Simplify the expression, if possible. 512 1/2

d1i1m1o1n [39]

Ah! I love these questions!

To find the area of the shaded region, you must find the area of the circle. Then, you must find the area of the triangle inscribed in the circle. Lastly, you must subtract the area of the triangle from the area of the circle.

Area of Circle: $\pi$ x $r^{2}$
= $\pi$ x 10^2
= $\pi$ x 100
Usually these problems will not require you to convert pi into a decimal, but if it does, then the area of the circle would be 314.

Area of Equilateral Triangle: $\frac{ s^{2} \sqrt{3} }{4}$
To find the side, draw a perpendicular line from the center to a side of a triangle. This line will create two more triangles inside the big triangle. You will notice how in these smaller triangles, the angles are 30, 60, 90. From that we can deduce that half the length of a side is 5 $\sqrt{3}$ because of the 30, 60, 90 ratio. Multiply that by 2 to get 10 $\sqrt{3}$ as the length of the side of the large triangle. Now substitute this value into the formula above.
$\frac{ (10 \sqrt{3}) ^{2} x \sqrt{3} }{4} = \frac{300 \sqrt{3} }{4} = 75 \sqrt{3}$

Final Answer: 100 $\pi$ - 75 $\sqrt{3}$

6 0

3 years ago

Camila and her children went into a grocery store and where they sell apples for $0.50 each and mangos for $0.75 each. Camila ha

shtirl [24]

Answer:

4

Step-by-step explanation:

5 0

3 years ago

Who defeated Rommel during WWII?

Firdavs [7]

Answer:

General Patton

Step-by-step explanation:

He kicked Rommel into next year. Simple as that.

5 0

3 years ago

Prime factorization of 48?

VikaD [51]

Answer: 2 x 2 x 2 x 2 x 3

Step-by-step explanation: To find the prime factorization of 48, first create a factor tree with two branches.

When a number is even, it's often easiest to start by dividing by 2 to find factors.

Since 48 ÷ 2 . is 24, we know that 2 and 24 are factors of 48 so we write 2 and 24 at the bottom of the branches.

Next, we circle any prime factors in the factor tree. Since 2 is classified as a prime number, we circle 2 but since 24 is not a prime number, we draw two new branches.

Since 24 ÷ 2 is 12, we know that 2 and 12 are factors of 24 so we write 2 and 12 at the bottom of the branches.

Next, we circle any prime factors in the factor tree. Since 2 is classified as a prime number, we circle 2. Since 12 is not a prime number, we draw two new branches.

Since 12 ÷ 2 is 6, we know that 2 and 6 are factors of 12. This means that we write 2 and 6 at the bottom of the branches. Next, we circle any prime factors in the factor tree. Since 2 is a prime number, we circle 2 but draw two new branches coming down from 6 because it's not prime.

Since 6 ÷ 2 is 3, we know that 2 and 3 are factors of 6 so we write 2 and 3 at the bottom of the branches. Next, we circle any prime factors in the factor tree. Since both 2 and 3 are prime meaning that the only factors they have are 1 and the number itself, we circle both 2 and 3.

Since we have circles at the bottom of all of the branches, we are finished.

So the prime factorization of 48 is 2 × 2 × 2 × 2 × 3.

Notice that the factor 2 is repeated 4 times. In this case, we can rewrite the prime factorization of 48 using exponents as $2^{4}$ x 3