The plastic cylinder has a diameter of 2 cm. There is a rectangular 0.6 cm square prism through the middle of the cylinder, extending from the top to the bottom. The height of the cylinder is 6 cm. Find the volume of the cylinder without the prism.

The Plastic Cylinder Has A Diameter Of 2 Cm. There Is A Rectangular 0.6 Cm Square Prism Through The Middle

Answers

Answer 1

Answer:

The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.

Step-by-step explanation:

The volume of the cylinder without the prism can be defined as the volume of the entire cylinder ([tex]V_{cy}[/tex]), measured in cubic centimeters, minus the volume of the prism ([tex]V_{pr}[/tex]), measured in cubic centimeters. That is:

[tex]V = V_{cy}-V_{pr }[/tex] (1)

[tex]V = \frac{\pi}{4}\cdot D^{2}\cdot h - l^{2}\cdot h[/tex]

[tex]V = \left(\frac{\pi}{4}\cdot D^{2}-l^{2} \right)\cdot h[/tex] (2)

Where:

[tex]D[/tex] - Diameter of the cylinder, measured in centimeters.

[tex]l[/tex] - Side of the square prism, measured in centimeters.

[tex]h[/tex] - Height of the square prism, measured in centimeters.

If we know that [tex]D = 2\,cm[/tex], [tex]l = 0.6\,cm[/tex] and [tex]h = 6\,cm[/tex], then the volume of the cylinder without the prism is:

[tex]V = \left[\frac{\pi}{4}\cdot (2\,cm)^{2}-(0.6\,cm)^{2} \right]\cdot (6\,cm)[/tex]

[tex]V \approx 16.690\,cm^{3}[/tex]

The volume of the cylinder without the prism is approximately 16.690 cubic centimeters.


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Step-by-step explanation:

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To find the perimeter of a shape, you need to add up the measurements of all the sides to find it. I hope this helps. Let me know if you need some help with some perimeter problems :)

Analyze the diagram below and complete the instructions that follow.
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Answers

Answer:

B.

y-Step-bstep explanation:

ok so

the triangle has 3 angle

45-45-90

one 45 points to x

that means the other side is also x

the 90 degrees points to 3

3=x√2

x=2.12132

The value of x in the given diagram is 3√2, Option C is correct.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle has 45-45-90 degrees.

We have to find the value of x in the given triangle.

The cosine function is ratio of the adjacent side by hypotenuse.

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The value of cos 45 degrees is one divided by root 2.

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Bill is looking for a job as a gym teacher. he plans to send resumes to 130 schools in his state. Kinko's charges $30 per 100 copies and sells them only in sets of 100.

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Answers

A. He will have to buy 200 copies
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Jamie puts an initial $900 into a savings account. The account has a 7% annual compound interest rate. What is the function that best represents Jamie's account and how much does he have in savings after 5 years? Round your answer to the nearest dollar.

Hint: Use the formula, f(x) = P(1 + r)x

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C. f(x) = 900(1.07)x, $1,081

D. f(x) = 900(0.07)x, $1,262

Answers

Answer:

D. f(x)=900(0.07)^x.1,262

Step-by-step explanation:

You would have to use the P(1+r)^x

P= starting amount

R= rate of change or the percentage changed into a decimal

x= time

So it would be, 900(1+0.07)^5

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Hope this helped

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Answers

Step-by-step explanation:

HERE,

a=[tex]\bold{\dfrac{1}{4} }[/tex]

b=6

so,

According to the question,

[tex]\bold{16a^2-4b }[/tex]

[tex]\bold{16\times(\dfrac{1}{4})^2-4\times 6 }[/tex]

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[tex]\bold{\cancel{16}\times \dfrac{1}{\cancel{16}}-24 }[/tex]

[tex]\bold{1-24 }[/tex]

[tex]\bold{ -23 }[/tex]

435,506 rounded to nearest ten thousand

Answers

Answer:

445,506

Step-by-step explanation:

math

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Answer:

a). x = 10.20 in

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Step-by-step explanation:

a). By applying Pythagoras theorem in the given right angle,

    (Hypotenuse)² = (Leg 1)² + (Leg 2)²

    (15)² = x² + (11)²

     225 = x² + 121

     x² = 225 - 121

     x² = 104

     x = √104

     x = 10.198 ≈ 10.20 in

b). By applying Pythagoras theorem,

    (3x)² = (2x)² + (5)²

     9x² = 4x² + 25

     9x² - 4x² = 25

     5x² = 25

      x² = 5

    x = √5 = 2.24

How many times do 8 go into 5

Answers

it goes into five 0 times

Answer:

0 Times

Step-by-step explanation:

The answer is 0 times!

This is due to the concept in which 8 is a bigger number than 5.

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Answers

Answer:

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Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

z=-3

Step-by-step explanation:

Answer:

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Step-by-step explanation:

10z + 3 = 9z

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Answer:

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Answers

Hello!

[tex]\large\boxed{x = 6}[/tex]

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JK ≅ JM

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Barbara has b bags of rice that each contain 4 pounds of rice. She has another bag that has 3 pounds of rice. Write an algebraic expression that shows how many pounds of rice Barbara has.

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The algebra expression is 4B+3

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Step-by-step explanation:

Which equation represents the line that passes through the points (-3, 7) and (9,-1)? oy--3x+5 o y=-x-7 o y=zx-7 oy - 12 2x+5​

Answers

Answer:

use the slope equation (y2-y1) / (x2 -x1). plug in values and solve

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then, plug in one of the points and the slope into the slope-point equation.

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

6 < x < 14;   answer = 8

Step-by-step explanation:

triangle inequality theorem: sum of any two sides must be greater than the third side

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Answers

Answer: 8 weeks

Step-by-step explanation:

He originally had $315 in his account. This figure increased to $955. It therefore increased by:

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Answers

Answer:

Step-by-step explanation:

Slope of this line will be= m= (600-200)/(1-5)

m = 400/-4 = -100

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Hey there!

The answer to your question is [tex]y = -100x + 500[/tex]

To write this equation in slope-intercept form, first we must figure out the slope. We can do this using the formula

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]:

[tex]\frac{200-600}{5-1}[/tex]

[tex]\frac{-400}{4}[/tex]

[tex]-100[/tex]

Now, we have part of the equation: y = -100x + b. We have to find b, and we can do so by plugging in one of the points into the equation, like so:

[tex]600 = -100(1) + b[/tex]

[tex]600 = -100 + b[/tex]

[tex]500 = b[/tex]

Now, we have our equation:[tex]y = -100x + 500[/tex]

Hope it helps and have an amazing day!

The tables correspond to two lines in the coordinate plane.What is the X- coordinate of the solution of the two lines? hint:what point is the same?

Answers

Answer:

2

Step-by-step explanation:

when x=2, both lines have a y of -4

check the picture below & help please!!

how many hours?

Answers

Answer:

I think it should be 11/3

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A) -11
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Answers

Answer:

-2

Step-by-step explanation:

you must follow the y=mx+b

m=slope

b=intercept

Answer:

B) -2

Step-by-step explanation:

y= -2x+11 is in slope-intercept form

y= mx+b

y= y-coordinate

x= x-coordinate

m= slope

b= y-intercept

m= -2

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In this assignment, you will be comparing two data
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scores and IQ scores.
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Answer:

The answer is IQ

Step-by-step explanation:

Edge 2021

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Answers

Answer:

AC=11.38 cm

Step-by-step explanation:

The Law of Cosines

It relates the length of the sides of a triangle with one of its internal angles.

Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

[tex]c^2=a^2+b^2-2ab\cos x[/tex]

The figure shows two triangles and we are required to calculate the length of the side AC, knowing two sides and the angle between them. Thus, applying the formula:

[tex]AC^2=17^2+13^2-2*17*13*\cos42^\circ[/tex]

[tex]AC^2=289+169-442*0.7431[/tex]

[tex]AC^2=129.53[/tex]

[tex]AC=\sqrt{129.53}[/tex]

AC=11.38 cm

Solve the following expression 8 + (-20)

Answers

Answer:

-12

Step-by-step explanation:

integer rule = when a + and - comes it is indicated as - so ..

8-20 = -12

we put a minus sighnbecause 20 is the bigger number  

Answer:

-12

Step-by-step explanation:

Note the rules of the signs:

If there are two positive signs next to each other, the resulting sign will be positive. Example + (+  ).

If there is one negative sign and one positive sign directly next to each other, the resulting sign will be negative Example - (+  ) or + (-  ).

If there are two negative signs directly next to each other, the resulting sign will be positive. Example - (-  ).

In this case, there is one negative, and one positive sign. Subtract 8 with 20:

8 + (-20) = 8 - 20 = -12

-12 is your answer.

~

(3 + 81)(3 - 81) =
DONE
h

Answers

Answer:

-6552

Step-by-step explanation:

First do 3+81 = 84 then 3-81 = -78. Then multiply them together to get -6552

Answer:

(3 + 81)(3-81)=9-6561

Stepby-step explanation:

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Answers

Answer: He was given 50 for his birthday

Answer:

It's b

Step-by-step explanation:

This was the first answer I gave. So I am going with it.

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