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Alchen [17]
3 years ago
9

100ft. Doing the ladder method

Mathematics
1 answer:
Alja [10]3 years ago
4 0
That will be 1,000ft cause that is the ladder method
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3 years ago
The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of
artcher [175]

Answer:

Third option.

Step-by-step explanation:

Some transformations for a function f(x), are:

If f(x)+k, the function is shifted down "k" units.

If f(x)-k, the function is shifted up "k" units.

If bf(x), and b>1, the functio is stretch vertically by a factor of "b".

If  -f(x), the function is reflected over the x-axis.

Therefore, knowing that the parent function f(x) = log_3(x)  was transformated by reflecting it over the x-axis, stretching vertically by a factor of 2 and shifting it down 3 units, we can determine that the following function represents the transformation:

f(x) = -2log_3(x)-3

3 0
3 years ago
Find the length of the following curve. If you have a​ grapher, you may want to graph the curve to see what it looks like.
stepladder [879]

The length of the curve y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

y = \frac{1}{27}(9x^2 + 6)^\frac 32 from x = 3 to x = 6

Start by differentiating the curve function

y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x

Evaluate

y' = x(9x^2 + 6)^\frac 12

The length of the curve is calculated using:

L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx

This gives

L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx

Expand

L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx

This gives

L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx

Express as a perfect square

L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx

Evaluate the exponent

L =\int\limits^6_3 {3x^2 + 1} \ dx

Differentiate

L = x^3 + x|\limits^6_3

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units

Read more about curve lengths at:

brainly.com/question/14015568

#SPJ1

7 0
2 years ago
The line passes through the points (-5,0) and (-1,-4)<br> The slope of the line is
kotykmax [81]

Answer:

-1.

Step-by-step explanation:

First, you find the distance from the first x coordinate to the second. This is done by doing -5 - -1 (aka -5 + 1), which equals -4. Then, you find the distance form the first y coordinate to the second. THis is done by doing 0 - -4 (aka 0 + 4), which equals 4. Then, you divide the distance of the y's over the distance of the x's, which gets you the slope, which is -1. Hope this helped!

8 0
4 years ago
Margo borrows $400, agreeing to pay it back with 5% annual interest after 18 months. How much interest will she pay?
IRISSAK [1]

Answer:

Step-by-step explanation:

V

3 0
3 years ago
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