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lorasvet [3.4K]
3 years ago
13

The sum of twice a number and five is greater than three times the number minus three.

Mathematics
2 answers:
AnnZ [28]3 years ago
5 0

Answer:

x<8

Step-by-step explanation:

2x+5>3x-3

2x+8>3x

8>x

strojnjashka [21]3 years ago
5 0

Answer:

n < 8

Step-by-step explanation:

Let n represent the unknown number.  Then:

2n + 5 > 3n - 3

Collecting like terms:

8 > n or n < 8

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Answer:

C

Step-by-step explanation:

We want to integrate:

\displaystyle \int\frac{4x^4+3}{4x^5+15x+2}\,dx

Notice that the expression in the denominator is quite similar to the expression in the numerator. So, we can try performing u-substitution. Let u be the function in the denominator. So:

u=4x^5+15x+2

By differentiating both sides with respect to x:

\displaystyle \frac{du}{dx}=20x^4+15

We can "multiply" both sides by dx:

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And divide both sides by 5:

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Rewriting our original integral yields:

\displaystyle \int \frac{1}{4x^5+15x+2}(4x^4+3\, dx)

Substitute:

\displaystyle =\int \frac{1}{u}\Big(\frac{1}{5} \, du\Big)

Simplify:

\displaystyle =\frac{1}{5}\int \frac{1}{u}\, du

This is a common integral:

\displaystyle =\frac{1}{5}\ln|u|

Back-substitute. Of course, we need the constant of integration:

\displaystyle =\frac{1}{5}\ln|4x^5+15x+2|+C

Our answer is C.

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