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Nataly [62]
4 years ago
8

Find dy/dx y = 5/8x^3/7 + 8x^4 + 6x - 9

Mathematics
1 answer:
aleksandrvk [35]4 years ago
5 0

Answer:

15/56x^(-4/7) + 32x^3 + 6.

Step-by-step explanation:

Using  the rule for algebraic differentiation:

If  y = ax^n, dy/dx = anx^(n-1).

So :

If  y = 5/8x^3/7 + 8x^4 + 6x - 9

dy/dx = 5/8* 3/7 x^(3/7-1) + 8*4 x^(4-1) + 6x(1-1)

=  15/56x^(-4/7) + 32x^3 + 6.

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Answer:

B

Step-by-step explanation:

The compound interest formula is A = P (1+r/n)^nt where:

  • P is the starting amount called the principle
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  • t is the number of years

Substitute a value into each variable to solve.

  • P = $147 since 10% of 1,470 is being invested which makes P = 0.10(1470) = 147.
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  • n = 12 because it is compounded monthly meaning 12 times a year.
  • t = 25 since it will earn for 25 years.

A = P (1+r/n)^{nt}\\A = 147(1 + \frac{0.035}{12})^{12*25}\\A = 147 ( 1 + 0.002916)^{300}\\A = 147(1.002916)^{300}\\A = 352.19

Repeat this process for each formula.

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The number which is express in each of the models as given in the image attached to the task content are as follows;

a). 1.37

b). 1.37

c). 1.37.

<h3>What numbers are expressed according to the given models in the task content?</h3>

It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.

It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.

Read more on place values;

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Answer:

\tt f(x)=2x^2+20x-10

let y=f(x)

\tt y=2x^2+20x-10

\tt 2x^2+10x=y+10

\tt x^2+10x=\frac{1}{2} y+5

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\tt (x+5)^2=\frac{1}{2} (y+60)

\tt 2(x+5)^2=f(x)+60

\boxed{\tt f(x)=2(x+5)^2-60}

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