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AlekseyPX
3 years ago
12

If a standard dartboard's diameter is 17.75 inches, what is the area of once sector?

Mathematics
1 answer:
Arturiano [62]3 years ago
8 0

Answer:

  12.37 square inches

Step-by-step explanation:

The area of the dartboard can be figured from the diameter as ...

   A = (π/4)d² = (π/4)(17.75 in)² ≈ 247.4495 in²

There are 20 sectors, all the same size, so the area of one of them is ...

  sector area = (1/2)(247.4495 in²) ≈ 12.37 in²

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1,-2,3,-4,5... <br><br> what’s the next two numbers in the pattern?
MrMuchimi

Answer:

The two numbers following 1,-2,3,-4,5...  are -6 and 7.

Step-by-step explanation:

index:   1   2   3   4   5 ....

value:    1  -2  3  -4   5

Let the index be n.  Then the first term is a(1), the secon is a(2), and so on.

a(2) = 2*(-1)^(2-1) = 2*(-1) = -2 (correct)

a(3) = 3*(-1)^(3-1)   =  3*(-1)^2 = 3 (correct)

a(4) = 4*(-1)^(4-1)    = 4*(-1)^3 = -4 (correct)

So the general formula for a(n)  is:    a(n)=n(-1)^(n-1)

Thus,

a(5) = 5(-1)^4 = 5

a(6) = 6(-1)^5 = -6

a(7) = 7(-1)^6 = 7

The "next two numbers in the pattern" are -6 and 7.  The first 7 numbers are

1,-2,3,-4,5, -6, 7

4 0
3 years ago
Which expression is equivalent to x y Superscript two-ninths?
crimeas [40]

Option D: x\sqrt[9]{y^2} is the expression equivalent to xy^{\frac{2}{9}}

Explanation:

Option A: \sqrt{xy^9}

The expression can be written as ({xy^9})^{\frac{1}{2}

Applying exponent rule, we get,

x^{\frac{1}{2}} y^{\frac{9}{2}}

Thus, the expression \sqrt{xy^9} is not equivalent to the expression xy^{\frac{2}{9}}

Hence, Option A is not the correct answer.

Option B: \sqrt[9]{xy^2}

The expression can be written as ({xy^2})^{\frac{1}{9}

Applying exponent rule, we get,

x^{\frac{1}{9}} y^{\frac{2}{9}}

Thus, the expression \sqrt[9]{xy^2} is not equivalent to the expression xy^{\frac{2}{9}}

Hence, Option B is not the correct answer.

Option C: x\sqrt{y^9}

The expression can be written as x(y^9)^{\frac{1}{2} }

Applying exponent rule, we get,

x y^{\frac{9}{2}}

Thus, the expression x\sqrt{y^9} is not equivalent to the expression xy^{\frac{2}{9}}

Hence, Option C is not the correct answer.

Option D: x\sqrt[9]{y^{2} }

The expression can be written as x(y^2)^{\frac{1}{9} }

Applying exponent rule, we get,

xy^{\frac{2}{9}}

Thus, the expression xy^{\frac{2}{9}} is equivalent to the expression xy^{\frac{2}{9}}

Hence, Option D is the correct answer.

4 0
3 years ago
Read 2 more answers
How do you write 0.5% as a fraction
bixtya [17]
1/2 in simplest form
4 0
3 years ago
Read 2 more answers
A park ranger is looking out from their station at a 30 degree angle , angle of depression. The ranger is 80 feet above the grou
vfiekz [6]

Answer:

\boxed{\text{160 ft}}

Step-by-step explanation:

The angle of depression from the ranger at point A and the angle of elevation from the fire on the ground at Point C are congruent (interior opposite angles).

The distance from the ranger up in the tower to the fire on the ground is the hypotenuse AC  of the right triangle ABC.

sin 30 = 80/AC

AC  = 80/sin30 = 80/0.5 = 160 ft

The distance is \boxed{\textbf{160 ft}}

3 0
2 years ago
The following table is for which exponential function?
sweet-ann [11.9K]
The answer is (y= 1/2)
3 0
3 years ago
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