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STatiana [176]
1 year ago
5

Find the area of the shaded region below. Give your answer in terms of T. 12m 5m

Mathematics
1 answer:
Step2247 [10]1 year ago
7 0

The area of the shaded region is [(169π/4)-60]m².

  • The length of the rectangle is 12 m.
  • The breadth of the rectangle is 5 m.
  • The area of the rectangle = length * breadth.
  • The area of the rectangle = 12 * 5
  • The area of the rectangle = 60m²
  • Let h be the diagonal of the rectangle.
  • Using the Pythagorean theorem,
  • h² = 12² + 5²
  • h² = 144 + 25
  • h² = 169
  • h = √169
  • h = 13
  • The diagonal of the rectangle is also the diameter of the circle.
  • Let r be the radius of the circle.
  • 2r = 13
  • r = 13/2m
  • The area of the circle is πr².
  • The area of the circle = π(13/2)²
  • The area of the circle = (169π/4)m²
  • The area of the shaded region equals the area of the circle minus the area of the rectangle.
  • The area of the shaded region = [(169π/4) - 60]m²

To learn more about area, visit :

brainly.com/question/27683633

#SPJ9

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Answer: 1/4

Step-by-step explanation:

Since the box box contains four equal-sized cards labeled 1 , 3, 5, and 7. The probability of selecting any number out of the four numbers will be 1/4 if they are selected once.

If Tim selects one card from the box, the probability that Tim will select a card labeled 3 will be: = 1/4

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Long Division: (3x^4-8x^3-x^2+9x+5) / (x-2) pleaseee answer this
Drupady [299]

3<em>x</em>⁴ = 3<em>x</em>³ • <em>x</em>, and

3<em>x</em>³ (<em>x</em> - 2) = 3<em>x</em>⁴ - 6<em>x</em>³

Subtract this from the numerator to get a remainder of

(3<em>x</em>⁴ - 8<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) - (3<em>x</em>⁴ - 6<em>x</em>³) = -2<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5

-2<em>x</em>³ = -2<em>x</em>² • <em>x</em>, and

-2<em>x</em>² (<em>x</em> - 2) = -2<em>x</em>³ + 4<em>x</em>²

Subtract this from the previous remainder to get a new remainder of

(-2<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) - (-2<em>x</em>³ + 4<em>x</em>²) = -5<em>x</em>² + 9<em>x</em> + 5

-5<em>x</em>² = -5<em>x</em> • <em>x</em>, and

-5<em>x</em> (<em>x</em> - 2) = -5<em>x</em>² + 10<em>x</em>

Subtract this from the last remainder to get a new one of

(-5<em>x</em>² + 9<em>x</em> + 5) - (-5<em>x</em>² + 10<em>x</em>) = -<em>x</em> + 5

-<em>x</em> = -1 • <em>x</em>, and

-1 (<em>x</em> - 2) = -<em>x</em> + 2

This gives a new remainder of

(-<em>x</em> + 5) - (-<em>x</em> + 2) = 3

3 does not divide <em>x</em>, so we're done.

So, we have

(3<em>x</em>⁴ - 8<em>x</em>³ - <em>x</em>² + 9<em>x</em> + 5) / (<em>x</em> - 2) = 3<em>x</em>³ - 2<em>x</em>² - 5<em>x</em> - 1 + 3/(<em>x</em> - 2)

7 0
3 years ago
Write and equation of the translated or rotated graph in general form (picture below)
WINSTONCH [101]

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

 xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

  the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ (\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=

 ( \frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0

* Lets open the bracket

∴ \frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0

* Lets add the like terms

∴ \frac{-4xy}{2}-16=0

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

6 0
3 years ago
Read 2 more answers
The area of a rectangular parking lot is 7081 m²
Lubov Fominskaja [6]

Step-by-step explanation:

So the question is easy ....The thing that you need to do here is ...You should divide area by length....and you will get your answer....

  • Area of square = l²
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Area of rectangular parking lot = 7081 m²

length of parking lot = 97 m

Width = ?

Now,

Area = l × b

7081 = 97 × b

7081 / 97 = b

b = 73 m

Hence the width is 73 m....

4 0
2 years ago
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