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alex41 [277]
3 years ago
10

What is the differentiation of f(x) =2x^4/5?

Mathematics
1 answer:
motikmotik3 years ago
6 0
\bf f(x)=\cfrac{2x^4}{5}\implies f(x)=\cfrac{2}{5}x^4\implies \cfrac{df}{dx}=\cfrac{2}{5}\cdot 4x^3\implies \cfrac{df}{dx}=\cfrac{8x^3}{5}

notice, the 2/5 is just a "scalar" value, so you can just get the derivative of the variable part and slap the scalar as its factor.
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What is the equation of the line expressed in slope-intercept form?
Alisiya [41]
(x,y)
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y=mx+2
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4 0
3 years ago
A first number plus twice a second number is 4. Twice the first number plus the second totals 20. Find the numbers
pychu [463]

Answer:

The first number is 6

The second number is -1

6+(-2)=4

6*2=12 12+(-1)=11

Step-by-step explanation:


4 0
3 years ago
Write in standard form an equation for the line with slope 1/3 through<br> the point (2,-2).
Alexxandr [17]

Answer:

x - 3y = 8.

Step-by-step explanation:

Use the point-slope form of the equation of a line:

y - y1 = m(x - x1)  where m = the slope and (x1, y1) is a point on the line.

So substituting the given values:

y - (-2) = 1/3(x - 2)

y + 2 = 1/3x - 2/3     Multiply through by 3:

3y + 6 = x - 2

x - 3y  =  6 + 2

x - 3y = 8  <---- Standard Form.

6 0
2 years ago
Activity 4: Performance Task
Nookie1986 [14]

An arithmetic progression is simply a progression with a common difference among consecutive terms.

  • <em>The sum of multiplies of 6 between 8 and 70 is 390</em>
  • <em>The sum of multiplies of 5 between 12 and 92 is 840</em>
  • <em>The sum of multiplies of 3 between 1 and 50 is 408</em>
  • <em>The sum of multiplies of 11 between 10 and 122 is 726</em>
  • <em>The sum of multiplies of 9 between 25 and 100 is 567</em>
  • <em>The sum of the first 20 terms is 630</em>
  • <em>The sum of the first 15 terms is 480</em>
  • <em>The sum of the first 32 terms is 3136</em>
  • <em>The sum of the first 27 terms is -486</em>
  • <em>The sum of the first 51 terms is 2193</em>

<em />

<u>(a) Sum of multiples of 6, between 8 and 70</u>

There are 10 multiples of 6 between 8 and 70, and the first of them is 12.

This means that:

\mathbf{a = 12}

\mathbf{n = 10}

\mathbf{d = 6}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{10} = \frac{10}2(2*12 + (10 - 1)6)}

\mathbf{S_{10} = 390}

<u>(b) Multiples of 5 between 12 and 92</u>

There are 16 multiples of 5 between 12 and 92, and the first of them is 15.

This means that:

\mathbf{a = 15}

\mathbf{n = 16}

\mathbf{d = 5}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{16} = \frac{16}2(2*15 + (16 - 1)5)}

\mathbf{S_{16} = 840}

<u>(c) Multiples of 3 between 1 and 50</u>

There are 16 multiples of 3 between 1 and 50, and the first of them is 3.

This means that:

\mathbf{a = 3}

\mathbf{n = 16}

\mathbf{d = 3}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{16} = \frac{16}2(2*3 + (16 - 1)3)}

\mathbf{S_{16} = 408}

<u>(d) Multiples of 11 between 10 and 122</u>

There are 11 multiples of 11 between 10 and 122, and the first of them is 11.

This means that:

\mathbf{a = 11}

\mathbf{n = 11}

\mathbf{d = 11}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{16} = \frac{11}2(2*11 + (11 - 1)11)}

\mathbf{S_{11} = 726}

<u />

<u>(e) Multiples of 9 between 25 and 100</u>

There are 9 multiples of 9 between 25 and 100, and the first of them is 27.

This means that:

\mathbf{a = 27}

\mathbf{n = 9}

\mathbf{d = 9}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{9} = \frac{9}2(2*27 + (9 - 1)9)}

\mathbf{S_{9} = 567}

<u>(f) Sum of first 20 terms</u>

The given parameters are:

\mathbf{a = 3}

\mathbf{d = 3}

\mathbf{n = 20}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{20} = \frac{20}2(2*3 + (20 - 1)3)}

\mathbf{S_{20} = 630}

<u>(f) Sum of first 15 terms</u>

The given parameters are:

\mathbf{a = 4}

\mathbf{d = 4}

\mathbf{n = 15}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{15} = \frac{15}2(2*4 + (15 - 1)4)}

\mathbf{S_{15} = 480}

<u>(g) Sum of first 32 terms</u>

The given parameters are:

\mathbf{a = 5}

\mathbf{d = 6}

\mathbf{n = 32}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{32} = \frac{32}2(2*5 + (32 - 1)6)}

\mathbf{S_{32} = 3136}

<u>(g) Sum of first 27 terms</u>

The given parameters are:

\mathbf{a = 8}

\mathbf{d = -2}

\mathbf{n = 27}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{27} = \frac{27}2(2*8 + (27 - 1)*-2)}

\mathbf{S_{27} = -486}

<u>(h) Sum of first 51 terms</u>

The given parameters are:

\mathbf{a = -7}

\mathbf{d = 2}

\mathbf{n = 51}

The sum of n terms of an AP is:

\mathbf{S_n = \frac n2(2a + (n - 1)d)}

Substitute known values

\mathbf{S_{51} = \frac{51}2(2*-7 + (51 - 1)*2)}

\mathbf{S_{51} = 2193}

Read more about arithmetic progressions at:

brainly.com/question/13989292

4 0
2 years ago
Read 2 more answers
The school purchased baseball equipment and uniforms for a total cost of $1836. the equipment cost $612 and the uniforms were $2
liraira [26]

Answer:

48 uniforms

Step-by-step explanation:

1836-612=1224.

1224/25.50=48.

Checked answer:

25.50 x 48= 1224

6 0
3 years ago
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