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3 years ago

Lauren earns $13 per hour at her after school job. If she has worked 64 hours at this job, how much has Lauren earned total?

Mathematics

1 answer:

disa [49]3 years ago

8 0

Answer: $832

Step-by-step explanation:

Lauren earned $13 per hour and she worked for 64 hours.

Total she would make is:

= 13 * 64

= $832

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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

A movie rental website charges $5.00 per month for membership and $1.25 per movie.How many movies did Andrew rent this month if

Oksanka [162]

So to start subtract $5 from $16.25 for the monthly membership
That gives you $11.25
So then you Just divide...
$11.25 divided by $1.25
which gives you 9
So bill rented 9 movies for the month

Hope this helped! :)

6 0

3 years ago

Fourteen less than the quotient of a number and 5

Ede4ka [16]

Answer:

Step-by-step explanation:

14-(a/5)

6 0

3 years ago

Cynthia was offered two different jobs for the summer. working as a camp counselor, she will earn $15 per hour plus an additiona

Natali [406]

The value of the composite function (f - g)(x) is 5x - 25

<h3>How to determine the function (f - g)(x)?</h3>

The function definitions are given as:

f(x) = 15x + 25

g(x) = 10x + 50

The function (f - g)(x) is calculated using

(f - g)(x) = f(x) - g(x)

This gives

(f - g)(x) = 15x + 25 - 10x - 50

Evaluate the like terms

(f - g)(x) = 5x - 25

Hence, the value of the composite function (f - g)(x) is 5x - 25

Read more about composite function at

brainly.com/question/28398656

#SPJ1

<u>Complete question</u>

Cynthia was offered two different jobs for the summer. working as a camp counselor, she will earn $15 per hour plus an additional $25 bonus. her earnings after x hours can be represented by the function f(x) = 15x + 25. working as a lifeguard, Cynthia will earn $10 per hour and an additional $50 bonus. her earnings after x hours can be represented by the function g(x) = 10x + 50. the arithmetic operation (f - g)x can be used to determine the difference in the salary Cynthia will earn working as a camp counselor instead of a lifeguard after x hours. what is the function (f - g)x?

7 0

1 year ago

96 sq meters

Vsevolod [243]

Answer:

84 sq meters

Step-by-step explanation:

1. Approach

In order to solve this problem, one will have to divide the figure up into simple shapes. A picture is attached showing how the shape is divided up for this answer. Find the area of each region, then add up the results to find the total area.

2. Area of Region 1

As one can see, the length of (Region 1), as given is (6), the width is (3). To find the area multiply the length by the width.

Length * width

6 * 3

= 18

3. Area of Region 2

In (Region 2), the length is given, (12). However, one must find the width, this would be the size of the total side, minus the width of (Region 1). Multiply the length by the side to find the area.

Length * width

= 12 * (8 - 3)

= 12 * 5

= 60

4. Area of Region 3

In (Region 3), the length of the figure is (2), the width is (3). To find the area, multiply the length by the width.

Length * width

= 2 * 3

= 6

5. Total area

Now add up the area of each region to find the total rea,

(Region 1) + (Region 2) + ( Region 3)

= 18 + 60 + 6

= 84

7 0

3 years ago