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Anon25 [30]
2 years ago
9

A circle has a diameter of 8 cm. An angle in the center of the circle creates an arc AB. That angle's measure is pi/4 rad. What

is the measure of arc AB
Mathematics
1 answer:
zhenek [66]2 years ago
8 0

Answer:

3.14 cm

Step-by-step explanation:

From the question,

Applying

s = πdФ/360................... Equation 1

Where s = length of arc AB, d = diameter of the circle, Ф = angle at the center of the circle, π = pie

From the question,

Given: d = 8 cm, Ф = π/4 rad = 45°

Constant: π = 22/7

Substitute these values into equation 1

s = (22/7)(8)(45)/360

s = 3.14 cm.

Hence the lenght of arc AB = 3.14 cm

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Answer:

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Step-by-step explanation:

7 0
2 years ago
Prove that under root 2 is a irrational number​
torisob [31]

Answer:

Let's suppose √2 is a rational number. Then we can write it √2  = a/b where a, b are whole numbers, b not zero.

We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.

From the equality √2  = a/b it follows that 2 = a2/b2,  or  a2 = 2 · b2.  So the square of a is an even number since it is two times something.

From this we know that a itself is also an even number. Why? Because it can't be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd. Check it if you don't believe me!

Okay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don't need to know what k is; it won't matter. Soon comes the contradiction.

If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:

2=(2k)2/b22=4k2/b22*b2=4k2b2=2k2

This means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!

WHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.

(I copied this from the internet, but hope it helps!)

4 0
2 years ago
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Making coconut cookies. The recipe calls for 420 g of coconut and 120 g of sugar. Only has 252 g of coconut. How much sugar must
geniusboy [140]

Answer: 72 grams.

Step-by-step explanation:

Let be "s" the amount of sugar in grams that  must be used for 252 grams of coconut to keep the same ratio of coconut to sugar.

Knowing that in the recipe for the coconut cookies, should be 420 grams of coconut and 120 grams of sugar, and you only have 252 grams of coconut, you can set up this proportion to find "s":

\frac{420grams}{120grams}=\frac{252grams}{s}

Now, you need to solve for "s":

\frac{420grams}{120grams}=\frac{252grams}{s}\\\\s(\frac{420grams}{120grams})=252grams\\\\s=(252grams)(\frac{120grams}{420grams})\\\\s=72grams

4 0
3 years ago
Examine the right triangle. A right triangle with side lengths 17 centimeters and 48 centimeters. The hypotenuse is unknown. Wha
Dimas [21]

Answer:

The answer to your question is  c = \sqrt{2593}

Step-by-step explanation:

Data

right triangle

short leg = 17 cm

long leg = 48 cm

hypotenuse = ?

Process

-Use the Pythagorean theorem to find the answer

              c² = a² + b²

c = hypotenuse

a = short leg = 17 cm

b = long leg = 48 cm

- Substitution

             c² = 17² + 48²

-Simplification

             c² = 289 + 2304

             c² = 2593

-Result

             c = \sqrt{2593}

5 0
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