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ser-zykov [4K]
3 years ago
15

Expand the logarithmic expression: log3 d/12

Mathematics
2 answers:
Anni [7]3 years ago
6 0

Answer:

Expanded form: \Rightarrow \log_3d-2\log_32-1  

Step-by-step explanation:

Given: \log_3\dfrac{d}{12}

Subtraction property of log: log a/b = log a - log b

Addition property of log: log(ab) = log a+ log b

\log_aa=1

\log_ab^m=m\log_ab

\log_3\dfrac{d}{12}=\log_3d-\log_312          (Subtraction property )

\Rightarrow \log_3d-\log_3(4\times 3)

\Rightarrow \log_3d-(\log_34+\log_33)       (Addition Property)

\Rightarrow \log_3d-\log_34-\log_33          (Distributive property)

\Rightarrow \log_3d-\log_34-1                    (\log_aa=1)

\Rightarrow \log_3d-2\log_32-1  

The expanded form of \log_3\dfrac{d}{12} is

\Rightarrow \log_3d-2\log_32-1  

Hence, Expanded form: \Rightarrow \log_3d-2\log_32-1  

 

Temka [501]3 years ago
5 0

Answer:

log(base 3)(d/12) = log(base 3)d - log(base 3)12

Step-by-step explanation:

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Convert the following into fractions in their simplest form
sladkih [1.3K]

Answer:

1/10

13/100

4/5

12/25

3/10

63/100

3/5

51/200

2/9

5/11

To prove the last 2 recurring ones:

0.222222... = x

10x = 10 * 0.22222... =  2.222222....

Notice how the decimal part of 10x is the same as for x:

10x - x = 2.2222222... - 0.222222... = 2

10x - x = 9x = 2

x = 2/9

Same procedure for the other one but times by 100 instead:

x = 0.454545...

100x = 45.454545...

100x - x = 45.454545... - 0.454545... = 45

100x - x = 99x = 45

x = 45/99 = 5/11

3 0
2 years ago
Which linear inequality is represented by the graph?
Dovator [93]

Answer:

The answer to your question is   the second choice (y ≥ 1/3x - 1)

Step-by-step explanation:

Process

1.- Find two points of the graph

A (0, -1)

B (3, 0)

2.- Find the slope

m = (0 + 1)/(3 - 0)

m = 1/3

3.- Find the equation of the line

     y - y1 = m(x - x1)

     y + 1 = 1/3(x - 0)

     y + 1 = 1/3x

     y = 1/3x - 1

4.- Find the equation of the inequality

      We need the upper part of the line so the inequality must be

       y ≥ 1/3x - 1

3 0
2 years ago
In right triangle ABC, ZC is a right angle, m ZA = 52, AC = 10.01, and AB = c.
nlexa [21]

Answer:

The measurement of AB is 16.25 units.

Step-by-step explanation:

In right triangle ABC, ∠C is a right angle, m∠A = 52° , AC = 10.01, and AB = c.

We need to find the measurement of AB.

∠C is a right angle, it means AB is hypotenuse.

In a right angle triangle,

\cos \theta=\dfrac{Base}{Hypotenuse}

\cos A=\dfrac{AC}{AB}

\cos (52^\circ)=\dfrac{10.01}{c}

0.616=\dfrac{10.01}{c}

c=\dfrac{10.01}{0.616}

c=16.25

Hence, the measurement of AB is 16.25 units.

6 0
2 years ago
Solve for x. z = 6 π x y z/6πy =x z/6π =x x = 6 π y z z/6 =x
IceJOKER [234]
The answer should be X = Z / 6piy
6 0
3 years ago
Attached as photo. Please help
Effectus [21]

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

<h3>How to estimate a definite integral by numerical methods</h3>

In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

  1. Define the function seen in the statement by the label f(x₀, y₀).
  2. Determine the different variables by the following formulas:

    xₙ₊₁ = xₙ + (n + 1) · Δx     (2)
    yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ)     (3)
  3. Find the integral.

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.

To learn more on Euler's method: brainly.com/question/16807646

#SPJ1

7 0
1 year ago
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