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ycow [4]
2 years ago
10

A stack of one hundred twenty cards is placed next to a ruler, and the height of stack is measured to be

Mathematics
1 answer:
Aliun [14]2 years ago
6 0
If you do 34/120 you will get 0.283333333333333
Which is the thickness of one card
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Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 y2 = 9 and the sphere x2 y2 z2 =
marissa [1.9K]
In Cartesian coordinates, the region is given by -3\le x\le3, -\sqrt{9-x^2}\le y\le\sqrt{9-x^2}, and -\sqrt{16-x^2-y^2}\le z\le\sqrt{16-x^2-y^2}. Converting to cylindrical coordinates, using

\begin{cases}\mathbf x(r,\theta,\zeta)=r\cos\theta\\\mathbf y(r,\theta,\zeta)=r\sin\theta\\\mathbf z(r,\theta,\zeta)=\zeta\end{cases}

we get a Jacobian determinant of r, and the region is given in cylindrical coordinates by 0\le\theta\le2\pi, 0\le r\le3, and -\sqrt{16-r^2}\le z\le\sqrt{16-r^2}.

The volume is then

\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\int_{z=-\sqrt{16-r^2}}^{z=\sqrt{16-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\dfrac{4(64-7\sqrt7)\pi}3
6 0
2 years ago
Evaluate 48/6-10/3 please and thank you :)))
vodomira [7]

Answer:

14/3

Step-by-step explanation:

Simplify the following:

48/6 - 10/3

Hint: | Reduce 48/6 to lowest terms. Start by finding the GCD of 48 and 6.

The gcd of 48 and 6 is 6, so 48/6 = (6×8)/(6×1) = 6/6×8 = 8:

8 - 10/3

Hint: | Put the fractions in 8 - 10/3 over a common denominator.

Put 8 - 10/3 over the common denominator 3. 8 - 10/3 = (3×8)/3 - 10/3:

(3×8)/3 - 10/3

Hint: | Multiply 3 and 8 together.

3×8 = 24:

24/3 - 10/3

Hint: | Subtract the fractions over a common denominator to a single fraction.

24/3 - 10/3 = (24 - 10)/3:

(24 - 10)/3

Hint: | Subtract 10 from 24.

| 2 | 4

- | 1 | 0

| 1 | 4:

Answer:  14/3

5 0
3 years ago
-4 1/5+3 2/3+ -1 2/5
Paul [167]

Answer:

-1.9

Step-by-step explanation:

I rounded it to the tenth

8 0
3 years ago
Read 2 more answers
Find the slope of the line passing through (-8,6) and (6,6)
frosja888 [35]

Answer:

0

Step-by-step explanation:

6-6 equals 0 and -8 minus 6 equals -14 and 0 divided by equals 0

8 0
3 years ago
PLEASE HELP IM STUCK ONLY 3 MORE QUESTIJONS
True [87]

Answer:

y = - 2x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \frac{1}{2} x - 9 ← is in slope- intercept form

with m = \frac{1}{2}

given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{1}{2} } = - 2

y = - 2x + c ← is the partial equation

to find c substitute (3, 2 ) into the partial equation

2 = - 6 + c ⇒ c = 2 + 6 = 8

y = - 2x + 8 ← equation of perpendicular line

3 0
2 years ago
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