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3 years ago

Suppose you earn 6 dollars per hour at your part-time job. What will your new hourly rate be after a 2.5 percent raise? Why

Mathematics

1 answer:

icang [17]3 years ago

7 0

#1: Change 2.5 percent to a decimal.

This is how you change 2.5 into a decimal: By dividing by 100.

2.5 divided by 100 = 0.025

#2: Multiply 6 by 0.025.

6 x 0.025 = 0.15

#3: Last but not least, add 0.15 and 6

6 + 0.15 = 6.15

The answer you are looking for would be 6.15 dollars.

= $6.15

Hope this helps!-Aparri

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Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.

FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

$\rho = \sqrt{x^{2}+y^{2}+z^{2}}$

$\phi = cos^{-1}\frac{z}{\rho}$

For angle θ:

If x > 0 and y > 0: $\theta = tan^{-1}\frac{y}{x}$ ;

If x < 0: $\theta = \pi + tan^{-1}\frac{y}{x}$ ;
If x > 0 and y < 0: $\theta = 2\pi + tan^{-1}\frac{y}{x}$ ;

Calculating:

a) (4,2,-4)

$\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}$ = 6

$\phi = cos^{-1}(\frac{-4}{6})$

$\phi = cos^{-1}(\frac{-2}{3})$

For θ, choose 1st option:

$\theta = tan^{-1}(\frac{2}{4})$

$\theta = tan^{-1}(\frac{1}{2})$

b) (0,8,15)

$\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}$ = 17

$\phi = cos^{-1}(\frac{15}{17})$

$\theta = tan^{-1}\frac{y}{x}$

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = $\frac{\pi}{2}$

c) (√2,1,1)

$\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}$ = 2

$\phi = cos^{-1}(\frac{1}{2})$

$\phi$ = $\frac{\pi}{3}$

$\theta = tan^{-1}\frac{1}{\sqrt{2} }$

d) (−2√3,−2,3)

$\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}$ = 5

$\phi = cos^{-1}(\frac{3}{5})$

Since x < 0, use 2nd option:

$\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }$

$\theta = \pi + \frac{\pi}{6}$

$\theta = \frac{7\pi}{6}$

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

$r=\sqrt{x^{2}+y^{2}}$

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

$r=\sqrt{4^{2}+2^{2}}$ = $\sqrt{20}$

$\theta = tan^{-1}\frac{1}{2}$

z = -4

b) (0, 8, 15)

$r=\sqrt{0^{2}+8^{2}}$ = 8

$\theta = \frac{\pi}{2}$

z = 15

c) (√2,1,1)

$r=\sqrt{(\sqrt{2} )^{2}+1^{2}}$ = $\sqrt{3}$

$\theta = \frac{\pi}{3}$

z = 1

d) (−2√3,−2,3)

$r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}$ = 4

$\theta = \frac{7\pi}{6}$

z = 3

5 0

4 years ago

At the last minute, the technology company decides to expand the warehouse and asks the general contractor to double the dimensi

Lesechka [4]

<span>The expansion of the warehouse will not affect the dimensions of the surrounding fence.</span>

3 0

3 years ago

Please help me out with this guys. No Links Please!

Sergio [31]

I think it is 29%? I am not 100% sure though...

5 0

2 years ago

An observer (O) spots a plane (P) taking off from a local airport and flying at a 33° angle horizontal to her line of sight and

docker41 [41]

Answer:

the distance of the Bird (B) from the plane (P) is = 10779 ft

Step-by-step explanation:

From the given information:

a diagrammatic representation is attached below for better understanding and solution to the question.

From the diagram;

Let the Bird (B) be represent as A

The plane (P) be represented by B

The observer be represented by O

and the tower T be represented by C

we will see that:

$\overline {AB} \ \| \ \overline {OC}$

Also;

$\angle ABO = \angle BOC = 33^0$

AO = BC = 7000

Let consider the trigonometry of triangle BAO

tan θ = opposite/adjacent

tan 33° = 7000/x

0.6494 = 7000/x

x = 7000/0.6494

x = 10779.18

x = 10779 ft ( to the nearest whole number)

Thus; the distance of the Bird (B) from the plane (P) is = 10779 ft

7 0

3 years ago

How would I find X? I tried using a2 + b2 =c2 but nothing worked

kozerog [31]

Can you please explain this a bit better? i dont understand

3 0

3 years ago