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3 years ago

Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

Mathematics

1 answer:

devlian [24]3 years ago

7 0

Answer:

Dy/Dx=x ( 2 ln ( x ) − 1 )/ ln ^2 ( x)

Step-by-step explanation:

We have this function and let's derive it in terms of x.

y =x^2/In x

Dy/Dx=(x^2/In x)'=2/lnx *(x^2)'-(x^2/In x)'=> 2 x *ln ( x ) − x *ln ^2 ( x ) =x ( 2 ln ( x ) − 1 )/ ln ^2 ( x)

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Convert 0.875 inch to a fraction in simplest form. Click to select the correct answer.

inna [77]

This isnt the simplist but 875/1000 . Thats 875 over 1000.

8 0

3 years ago

Mateo reproducira una foto que mide 5 cm por lado a una escala de 3/4

Aneli [31]

the question in English

Mateo will reproduce a photo measuring 5 cm per side on a scale of 3/4

How much will the square side of the copy measure?

Will the size of the copy be larger or smaller than the original?

we know that

the scale factor is equal to $\frac{3}{4}$

Let

x----------> the original length side

y--------> the copy length side

$y=\frac{3}{4}*x$

we have that

$x=5\ cm$

substitute the values

$y=\frac{3}{4}*5=3.75\ cm$

therefore

the answer Part a) is

the length side of the copy measure is $3.75\ cm$

Part b)

we know that

the size of the original photo is------> $5*5=25\ cm^{2}$

the size of the copy is------> $3.75*3.75=14.06\ cm^{2}$

$14.06\ cm^{2} < 25\ cm^{2}$

therefore

the answer part b) is

The size of the copy be smaller than the original

3 0

3 years ago

To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s

inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0

3 years ago

Plz help Thank you! If you can

aleksklad [387]

Answer: 140

Step-by-step explanation: It doesn't change because they arethe same proportional angle.

8 0

3 years ago

Read 2 more answers

Determine the length of the longest metal rod which could be stored in a rectangle box 20 cm by 50 cm by 30 cm.

navik [9.2K]

Answer:

61.64 cm

Step-by-step explanation:

The longest metal rod which could be stored in a rectangular box will be equal to its diagonal:

$\therefore \: length \: of \:metal \: rod \\ = \sqrt{ {l}^{2} + {b}^{2} + {h}^{2} } \\ = \sqrt{ {20}^{2} + {50}^{2} + {30}^{2} } \\ = \sqrt{400 + 2500 + 900} \\ = \sqrt{3800} \\ = 61.64414 \\ = 61.64 \: cm$

5 0

4 years ago

Read 2 more answers