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AnnyKZ [126]
3 years ago
9

Use compatible numbers to estimate:4×26×7

Mathematics
1 answer:
Vlada [557]3 years ago
7 0

4 times 25= 100 100 times 7= 700

mark brainliest plsss

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Equilateral triangle ABC has an area of \sqrt{3}√ ​3 ​ ​​ . If the shaded region has an area of \piπK − \sqrt{3}√ ​3 ​ ​​ , what
Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

  and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

   arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

  of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ (2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)

∴ 4=r^{2}+r^{2}-2(r)(r)(-0.5)

∴ 4=r^{2}+r^{2}-(-r^{2})

∴ 4=r^{2}+r^{2}+r^{2}

∴ 4=3r^{2}

- Divide both sides by 3

∴ r^{2}=\frac{4}{3}

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

7 0
3 years ago
224 is what % of 640?
lakkis [162]
There is a percent formula for all of these types of percent problems.

It is : is/of = %/100

224 is what % of 640
is = 224
of = 640
% = x
now just sub
224/640 = x/100
cross multiply because this is a proportion
(640)(x) = (224)(100)
640x = 22400
x = 22400/640
x = 35......so 224 is 35% of 640


5 0
3 years ago
Read 2 more answers
4) -4+5n=18+3n<br>plz help
GuDViN [60]

-4+5n=18+3n=?  so n=18+3n group like terms which would be

18+4n my beautiful queen

hope this helps

4 0
3 years ago
Hillside Travel pays its employees $16 per hour plus 8% commission on all trips booked. Tyrus worked 20 hours last week and book
4vir4ik [10]

Answer:

$488

Step-by-step explanation:

16×20=320

8%×2100

0.08×2100

168

320+168=$ 488

3 0
2 years ago
A property sells for $140,000 two years after it was purchased. If the annual appreciation rate is 6%, how much did the original
kykrilka [37]

Answer:

$123,200

Step-by-step explanation:

0.06 x 2 = 0.12

140,000 x 0.12 = 16,800

140,000 - 16,800 = 123,200

3 0
3 years ago
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