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3 years ago

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 numerical approximate solution of the definite 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 definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral 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:

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

xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (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 numerical approximation of the definite integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

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

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

#SPJ1

7 0

1 year ago