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3 years ago

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inc

hes.
Use π = 3.14.

What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.

Mathematics

1 answer:

Elan Coil [88]3 years ago

4 0

$\sf Cylinder ~volume = \pi r^2 h \\ \\ v = \pi (4)^2(9) \\ \\ v=\pi (16)(9) \\ \\ v=144 \pi \\ v=452.16\\ \\ \\ Cone~volume = \frac{1}{3} \pi r^2 h \\ \\ v = \frac{1}{3} \pi (4)^2 (18) \\ \\ v=96 \pi \\ v=301.44 \\ \\ \\ The~ volume ~of ~a ~cylinder ~is~ 1.5~ times~ more ~than ~the ~volume ~of~a~cone.$

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A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P (red or blue)

AnnyKZ [126]

The answer is B.

If there are 6 red marbles, 6 white marbles, and 4 blue marbles, then there are 16 marbles total. To find the probability (P) of either the red or blue marbles, you will add together the number of red and blue marbles, and divide that by the total:

(6 + 4) / (6 + 6 + 4)
10/14

This fraction can further reduce to 5/8 (by dividing both the numbers by 2).

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3 years ago

The perimeter of a quadrilateral (four-sides polygon) is 50 inches. The longest side is three times as long as the shortest side

kkurt [141]

The side lengths of quadrilateral are 21 inches; 11 inches; 11 inches; 7 inches.

<u>SOLUTION:</u>

Given, the perimeter of a quadrilateral (four-side polygon) is 50 inches.

Let the length of shortest side be n inches. The longest side is three times as long as the shortest side.

That is, length of largest side = 3n inches

The other two sides are equally long and are 4 inches longer than the shortest side.

Then, length of remaining two sides = 4 + n inches

We have to find the length of all four sides.

Now, we know that, perimeter = 50 inches

$\begin{array}{l}{\rightarrow \text { Sum of all sides }=50} \\\\ {\rightarrow n+3 n+n+4+n+4=50} \\\\ {\rightarrow n+3 n+n+n=50-4-4} \\\\ {\rightarrow 6 n=42} \\\\ {\rightarrow n=7}\end{array}$

So, length of sides will be,

$7 \text { inches; } 3\times7=21 \text { inches; } 7+4=11 \text { inches; } 7+4=11 \text { inches. }$

6 0

3 years ago

Consider the differential equation <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D6%20y%5E%7

Nutka1998 [239]

As a Bernoulli equation:

$x^2\dfrac{\mathrm dy}{\mathrm dx}=6y^2+6xy\iff x^2y^{-2}\dfrac{\mathrm dy}{\mathrm dx}-6xy^{-1}=6$

Let $z=y^{-1}\implies\dfrac{\mathrm dz}{\mathrm dx}=-y^{-2}\dfrac{\mathrm dy}{\mathrm dx}$ . The ODE becomes

$-x^2\dfrac{\mathrm dz}{\mathrm dx}-6xz=6$
$x^6\dfrac{\mathrm dz}{\mathrm dx}+6x^5z=-6x^4$
$\dfrac{\mathrm d}{\mathrm dx}[x^6z]=-6x^4$
$x^6z=-6\displaystyle\int x^4\,\mathrm dx$
$x^6z=-\dfrac65x^5+C$
$z=-\dfrac6{5x}+\dfrac C{x^6}$
$y^{-1}=-\dfrac6{5x}+\dfrac C{x^6}$
$y=\dfrac1{\frac C{x^6}-\frac6{5x}}$
$y=\dfrac{5x^6}{C-6x^5}$

With $y(3)=6$ , we get

$6=\dfrac{5(3)^6}{C-6(3)^5}\implies C=\dfrac{4131}2$

so the solution is

$y=\dfrac{5x^6}{\frac{4131}2-6x^5}=\dfrac{10x^6}{4131-12x^5}$

which is valid as long as the denominator is not zero, which is the case for all $x\neq\sqrt[5]{\dfrac{4131}{12}}$ .

8 0

3 years ago

If 3(x-3)=24, then x=?

Alexeev081 [22]

Answer: x=11

Step-by-step explanation:

First distribute 3 to both x and -3.

3x-9=24

Then add 9 to both sides to leave the x on its own.

3x=33

Divide by 3 on both sides.

X=11

4 0

3 years ago

Read 2 more answers

Given that f(x)=12(3x+4)what is the value of (3)

kumpel [21]

Answer:

f(3)= 156

Step-by-step explanation:

f(x)=12(3x+4)

f(x)=12(3(3)+4) =12(9+4) = 12(13) = 156

f(3)= 156

4 0

2 years ago