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Can someone help me please?

1. Refer to the triangle below. If a = 3 and b = 3,
A. Find the exact length of c in unsimplified radical form
B. Find the exact length of c in simplified radical form
C. Find c to the nearest hundredth
**I put the pic down below**

2. Consider the numbers 4/13 and 3/10 .
A. Compare the numbers.
B. Find a rational number between the two given numbers.

3. Use the Babylonian method to approximate √19 to the nearest hundredth.

Can Someone Help Me Please 1 Refer To The Triangle Below If A 3 And B 3 A Find The Exact Length Of C In Unsimplified Radical Form B Find The Exact Length Of C I class=

Sagot :

brandontucker1
For 1) Use the pythagorean theorem and the formula for it is a^2+b^2=c2 
so that will be 3^2+3^2=c^2
  9+9=c^2
18=c2
 then 
[tex] \sqrt{18} which is \sqrt{9(2)} \sqrt{9} \sqrt{2} the finally 3 \sqrt{2} ---- is the unsimplified form simplified form is [/tex]≈4.2426
and the nearest hundredth 4.24

The correct answers are:


#1: A) c = √18

B) c = 3√2

C) c = 4.24

#2: A) 4/13 > 3/10

B) 79/260

#3: 4.36


Explanation:


#1: A) We use the Pythagorean Theorem to solve this:

a² + b² = c²

3² + 3² = c²

9 + 9 = c²

18 = c²


Taking the square root of each side:

√18 = √c²

√18 = c


B) To simplify √18, we first find the prime factorization of 18:

18 = 9*2

9 = 3*3


This gives us

18 = 3*3*2


When we take the square root, we are looking for pairs. We have a pair of 3's; this means we take a 3 out:


3√2


C) In the calculator, we see that 3√2 = 4.24.


#2: A) First, we find a common denominator. The first thing that both 13 and 10 will divide into is 130:


(4*10)/130; (3*13)/130

40/130; 39/130


Since 40 > 39, this means that 4/13 > 3/10.


B) There is not enough space between the two fractions to use 130 as the denominator; we will double that to 260:

(40*2)/260; (39*2)/260

80/260; 78/260


The fraction between these two would be 79/260.


#3: Using the Babylonian method, we first make a guess. Since 9 is nearly half of 19, we will start there.


Next, we divide 19 by our guess:

19/9 = 2.111


We average this quotient with our guess:

(9 + 2.111)/2 = 11.111/2 = 5.5555


This is our new guess. Now divide 19 by this guess:

19/5.5555 = 3.4200342


Average this with our guess:

(5.5555+3.4200342)/2 = 4.4877671


This is our new guess. Divide 19 by this guess:

19/4.4877671 = 4.233731291


Average this with our new guess:

(4.4877671+4.233731291)/2 = 4.360749196


This is our new guess. Divide 19 by this guess:

19/4.360749196 = 4.357049476


Average this with our new guess:

(4.360749196+4.357049476)/2 = 4.358899


Make this our new guess. Divide 19 by this guess:

19/4.358899 = 4.3588988


Average this with our guess:

(4.358899+4.3588988)/2 = 4.3588989


Since the hundredths place has been the same the last few lines, we round to that: 4.36.

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