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3 years ago

(05.05)Polygon ABCD has the following vertices:

Mathematics

1 answer:

Kaylis [27]3 years ago

4 0

Answer is option b)38.5 sq.units

Given vertices are A(-4,2) ,B(3,2),C(3,-5) and D(-4,-2)

Area of polygon is defined in the image.

If you have any doubts see the image or ask in comments box.

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The circle below has center P, and its radius is 3 m. Given that m 2 QPR=170°, find the length of the minor arc OR.

QveST [7]

Any smooth curve connecting two points is called an arc. The length of the arc m∠QPR is 2.8334π m.

<h3>What is the Length of an Arc?</h3>

Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,

$\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360} = 2\pi r \times \dfrac{\theta}{2\pi}$

where

θ is the angle, that which arc creates at the centre of the circle in degree.

Given the radius of the circle is 3m, while the angle made by the arc at the centre of the circle is 170°. Therefore,

The length of an arc = 2πr×(θ/360°) = 2π × 3 ×(170/360°) = 2.8334π m

Hence, the length of the arc m∠QPR is 2.8334π m.

Learn more about Length of an Arc:

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4 0

2 years ago

C = 5/9(F - 32) for F

grigory [225]

Answer:

Step-by-step explanation:

5 0

2 years ago

Simplify the expression<br> –2 + 7(x + 8)

anastassius [24]

Answer:

54+7x

Step-by-step explanation:

-2+7(x+8)

-2+7x+56

54+7x

7 0

2 years ago

Read 2 more answers

You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material fo

zepelin [54]

Answer:

The dimensions of the box are:

x = 8,93 cm and h = 5,95 cm

C(min) = 850,69 cents

Step-by-step explanation:

The volume of the box is:

V = x²*h where x is the side of the square base and h the height

then h = V/ x² ⇒ h = 475 / x²

The total cost of box C is:

C = C₁ + 4*C₂ Where C₁ and C₂ are the costs of the base and one lateral side respectevily

Then cost C = 8*x² + 4* 6*h*x

The cost C as a function of x is

C(x) = 8*x² + (24* 475 /x² )*x

C(x) = 8*x² + 11400/x

Tacking derivatives on both sides of the equation

C´(x) = 16*x - 11400/x²

C´(x) = 0 ⇒ 16*x - 11400/x² = 0

16*x³ = 11400 ⇒ x³ = 11400/16

x³ = 712,5

x = 8,93 cm

and h = 475 / (8,93)² ⇒ h = 5,95 cm

C(min) = 8*79,77 + 4* ( 8,93)*5,95

C(min) = 638,16 + 212,53

C(min) = 850,69 cents

To check if value x = 8,93 would make C(x) minimum we go to the second derivatives

C´´(x) = 16 + 22800/x³ > 0

Then we have a minimum of C at x = 8,93

4 0

3 years ago

What is the solution of c² + 9 = 9

Lisa [10]

Answer:

The answer is 0

Step-by-step explanation:

0^2 is just 0x1 so 0+9=9

7 0

2 years ago

Read 2 more answers