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klemol [59]
3 years ago
10

A banner is made of a square and a semicircle. The square has side lengths of 22 inches. One side of the square is also the diam

eter of the semicircle. What is the total area of the banner? Use 3.14 for π
Mathematics
1 answer:
anastassius [24]3 years ago
7 0
Assuming the square and the semicircle aren't merged somehow, and we need to calculate their full area, we should take into account:

Area of a square:
(Side length)² = 22² = 484 square inches

Area of a circle with a diameter of 22inch:
3'14 · (radius)² = 3'14 · 11² = 379'94 square inches

Since we have half a circle, the total areas to add will be:
1/2 · 379'94 + 484 = 673'97
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Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
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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

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3 years ago
Use the drop down menus to complete the statements to match the information shown<br> by the graph.
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Answer:

less than, slope, higher (the rest in not sure)

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

You have to divide the dollar count by the pound count.

So basically:

6/5

This gives you 1.2 dollars.

When you do unit rate, you just have to divide one value by the other value.

The value you divide by, and the value you divde, vary depending on what the question asks.

For instance, if this question asked what the pound count for 1 dollar would be, you would end up divide the 5 pounds by 6 dollars(5/6) instead of divideing the 6  dollars by 5 pounds like we did above(6/5).

Hope this helps!

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Step-by-step explanation:

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