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3 years ago

HELP IN NEED!

Mathematics

1 answer:

laiz [17]3 years ago

6 0

Answer:

$AB=12\sqrt{3}\ cm$

Step-by-step explanation:

If AB is tangent to the circle, then angle ABO is right angle and triangle AOB is special $30^{\circ}-60^{\circ}-90^{\circ}$ triangle. In this triangle, the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,

$AO=2BO=2\cdot 12=24\ cm.$

By the Pythagorean theorem,

$AB^2=AO^2-BO^2,\\ \\AB^2=24^2-12^2,\\ \\AB^2=576-144=432,\\ \\AB=12\sqrt{3}\ cm.$

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Explain how you could convert 152 cups into gallons.

Mila [183]

Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.

Step-by-step explanation:

4 0

3 years ago

Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496

coldgirl [10]

Answer:

(a) $gcd(20, 12)=4$

(b) $gcd(100, 36)=4$

(c) $gcd(496,207 )=1$

Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

Given integers $a, b$ , find $d=gcd(a,b)$

Here is an outline of the steps:

Let $a=x$ , $b=y$ .
Given $x, y$ , use the division algorithm to write $x=yq+r$ .
If $r=0$ , stop and output $y$ ; this is the gcd of $a, b$ .
If $r\neq 0$ , replace $(x,y)$ by $(y,r)$ . Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find $gcd(20, 12)$ we apply the Euclidean algorithm:

$20 = 12\cdot 1 + 8\\ 12 = 8\cdot 1 + 4\\ 8 = 4\cdot 2 + 0$

The process stops since we reached 0, and we obtain $gcd(20, 12)=4$ .

(b) To find $gcd(100, 36)$ we apply the Euclidean algorithm:

$100 = 36\cdot 2 + 28\\ 36 = 28\cdot1 + 8\\ 28 = 8\cdot 3 + 4\\ 8 = 4\cdot 2 + 0$

The process stops since we reached 0, and we obtain $gcd(100, 36)=4$ .

(c) To find $gcd(496,207 )$ we apply the Euclidean algorithm:

$496 = 207\cdot 2 + 82\\ 207 = 82\cdot 2 + 43\\ 82 = 43\cdot 1 + 39\\ 43 = 39\cdot 1 + 4\\ 39 = 4\cdot 9 + 3\\ 4 = 3\cdot 1 + 1\\ 3 = 1\cdot 3 + 0$

The process stops since we reached 0, and we obtain $gcd(496,207 )=1$ .

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2 years ago

A stone dropped from a bridge strikes the water 2.2 s later. How high is the bridge above thewater

vivado [14]

Let the only force acting on the ball is the gravity (free-failing) and the ball was initially stationary
vo = 0

s = vot + 1/2 gt^2

s = 1/2 x 10 x (2.2) ^2 = 24.2 m

3 0

3 years ago

Read 2 more answers

What does x equal in 5x + 15 = 28

Minchanka [31]

Answer: 2.6

Step-by-step explanation:

28-15=13

13/5=2.6

Good luck! :)

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2 years ago