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3 years ago

How many minutes are there in 3 hours and 53 minutes

Mathematics

2 answers:

Sveta_85 [38]3 years ago

6 0

(3 hours) + (23 minutes) = 233 minutes

Aleks04 [339]3 years ago

3 0

Answer:

233 minutes

Step-by-step explanation:

3 x 60 (# of minutes in an hour) = 180 minutes

180 + 53 = 233 minutes

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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

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

4 0

2 years ago

The volume of a cube is related to the area of s face by the formula v= a^3/2. What is the volume of a cube whose face has an ar

Sophie [7]

Answer:

1000 m³

Step-by-step explanation:

Put the number into the formula and do the arithmetic.

v = a^(3/2) = (100 m²)^(3/2) = (√100)³ m³ = 1000 m³

The volume is 1000 cubic meters.

4 0

3 years ago

There are 24 boys and 16 grils on a playground. What is the ratio of boys tototal number of children on the playground

tatuchka [14]

Answer:

24:40 or 3:5

Step-by-step explanation:

Boys: 24

All children: 24 + 16 = 40

Boys to total amount of children: 24:40

Simplify: 24:40 = 3:5

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3 years ago

Which transformation of y = f(x) moves the graph 7 units to the left and 3 units down?

Svetlanka [38]

Answer:

b) y = f(x - 7) - 3

Step-by-step explanation:

it adds if its goes to the right and subtracts if it goes to the left

And when it goes down then it will also decrease in number.

that is why b) y = f(x - 7) - 3 is the correct answer to put

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3 years ago

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<span>C.
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