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pashok25 [27]
3 years ago
10

Given log630 ≈ 1.898 and log62 ≈ 0.387, log615 =

Mathematics
2 answers:
Tom [10]3 years ago
6 0

\log_630\approx1.898\\\\\log_62\approx0.387\\\\\log_615=\log_6\dfrac{30}{2}=\log_630-\log_62\approx1.898-0.387=1.511\\\\Used:\\\\\log_ab-\log_ac=\log_a\dfrac{b}{c}

Oksi-84 [34.3K]3 years ago
4 0

Answer:

The value of log_6{15} is 1.511.

Step-by-step explanation:

It is given that log_6{30}\approx 1.898 and log_6{2}\approx 0.387.

We have to find the value of log_6{15}.

It can be written as

log_6{15}=log_6\frac{30}{2}

Using property of lo, we get

log_6{15}=log_630-log_62          log_m\frac{a}{b}=log_ma-log_mb

Substitute log_6{30}\approx 1.898 and log_6{2}\approx 0.387 in the above equation.

log_6{15}=1.898-0.387

log_6{15}=1.511

Therefore the value of log_6{15} is 1.511.

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Jorge bought 6 large balloons for a party. This was 25% of all the balloons he bought. How many total balloons did Jorge buy sho
riadik2000 [5.3K]

Answer:

The answer would be 24 balloons in total.

Step-by-step explanation:

Jorge bought 6 large balloons, which was 25% of ALL the balloons he bought.

Meaning that since 6 is 25% of the number 24, he bought 24 balloons in total.

PROOF:

25% * 24 = 6

24 / 6 = 4

6 * 4 = 24

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36 x 10^5 in scientific notation
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Answer:

3.6 x 10^6

Hope this helps :)

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24 dollars.

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3 years ago
Read 2 more answers
Not sure what to do here can someone please help
kumpel [21]

Answer:

  x = 2

Step-by-step explanation:

These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.

__

<h3>Squaring</h3>

The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.

  \sqrt{x+2}+1=\sqrt{3x+3}\qquad\text{given}\\\\(x+2)+2\sqrt{x+2}+1=3x+3\qquad\text{square both sides}\\\\2\sqrt{x+2}=(3x+3)-(x+3)=2x\qquad\text{isolate the root term}\\\\x+2=x^2\qquad\text{divide by 2, square both sides}\\\\x^2-x-2=0\qquad\text{write in standard form}\\\\(x-2)(x+1)=0\qquad\text{factor}

The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.

  x = -1: √(-1+2) +1 = √(3(-1)+3)   ⇒   1+1 = 0 . . . . not true

  x = 2: √(2+2) +1 = √(3(2) +3)   ⇒   2 +1 = 3 . . . . true . . . x = 2 is the solution

__

<h3>Substitution</h3>

Another way to solve this is using substitution for one of the radicals. We choose ...

  u=\sqrt{x+2}\qquad\text{requires $u\ge0$}\\\\u^2-2=x\qquad\text{solve for x}\\\\u+1=\sqrt{3(u^2-2)+3}\qquad\text{substitute for x in the original equation}\\\\(u+1)^2=3u^2-3\qquad\text{square both sides, simplify a little}\\\\2u^2-2u-4=0\qquad\text{subtract $(u+1)^2$}\\\\2(u-2)(u+1)=0\qquad\text{factor}

Solutions to this equation are ...

  u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution

The value of x is ...

  x = u² -2 = 2² -2

  x = 2 . . . . the solution to the equation

_____

<em>Additional comment</em>

Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.

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Angle bec= 20 and angle abe =160
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