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umka21 [38]
3 years ago
10

A hemisphere of radius 9 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the cen

ter of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
radius=
height=

Mathematics
1 answer:
ikadub [295]3 years ago
5 0

Answer:

The radius and height of the cylinder of maximum volume is 9 unit and 9 unit.

Step-by-step explanation:

Given that,

Radius = 9

According to figure,

Radius of cylinder = Radius of hemisphere

Center of cylinder base is also center of sphere.

Circular top of cylinder touching the top of hemisphere.

So, Height of cylinder = radius of hemisphere

h = r

h = 9\ unit

Hence, The radius and height of the cylinder of maximum volume is 9 unit and 9 unit.

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Is (2,3) a solution to the system of inequalities 4x+3y&lt;20 <br> 10x+y&gt;10
stiks02 [169]
Yes it is a solution because if you take the equation and plug the point in for the x and y :

4 (2) + 3 (3) < 20 
 8 + 9 < 20 
17 < 20
which is true

10 (2) + (3) > 10
20 + 3> 10
23>10
which is also true
7 0
3 years ago
Read 2 more answers
Write in simplest form 1/3 times 1 1/3
IRINA_888 [86]

Answer:

3 2/3

Step-by-step explanation:

Use a calculator please

8 0
3 years ago
Match the phenomenal expression on the left with the simplified version on the right
nalin [4]

Given the polynomial expression:

(y + 5)²

(y - 5)(y + 5)

Let's simplify each of the given expression:

a.) (y + 5)²

The given equation is a factor of a perfect square trinomial. For this type of expression, the following is the formula for expanding it.

\text{ (a+b)}^2\text{ = }a^2\text{ + 2ab + }b^2

We get,

\mleft(y+5\mright)^2=(y)^2+2(y)(5)+(5)^2(y+5)^2=y^2+10y+25

b.) (y - 5)(y + 5)

To be able to simplify the following expression. We will be using the formula for the difference of two squares.

(a+b)(a-b)=a^2-b^2

We get,

\mleft(y-5\mright)\mleft(y+5\mright)=(y)^2-(5)^2(y-5)(y+5)=y^2-25^{}

8 0
1 year ago
The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minute
KATRIN_1 [288]

After 85 minutes of calls, there are $27.25 left on the card.

<h3>What is the remaining credit after 85 minutes of calls?</h3>

A linear equation in slope-intercept form is:

y = a*x + b

Where a is the slope.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)

(points of the form (time, dollars)).

So the slope is:

a = \frac{32.2 - 36.7}{52 -22} = -0.15

The linear equation is then:

y = -0.15*x + b

To find the value of b, we use the point (22. 36.7)

36.7 = -0.15*22 + b

36.7 + 0.15*22 = b = 40

Then the linear equation is:

y = -0.15*x +40

The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.

y = -0.15*85 + 40 = 27.25

This means that after 85 minutes of calls, there are $27.25 left on the card.

If you want to learn more about linear equations:

brainly.com/question/1884491

#SPJ1

7 0
2 years ago
Help me please...........?
Makovka662 [10]
189 inches is 15.75 feet

16 ft - 15.75 ft = 0.25 ft

0.25ft = 3 inches

He must vault 3 inches higher
4 0
3 years ago
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