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DiKsa [7]
3 years ago
11

9.) Find the following antiderivative

Mathematics
2 answers:
Studentka2010 [4]3 years ago
8 0
◆ Indefinite Integration ◆

IrinaVladis [17]3 years ago
5 0

Let u = 5x+1. Then du = 5·dx, and your integral is

\displaystyle\frac{1}{5}\int{\frac{5}{5x+1}}\, dx=\frac{1}{5}\int{\frac{1}{u}} \, du}\\\\ =\frac{1}{5}\ln(u)=\frac{1}{5}\ln(5x+1)

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What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?
Umnica [9.8K]

Answer:

26042.

Step-by-step explanation:

What's the first term of this geometric series?

2.

What's the common ratio of this geometric series?

Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.

\displaystyle r = \frac{-10}{2} = -5.

What's the sum of this series to the seventh term?

The sum of the first n terms of a geometric series is:

\displaystyle a_1 \cdot \frac{1-r^{n}}{1-r},

where

  • a_1 is the first term of the series,
  • r is the common ratio of the series, and
  • n is the number of terms in this series.

\displaystyle 2 \times\frac{1- (-5)^{7}}{1- (-5)}=26,042.

3 0
4 years ago
Enter the numerator and the denominator of the fraction in simplest form that is equal to 0.7 repeating
valentinak56 [21]

Answer:

\frac{7}{9\\}

Step-by-step explanation:

8 0
1 year ago
Mine A is 225 feet underground and Mine B has an elevation of -223 feet. Which mine is further underground
LUCKY_DIMON [66]

Answer: Mine A

Step-by-step explanation: Mine A is further underground because elevation means height and when it’s shows a number that is negative that means underground. 225 is greater than 223. So Mine A is further underground.

3 0
3 years ago
Read 2 more answers
Match each equation on the left to the mathematical property it uses on the right.
erma4kov [3.2K]

Answer:

The answer to your question is:

Step-by-step explanation:

(4 + 5) + 2 = 4 + (5 + 2)                     Associative property of addition

2(2x + 4) = 4x + 8                             Distributive property

( 7 x ) 3 = 7 (x 3)                                Associative property of multiplication

( 8 x 2) = (x 8 2)                                Commutative property of multiplication

( 7 + 3) + 1 = 1 + (7 + 3)                       Commutative property of addition

6 0
4 years ago
Read 2 more answers
Find x. Round to the nearest degree.
jeka94

The Law of Cosines features the 3 side lengths of a triangle, plus the measure of the angle opposite one of those sides.


We want angle x, which is opposite the side of length 39.


Then: a^2 = b^2 - 2ab cos C becomes 39^2 = 36^2 + 59^2 - 2(36)(59)cos x


or 1521 = 3481 + 1296 - 2(36)(59) cos x


Subtract (3481+1296) from both sides: 1521 - 4777 = -4248cos x

-3256 = -4248cos x

-3256

Then: cosx = --------------- = 0.766

-4248


Solving for x: x = arccos -0.766 = 0.698 radian, or 40 degrees (answer)

5 0
4 years ago
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