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3 years ago

A sector has a radius of 4 and a central angle of 40 degrees. Find the arc length and area of sector

Mathematics

1 answer:

g100num [7]3 years ago

4 0

Answer:

Step-by-step explanation:

θ = 2π/9 radians

arc length = rθ = 8π/9 units

area of sector = πr²/9 = 16π/9 square units

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Write in its simplest form, the ratio 3.5kilograms:800grams

MA_775_DIABLO [31]

3.5 kg:800g
3500g:800g
35g:8g

4 0

2 years ago

the area of a rectangular picture frame is 30 3/1 square inches. The length of the frame is 6 1/2 inches. Find the width of the

Rudiy27

I hope this helps you

Area=length ×width

30 1/3=30.3+1/3=91/3

6 1/2=6.2+1/2=13/2

91/3=13/2.width

width =7.13.2/3.13

width =14/3

width = 4 2/3

3 0

3 years ago

Polynomial expressions with matching

yuradex [85]

Answer:

The difference of 27x³ and 8y³ → [3x - 2y][9x² + 6xy + 4y²]

The difference of 27x³ and 64y³ → [3x - 4y][9x² + 12xy + 16y²]

The sum of 27x³ and 64y³ → [3x + 4y][9x² - 12xy + 16y²]

The sum of 27x³ and 8y³ → [3x + 2y][9x² - 6xy + 4y²]

Step-by-step explanation:

For the first two, we use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

$\displaystyle 3x - 2y = \sqrt[3]{27x^3 - 8y^3} \\ 3x - 4y = \sqrt[3]{27x^3 - 64y^3}$

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign in your given expression, which will be a plus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ - 64y³

[3x - 4y][9x² + 12xy + 16y²]

↑ ↑ ↑

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ - 8y³

[3x - 2y][9x² + 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Now, for the last two, we use the Sum of Cubes [(a³ + b³)(a² - 2ab + b²)] first by taking the cube root of the given expression to get our first factor[s]:

$\displaystyle 3x + 2y = \sqrt[3]{27x^3 + 8y^3} \\ 3x + 4y = \sqrt[3]{27x^3 + 64y^3}$

Then, use the acronym of SOAP {whether the next operations symbols will be negative or positive [SAME (your cube-rooted factor has an IDENTICAL OPERATION SYMBOL as your given expression), OPPOSITE (the first sign in your second factor in the second set of parentheses will be the opposite of what the sign is in your given expression, which will be a minus sign), ALWAYS POSITIVE (the last sign in your second factor in the second set of parentheses will ALWAYS stay positive NO MATTER WHAT)]} to get the second factor:

Given: 27x³ + 64y³

[3x + 4y][9x² - 12xy + 16y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

Given: 27x³ + 8y³

[3x + 2y][9x² - 6xy + 4y²]

↑ ↑ ↘

same as opposite ALWAYS POSITIVE

given of given

I am delighted to assist you anytime!

* As you can see, when using the <em>Difference\Sum of Cubes</em>, SOAP can vary depending on how an expression is given to you. They resemble each other though.

6 0

3 years ago

(7x-49x^2)/(7x) can smeone solve this? Thank you! I hope you have a great day!

svp [43]

Answer:

x = 1/7

Step-by-step explanation:

$\frac{(7x-49x^2)}{7x}\\\\\frac{7x(1-7x)}{7x} \\\\1-7x=0\\\\1=7x\\\\$

x = 1/7

3 0

3 years ago

Can someone help me out ASAP and possible step by step

OlgaM077 [116]

Answer:

49°

Step-by-step explanation:

The given information that BC=DC tells you triangle BCD is an isosceles triangle and that angle y is one of the two equal base angles. Then ...

y + y + 82 = 180 . . . . . the sum of angle measures is 180 degrees

2y = 98 . . . . subtract 82

y = 49 . . . . . divide by 2

The measure of y is 49°.

8 0

3 years ago