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3 years ago

What is 2 and 1/2 divided into 3/4

Mathematics

2 answers:

jasenka [17]3 years ago

8 0

Answer:

3 1/3

Step-by-step explanation:

2 and 1/2 = 2 1/2.

2 1/2 = 5/2.

5/2 = 10/4.

10/4 ÷ 3/4 = 3.333333333333333333333333333333333333333333333333333333 and goes on forever, so we change it to a fraction.

Final answer: 3 1/3

hope this helps :)

Fed [463]3 years ago

5 0

It would be 3 and 1/3

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Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

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2 years ago

What is the range of the function represented by these ordered pairs?

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Answer:

Choice 2

Step-by-step explanation:

Range is talking about the y value of the coordinates. Choice 2 has all the y value in the function

6 0

3 years ago

24 23 22 21十 20- 4 8 12 16

DochEvi [55]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

A bag contains white matarles and red marables,126 in total.The number of whit marables is 6 more than 5 than 5 times the number

denis-greek [22]

Answer:106

Step-by-step explanation:

Let number of white marbles be w

Let number of red marbles be r

w+r = 126---------1

w = 6 +5r-----------2

Put eqn 2 in eqn 1

6+ 5r + r = 126

6 + 6r = 126

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3 0

4 years ago

Please show work for both problems

kirill [66]

Answer:

3) x = 15; 95 and 85 4) x = 12; 98 for both angles

Step-by-step explanation:

2x + 65 + 3x + 40 = 180 Set the equations equal to 180

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- 105 - 105 Subtract 105 from both sides

5x = 75 Divide both sides by 5

x = 15

Plug 15 into both equations

2(15) + 65 = 95

3(15) + 40 = 85

4) 5x + 38 = 9x - 10 Set the equations equal to each other

- 5x - 5x Subtract 5x from both sides

38 = 4x - 10

+ 10 + 10 Add 10 to both sides

48 = 4x Divide both sides by 4

12 = x

Plug 12 into both equations

5(12) + 38 = 98

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3 years ago