radius of 3 cm.

Volume of a cylinder = π r² h

V = 3.14 * (3cm)² * 18 cm

V = 508.68 cm³

Volume of rubber ball = 4/3  π r³

V = 4/3 * 3.14 * (3cm)³

V = 113.04 cm³

113.04 cm³  * 3 balls = 339.12 cm³

508.68 cm³ - 339.12 cm³ = 169.56 cm³ or 170 cm³

Find the equation of the exponential function represented by the table below:
X
0
1
2
3
Y
4
16
64
256
Y= ?

Answers

Answer:

y = [tex]4^{x+1[/tex]

Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.

What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?



Enter your answer, in simplest fraction form, in the box.

Answers

Answer:

2/3

Step-by-step explanation:

Y’ALL MIND TO HELP ME I HATE SCHOOL SO MUCH THAT IT MAKES ME WANT TO STAB MYSELF WITH A FORK BECAUSE I DONT UNDERSTAND ANYTHING IN THIS. anyway can y’all help me wit this ? I would appreciate it

Answers

Answer: Are you in summer school pfft

Step-by-step explanation: I won’t help you cheat

I need help with this question pls

Answers

Answer:

2^-2

Step-by-step explanation:

2^(3-5)

=2^-2

Answer:

[tex] \frac{ {2}^{4 + 3} }{2^{5 + 4} } [/tex]

[tex] \frac{ {2}^{7} }{2^{9} } [/tex]

= 2^7-9

= 2^-2


1) 2x – y = 1
2x +2y = 10


2) 5x – y =15

x + y = -3


please do both of these with explanation!!

Answers

Answer:

1) (2, 3)

2) (2, -5).

Step-by-step explanation:

2x – y = 1

2x +2y = 10   Subtract to eliminate  the 2x:

2x - 2x - y - 2y = 1  - 10

-3y = -9

y = 3.

Plug this into the first equation:

2x - 3 = 1

2x = 4

x = 2.

2)

5x – y =15

x + y = -3     Adding to eliminate y:

5x + x - y + y = 15 + -3

6x = 12

x = 2

Plug this into the first equation:

5(2) - y = 15

-y = 15 - 10 = 5

y = -5.

Pick out the definition of the word.
Irregular
A
not normal
B
not registered
C
not unusual

Answers

Answer: Not normal

Step-by-step explanation:

Regular (in math) refers to an integer that is a whole number or the integers that make up a whole number.

If it’s irregular then it’s not a normal integer like a whole number.

Find the greatest common factor of 26 and 14.

Answers

Answer:

2

Step-by-step explanation:

A factor is a number that can evenly divide into another number.

Let’s list all the factors of both numbers.

26: 1, 2, 13, 26

14: 1,2, 7, 14

Now find the GCF, or greatest common factor. The biggest number that is a factor of both 26 and 14 is 2.

Therefore, the GCF of 26 and 14 is 2.

LAST QUESTION AND LAST TRY!!! WILL GIVE BRANLIEST!!!! AT LEAST TAKE A LOOK, SHARE YO SMARTNESSS!!!!!!!! PLS

2. All of the following constructions start with a line segment except what?
A) constructing a line perpendicular to a point on a line
B) constructing equilateral triangles

Answers

I think it’s a because it sounds right idk

Answer:

A) Constructing a line perpendicular to a point on a line

A focus group is made up 12 males and 4 females. Half of the males have college degrees. A member is selected at random from the geoup. What is the probability that the member is a male with a college degree?

Answers

Answer:

3/8

Step-by-step explanation:

We first have to find the probability that the person selected is a male and then multiply that by the probability that the male has a college degree.

There are 12 males and 4 females. There are 16 people in total. The probability of selecting a male is:

12/16 = 3/4

Half of the males have a college degree. Therefore, 6 males have a college degree. The probability that a selected male has a college degree is:

6/12 = 1/2

Therefore, the probability that a male is selected and that the male has a college degree is:

3/4 * 1/2 = 3/8

One cubic centimeter of sand weighs 1.9 grams. Find the amount of sand that the sandcastle bucket can hold.

Answers

Answer:

2160

Step-by-step explanation:

1872(volume of the cube)+288(volume of the square pyramid)=

2160

v of cube= lwh

v of square pyramid= a² times h/3

please mark brainliest!

Two lions, Fluffy and Fireball, met at the zoo. Fluffy's tail is 1 1/3 of a meter long. Fireball's tail is 1 1/4 of a meter long. How much longer is Fluffy's tail than Fireball's tail?

Answers

Answer:

11 / 12 m

Step-by-step explanation:

11/3 - 11/4

LCM= 4*3=12

11/3 * 4/4 = 44/12

11/4 * 3/3 = 33/12

11/3 - 11/4

44/12-33/12= 11/12

Answer:

1/12

Step-by-step explanation:

First, simply convert the fractions into an improper fraction.

1 1/3= 4/3

1 1/4= 5/4

Then make conevrt it so the denominator  is the same. In this case, the denominatorwould be 12.

4/3= 16/12

5/4=  15/12

Finally subtract regularly.

16/12-15/12= 1/12


What is the midpoint of the segment shown below?

Answers

Answer:

B

Step-by-step explanation:

3 is too high up to be in the middle of the line, so the y value must be [tex]\frac{3}{2}[/tex] and this eliminates C and D as possible answers. -7 is too far back on the y axis, so this eliminates A. We are left with B.

(algebra) i think of a number add 3 to it and multiply the result by seven what is the answer

Answers

Answer:

[tex]7x+21[/tex]

Step-by-step explanation:

Let the number be [tex]x[/tex].

[tex]x+3[/tex]

[tex]7(x+3)[/tex]

Expand the brackets.

[tex]7x+21[/tex]

7x + 21
seven x plus twenty-one

Which expession is equivalent to 4-(-7)

Answers

Answer:

4 + 7 = 11

Step-by-step explanation:

Subtracting a negative means adding.

To subtract a number, add its opposite. The opposite of -7 is 7, so to subtract -7, add 7.

4 - (-7) = 4 + 7 = 11

Answer:

4+7

Step-by-step explanation:

The perimeter of a right triangle is 24 meters, and the area is 24 square meters. The lengths of the sides are each multiplied by 4. What is the area of the new triangle? help

Answers

Answer:

384m

Step-by-step explanation:

24 x 4 = 96

96 x 4 = 384

Answer:

the real answer is 96

Step-by-step explanation:

3x^2 -5x -2=0
help factor left side please!!
y’all i didn’t sleep at all last night and i cannot remember how to factor the first half of the equation help me out asap please guys

Answers

Answer:

Step-by-step explanation:

1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)

Two numbers that work are -6 and +1

-6 x +1 = -6

-6 + -1 = -5

2. Split the middle term into the two numbers that you found.

3x^2 -6x +x -2 = 0

I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.

3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'

3x (x-2) +1 (x-2) = 0

4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.

(3x + 1) (x-2) = 0

5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.

3x + 1 = 0              x-2 = 0

3x = -1                   x = 2

x = -1/3

6. The solutions to this equation are x = 2 and x = -1/3

Answer:

Step-by-step explanation:

Start by separating (not factoring) -5x.  For example, we might get {-2x, - 3x} (note how these combine to produce -5x).  Might have to try several combinations to find the right one.

Then 3x^2 -5x -2=0 could possibly be x(3x - 2) - (3x - 2), or

                                                                x(3x - 2) - 1(3x - 2).

Notice how the factor (3x - 2) shows up twice.  If we factor out (3x - 2) we are left with (x - 1).  We check these results by multiplying (3x - 2) and (x - 1) together, so we can be sure that the result is the original 3x^2 -5x -2=0.

(3x - 2)(x - 1) = 3x^2 - 3x - 2x + 1 results in 3x^2 - 5x + 2.  Unfortunately, the sign of that 2 is incorrect; we'd hoped for -2, not +2.

To check this further, I used synthetic division with 1 as divisor; the remainder is -4, which tells us that (x - 1) is not a factor of 3x^2 -5x -2=0.

Please double check to ensure that you have copied this problem down correctly.

what is the output value for the following function if the input value is 1?
y=3x + 1

Answers

Answer:

The output value is 4

Step-by-step explanation:

The output value is the y value, so y=3(1)+1

y=3+1

y=4

1. Steven delivers 56 newspapers every day of the week except Sunday. How
many papers does he deliver in all?
Ans:​

Answers

Answer: 336 papers

Step-by-step explanation:

A week except Sunday = 6 days

56 newspapers * 6 days = 336 newspapers in all

Answer:

336

Step-by-step explanation:

Given That:

Days : 7 - 1 = 6

Number of papers per day : 56

SO,

all papers: 56 x 6 = 336

Hope this helps.

What are the zeros of the function g(x)=2(x+2)(x-9) located at

Answers

Answer:

x = - 2, x = 9

Step-by-step explanation:

Given

g(x) = 2(x + 2)(x - 9)

To find the zeros let g(x) = 0, that is

2(x + 2)(x - 9) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 9 = 0 ⇒ x = 9

The zeros of the function g(x)=2(x+2)(x-9) are -2 and 9.

What is the zeros and y-intercept of a function?

Zeros is the Intersection points of the considered function's curve on input axis(usually represented by values of x)

y-intercept = Intersection points of the considered function's curve on output axis. On x-axis, value of y-coordinate is 0, On y-axis, value of x-coordinate is 0.

Thus, if function is y=f(x) then putting y = 0 gives zeros of the function.

And putting x = 0 gives the y-intercept of the function. (if any, for both cases).

Given the function as;

g(x) = 2(x + 2)(x - 9)

To find the zeros let g(x) = 0, that is;

2(x + 2)(x - 9) = 0

Then Equate each factor to zero and solve for x;

x + 2 = 0 ⇒ x = - 2

x - 9 = 0 ⇒ x = 9

Hence, the zeros of the function g(x)=2(x+2)(x-9) are -2 and 9.

Learn more about function here:

https://brainly.com/question/2253924

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Two bags contain coloured cubes.
Bag 1 has 3 red cubes and 1 blue cube.
Bag 2 has 3 green cubes, 1 yellow cube, and 1 red cube.
Is the probability that you will get a red cube from Bag 1 and the yellow cube from Bag 2 more or less than the probability of getting the blue cube from Bag 1 and a green cube from Bag 2? Explain.

Answers

Answer:

equal

Step-by-step explanation:

Bag 1 has 3 red cubes and 1 blue cube.  = 4 cubes

Bag 2 has 3 green cubes, 1 yellow cube, and 1 red cube.= 5 cubes

P ( red bag 1) = red /total = 3/4

P (yellow  bag 2) = yellow /total = 1/5

P(red bag1 , yellow bag2) = 3/4* 1/5 = 3/20

P ( blue bag 1) =blue /total =1/4

P (green  bag 2) = green /total = 3/5

P(blue bag1 , green bag2) = 1/4* 3/5 = 3/20

The probabilities are equal

25 points:)

question 2-3

Answers

Answer:

2) r=73

Step-by-step explanation:

all 4 sided shapes add up to 360.

so 90+90=180

180+107=287

360-287=73

so r=73

Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

Take you ruler and draw a horizontal line from point (0,-2)

When you do, the point where y = -2 is when x = - 3

Answer:

x = -3

Step-by-step explanation:

the question asks for what x the function = -2

if you imagine horizontal line passing through -2 then you cann see that it crosses graph when x = -3 and 0

What is the next term in the following set of numbers: {1,3,7,15,31,...? a. 63 b. 47 c. 39 d. 35 e. Other:

Answers

Answer:

[tex]63[/tex]

Step-by-step explanation:

[tex]1 + 2^1 = 3\\3 + 2^2 = 7\\7 + 2^3 = 15\\15 + 2^4 = 31\\31 + 2^5 = 63[/tex]

HELPPPP, giving brainlists The question, “How many ways can 4 different students be selected in order from a class of 30 students?”, is a(n) _____.

Answers

Answer:

³⁰C₄ = (30!)/(4!)(30-4)! = 27,405 WAYS

find the missing number pleasee i really need help


1. 6x - ? = 6

2. 6x - ? = 4x - 10


find the missing number where the ? is at .

Answers

Answer:

1) -1

2) -6.66666666667

Step-by-step explanation:

brainiest pls


A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up?

Answers

Answer:

The answer is 13! which equals 6227020800.

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