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iris [78.8K]
2 years ago
11

Can someone please help me on this question! Thank you very much!!

Mathematics
2 answers:
Elis [28]2 years ago
7 0
First find the area of the triangle (on top) and then subtract the area of the circle (on bottom) since the triangle is Equilateral, you can assume that the height can be found by using the 30 60 90 angle relationship. To find the radius of the circle, divide the height by 2.

Kisachek [45]2 years ago
4 0

Answer:

(9√3 - 3π) cm²  or ≈ 6.16 cm²

Step-by-step explanation:

<em>Refer to attached pictures</em>

We have equilateral triangle with side of 6 cm and inscribed circle, we need to find the shaded area inside the triangle not covered by the circle.

The shaded are is the difference of areas of the triangle and circle

<u>Area of equilateral triangle is calculated as per formula:</u>

  • A= √3 /4 × a², where a is side of triangle
  • A= √3 /4 × 6² = 9√3 cm²

<u>Area of circle is calculated as per formula:</u>

  • A= πr², where r is the radius of circle

<u>Let's find the value of r:</u>

Δ ADB is the right triangle with angles 30° and 60°

It has sides of 3 cm, 6 cm and AD= m cm

As per attached, m is the long leg and equal to a√3, so

  • m = 3√3

also,

  • AD= AO+OD= AO +r

<u>We can find AO in the same way as above using Δ AOF</u>

AO= 2r as it is the hypotenuse and the hypotenuse is twice a short leg in the right triangle with angles 30° and 60°

So,  

  • AD= 2r+r= 3r
  • ⇒ r= AD/3 = 3√3/3= √3 cm

<u>Now we can get the area of circle:</u>

  • A= πr²= π×√3²= 3π cm²

<u>Shaded are is:</u>

  • (9√3 - 3π) cm²  or ≈ 6.16 cm²

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Write a polynomial f (x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -4 (multiplicity 3), 1 (
yuradex [85]

Answer:

Step-by-step explanation:

Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.

The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.

The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).

The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320

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