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12345 [234]
2 years ago
6

Find the derivative using the first principles. ​

Mathematics
1 answer:
lubasha [3.4K]2 years ago
3 0

~~~~\dfrac{d}{dx} \left( \sqrt[5]{1+x} \right)\\\\\\=\dfrac{d}{dx} (1+x)^{\tfrac 15}\\\\\\=\dfrac 15 \left(1 + x\right)^{\tfrac 15 -1} \cdot \dfrac{d}{dx}(1+x)\\\\\\=\dfrac 15 (1+x)^{-\tfrac 45} \cdot(0+1)\\\\\\=\dfrac{1}{5(1+x)^{\tfrac 45}}

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guapka [62]

Answer:

a. 2,440 km

b. 1.33*10^{27} kg

Step-by-step explanation:

a. Diameter of Mercury = 4.88*10^3

Radius of Mercury = ½ of its diameter = \frac{4.88*10^3}{2}

Radius of Mercury = 2.44*10^3

To convert the radius to ordinary number, multiply 2.44 by 1,000.

Radius of Mercury as an ordinary number = 2.44*1,000 = 2,440 km

b. Mass of Jupiter = 1.898*10^{27} kg

Mass of Saturn = 5.68*10^{26} kg

Difference between mass of Jupiter and mass of Saturn = 1.898*10^{27} - 5.68*10^{26} (subtract 5.68 from 1.898 = 5.68. we would retain the largest exponent, which is raised to the lower of 27.)

= 1.33*10^{27}

7 0
3 years ago
Cody said that dividing a unit fraction by a whole number is the same as multiplying the unit fractions by a unit fraction with
LekaFEV [45]

Answer:

True

Step-by-step explanation:

Hi, the statement is true, because to divide a fraction we have to turn the second fraction upside down and multiply them. Since a whole number x can be written as x/1, it also applies to the case of dividing a fraction by a whole number.

We can prove it with an example.

Dividing a unit fraction by a whole number  

1/2 ÷ 2 = (1x1) / (2x2) = 1/4

Multiplying the unit fractions by a unit fraction with a whole number as a denominator

1/2 x 1/2= (1x1) / (2x2) = 1/4

4 0
3 years ago
Read 2 more answers
Lisa drinks 20 fl oz of water after she runs 1 mile. She wants to make a table to see how much water she will need to drink as s
jeyben [28]

Answer:

20=1

She drinks 20 fl oz per 1 mile she runs.

5x20=100

Your answer is C) 100.

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3 years ago
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Find the slope of the line that passes through each pair of points.
kotegsom [21]
6. m=2
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8. m=0
Hope it help
6 0
2 years ago
Helpppppoppp meeeeeee
madreJ [45]

Answer:

9 feet

Step-by-step explanation:


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3 years ago
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