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alexdok [17]
4 years ago
10

PLEASE HELP!!! The question is above^

Mathematics
1 answer:
RoseWind [281]4 years ago
4 0

Answer:

C

Step-by-step explanation:

Since the figure is a square with all 4 sides equal, then calculate the length of EF and multiply by 4 for the perimeter.

Calculate EF using the distance formula

EF = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = E(0, 5) and (x₂, y₂ ) = F(5, 0)

EF = \sqrt{(5-0)^2+(0-5)^2}

    = \sqrt{5^2+(-5)^2}

    = \sqrt{25+25} = \sqrt{50}

Hence

Perimeter = 4EF = 4 × \sqrt{50} ≈ 28.3 → C

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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
What are three ordered pairs that have a proportional relationship
MaRussiya [10]
1-3
2-6
3-9 This is an example of porportional.

1-4
2-3
3-9 There is no pattern so thin is Non-Porportional.
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3 years ago
a fair coin is tossed three times in succession.the sample space is shown,where H represents avhaed and T represents a tail. Fin
hodyreva [135]
Because the probability of getting heads is 1/2, in a scenario in which it is tossed 3 times, the probability of getting exactly one head is 1/3.
5 0
3 years ago
The difference of twice a number and another number is 5. The sum of the two numbers is 19. Find the numbers
joja [24]

Answer:

12 & 7

Step-by-step explanation:

12 + 7=19

12 - 7=5

7 0
3 years ago
Read 2 more answers
I need a help with this
Anvisha [2.4K]

Answer:

130.356 g

Step-by-step explanation:

The problem tells you there is a proportional relationship, so set up a proportion and solve..

99.684 is to 11.7 as X is to 15.3

Written as a math equation like this...

99.684/11.7 = X/15.3

Now solve for X

130.356 = X    (multiply both sides by 15, then simplify)

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