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UkoKoshka [18]
2 years ago
7

A circle has radius of 18 cm. Find the area of the smaller of the two regions determined by a chord with length of 18√2 cm . Hin

t: (Look for right triangles using Pythagorean Theorem Converse)
Mathematics
2 answers:
boyakko [2]2 years ago
8 0
The area is 81*pi-162. Look at the triangle formed by the chord and the two radii connected to the endpoints of the chord. Since 18^2+18^2=(18*\sqrt2)^2, this is an isosceles right triangle by Pythagorean theorem. The area of the quarter circle containing the region we look for is pi*18^2/4=81*pi. The area of the right triangle is 18*18/2=162. The difference between these two areas, or 81*pi-162, is the area of the smaller region.
madreJ [45]2 years ago
3 0

Answer:

81pi - 162

Step-by-step explanation:

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For each container of tea, McKenzie uses 16 tea bags and 3 cups of sugar. If McKenzie uses 64 tea bags, how many cups of sugar w
cestrela7 [59]
So tis is a ratio  16 is to 3 or 16:3
if use 64 tea bags then how many cups of sugar so
turn 16:3 into fraction
16:3=16/3 or 3/16, it doesn't matter
then you want to find 64:x or 64/x or x/64

we know that 16/3=64/x because it tis an equivalent ratio
so 16/3=64/x
multiply both sdies by (3 times x)
16 times x times 3/3=64 times 3 times x/x
16 times x=64 times 3
16x=192
divide both sdies by 16
x=12
theanswer is 12 cups of sugar
5 0
3 years ago
HELP PLEASE!
olasank [31]

Answer        

Find out the Area of a triangle .

To proof  

Formula

Area of Triangle

= \frac{1}{2}\times( {x_1(y_{2}-y_{3}) +x_{2}(y_{3} - y_{1})+x_{3}(y_{1}-y_{2})})

Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .

= \frac{1}{2} (3\times(-1 +5) + 3\times(-5-3)-2\times(3+1))

Solving the above

= \frac{1}{2}(3\times4+3\times-8 -2\times4)

=\frac{1}{2} (12-24-8)\\ =\frac{1}{2} (-32+12)\\=\frac{1}{2} (-20)

= -10 units²

(Neglected the negative sign as area cannot be negative.)

= 10 units ²

Area of  a triangle is 10 units ²

Hence proved

6 0
3 years ago
How do you find DE, Round to nearest 10th
Sergeu [11.5K]

Answer:  DE\approx6.0

Step-by-step explanation:

Observe in the figure given in the exercise that four right triangles are formed.

In this case you can use the following Trigonometric Identity to solve this exercise:

cos\alpha=\frac{adjacent}{hypotenuse}

From the figure you can identify that:

\alpha =53\°\\\\hypotenuse=10\\\\adjacent=BE=DE

Then, you can substitute values:

cos(53\°)=\frac{DE}{10}

The next step is to solve for DE in order to find its value. This is:

10*cos(53\°)=DE\\\\DE=6.01

Finally, rounding the result to the nearest tenth, you get that this is:

DE\approx6.0

7 0
3 years ago
What fraction of the shape is white
ICE Princess25 [194]

Answer:

3 over 8

Step-by-step explanation:

The total of box numbers is 8 and there are 3 white boxes. So, the total goes on the bottom and the amount of white boxes goes on top.

Hope this helped!

7 0
2 years ago
Read 2 more answers
De moirve's <br> (√3-i ÷ √3+i)^6 = 1
bulgar [2K]

(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)

… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)

… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))

… = (2 - 2√3 <em>i</em> ) / 4

… = 1/2 - √3/2 <em>i</em>

… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))

… = exp(<em>i</em> arctan(-√3))

… = exp(-<em>i</em> arctan(√3))

… = exp(-<em>iπ</em>/3)

By DeMoivre's theorem,

[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1

7 0
3 years ago
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