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Sonja [21]
4 years ago
5

PLEASE HELP ME!! IM CURRENTLY DOING A DIAGNOSTIC AND HAVE ONLY 15 MINS LEFT !!!!! A toilet paper roll has a diameter of 8x and a

height of 6x. The hole in the middle has a diameter of 2x. What is the simplified expression for the volume? NOTE THE FORMULA TO CALCULATE THE VOLUME OF A CYLINDER IS Volume= Pi * R ^2 * H Note: Use Pi for the answer. (EXAMPLE: 5pix^2)
Mathematics
1 answer:
drek231 [11]4 years ago
8 0

Answer:

284/3 πx³

Step-by-step explanation:

Volume of a cylinder is expressed as shown:

V = πr²h

r is the radius of the cylinder

r = diameter/2

r = 8x/2

r = 4x

Height of the cylinder = 6x

Volume of the roll with out the hole

V = π(4x)²(6x)

V = 16x²π(6x)

V = 96πx³

The hole in the middle will be a solid sphere with diameter 2x (radius will be x)

Volume of the hole = 4/3πr³

Volume if the hole = 4/3πx³

Volume of the toilet paper roll = volume of the roll without a hole - volume of the hole

= 96πx³ - 4/3πx³

= (96-4/3)πx³

= 284/3 πx³

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How many different 6-digit numbers can be formed by arranging the digits in 332345?
Feliz [49]

Answer- 120

Solution-

There are digits to be arranged,they are {3,3,2,3,4,5}. And from those ,3 digits are repeated .

so the total number of distinct number that can be formed = \frac{6!}{3!} = \frac{720}{6} = <em>120</em><em> </em>(ans)


7 0
4 years ago
Could someone help me, please?
k0ka [10]

We can rewrite the expression under the radical as

\dfrac{81}{16}a^8b^{12}c^{16}=\left(\dfrac32a^2b^3c^4\right)^4

then taking the fourth root, we get

\sqrt[4]{\left(\dfrac32a^2b^3c^4\right)^4}=\left|\dfrac32a^2b^3c^4\right|

Why the absolute value? It's for the same reason that

\sqrt{x^2}=|x|

since both (-x)^2 and x^2 return the same number x^2, and |x| captures both possibilities. From here, we have

\left|\dfrac32a^2b^3c^4\right|=\left|\dfrac32\right|\left|a^2\right|\left|b^3\right|\left|c^4\right|

The absolute values disappear on all but the b term because all of \dfrac32, a^2 and c^4 are positive, while b^3 could potentially be negative. So we end up with

\dfrac32a^2\left|b^3\right|c^4=\dfrac32a^2|b|^3c^4

3 0
3 years ago
Samantha visits for local farmers market to buy apples and oranges to make a fruit salad. she has $10 to spend. Apples are $.26.
GrogVix [38]
She can buy 38 apples.

10/0.26 = 38.5 but you can’t buy half an apple so you round down to 38.

Hope this helped!
5 0
3 years ago
Read 2 more answers
Callie is starting a fruit basket business the largest basket has 30 pieces of fruit but the others have 12 pieces of fruit in e
Elis [28]

Answer:

In the first basket, Callie can make 15 apples, 10 oranges and 5 bananas.


In the second basket, she can make 12 apples, 8 oranges and 4 bananas and


in the third basket, she can make 9 apples, 6 oranges and 3 bananas.

Step-by-step explanation:

The largest basket contains 30 pieces of fruit. So, it contains


1/2 of 30 = 15 apples


1/3 of 30 = 10 oranges and


1/6 of 30 = 5 bananas.


The second and third baskets should contain at least 12 pieces and at most 30 pieces (since the largest basket contains 30 pieces). Also, the number should be divided by 2, 3 and 6. So, it must be a multiple of 6.


Clearly, the number of multiples of 6 between 12 and 30 are 18 and 24.


Hence, the second basket contains 24 pieces of fruits and it contains


1/2 of 24 = 12 apples


1/3 of 24 = 8 oranges and


1/6 of 24 = 4 bananas


The third basket contains 18 pieces of fruits and it contains


1/2 of 18 = 9 apples


1/3 of 18 = 6 oranges and


1/6 of 18 = 3 bananas.


5 0
3 years ago
What is the value of x in the solution set of -5x-15&gt;10+20x
spayn [35]

Answer:

The answer is x < -1

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Hoped this helped!

brainly, please?

3 0
3 years ago
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