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1 year ago

If log(16)=s, what is the value of 2/3 log(6400) - 1/3 log(1600) in terms of s?

Mathematics

1 answer:

eduard1 year ago

8 0

The value of $\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)$ in terms of s will be

$\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)$

<h3>What is Logrithm?</h3>

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Here we have the expression:-

$\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)$

So in terms of s the expression will become:-

$\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)$

To know more about logarithm follow

brainly.com/question/25710806

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If Gage gets 40 bucks a month how much months would it take him to get 300 bucks.

USPshnik [31]

Answer:

7 to 8 months / most probably 8 months

7.5 months to be exact

Step-by-step explanation:

Hi there!! Let's work!

So lets Break it down,

Given: $40 every month

Prove: How many months till he has in total $300

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<h2>We need to multiply the number of months to 40 to get 300</h2>

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<h3>So lets refer to a multiplication chart to make it easier:</h3>

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<h3>Here is an example of the equation we will use:</h3>

<u>400 x (months) = $300 / (or how much ever we get)</u>

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We have 2 final equations because we don't have a straight forward answer. (Refer to explanation below)

40 x 7 = 280

and

40 x 8 = 320

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So in problems like these we have to think like we would in real life, if you have an option you can write 7 to 8 months or you should write 8 instead of seven since they may be asking for a specific amount of months and after 8 months Gage will reach (surpass) his goal of $300 by $20.

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8 0

2 years ago

The ratio of coffee drinkers to tea drinkers at a local café is 4:3. If there are 21 people at the

qaws [65]

Answer:

ghyohgfyu

Step-by-step explanation:

6 0

2 years ago

The figure shows Polygon ABCD and some of its transformed images on a coordinate grid:

Black_prince [1.1K]

Based on the fact that the Polygon ABCD was translated, then the polygon that is a translation of it will be Polygon 3.

<h3>What polygon is the translation of Polygon ABCD?</h3>

When a shape is translated, it is taken as it is from one area of the coordinate plane, to another area of the plane.

This means that it doesn't change in height, or orientation.

The only polygon that still looks like Polygon ABCD is Polygon 3 which means that it is the translated version.

Find out more on transformations at brainly.com/question/4289712

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3 0

9 months ago

How do you do this question?

Sergeeva-Olga [200]

Answer:

V = 2000r³/3

Step-by-step explanation:

We know that the base is a circular disk, so it creates a circle on the xy plane. It would be in the form x² + y² = r². In other words x² + y² = (5r)². Let's isolate y in this equation now:

x² + y² = (5r)²,

x² + y² = 25r²,

y² = 25r² - x²,

y = √25r² - x² ---- (1)

Now remember that parallel cross sections perpendicular to the base are squares. Therefore Area = length^2. The length will then be = 2√25r² - x² --- (2). Now we can evaluate the integral from -5r to 5r, of [ 2√25r² - x² ]² dx.

$\int _{-5r}^{5r}\:\left[\:2\sqrt{\left(25r^2\:-\:x^2\right)}\:\right]\:^2\:dx\\=\int _{-5r}^{5r}4\left(25r^2-x^2\right)dx\\\\= 4\cdot \int _{-5r}^{5r}25r^2-x^2dx\\\\= 4\left(\int _{-5r}^{5r}25r^2dx-\int _{-5r}^{5r}x^2dx\right)\\\\= 4\left(250r^3-\frac{250r^3}{3}\right)\\\\= 4\cdot \frac{500r^3}{3}\\\\= \frac{2000r^3}{3}$

As you can see, your exact solution would be, V = 2000r³/3. Hope that helps!

3 0

2 years ago

Simplify.<br><br> 1/4 (1 - 2/3)² + 1/3.<br><br> The answer must be a simplified fraction.

loris [4]

Answer:

$\large\boxed{\dfrac{13}{36}}$

Step-by-step explanation:

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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$\dfrac{1}{4}\left(1-\dfrac{2}{3}\right)^2+\dfrac{1}{3}=\dfrac{1}{4}\left(\dfrac{3}{3}-\dfrac{2}{3}\right)^2+\dfrac{1}{3}=\dfrac{1}{4}\left(\dfrac{3-2}{3}\right)^2+\dfrac{1}{3}\\\\=\dfrac{1}{4}\left(\dfrac{1}{3}\right)^2+\dfrac{1}{3}=\dfrac{1}{4}\cdot\dfrac{1^2}{3^2}+\dfrac{1}{3}=\dfrac{1}{4}\cdot\dfrac{1}{9}+\dfrac{1}{3}=\dfrac{1}{36}+\dfrac{1}{3}\qquad(*)\\\\\text{the common denominator is}\ 36.\\\\36=3\cdot12\to\dfrac{1}{3}=\dfrac{1\cdot12}{3\cdot12}=\dfrac{12}{36}\\\\(*)\qquad=\dfrac{1}{36}+\dfrac{12}{36}=\dfrac{1+12}{36}=\dfrac{13}{36}$

4 0

2 years ago