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3 years ago

1 ln(1) + 2 ln(2) + 3 ln(3) + ⋯ + 10 ln(10)

Mathematics

1 answer:

Lapatulllka [165]3 years ago

6 0

Answer:

$\ln(1\cdot2^{2} \cdot3^{3}\cdot4^{4} ...\cdot10^{10} )$

Step-by-step explanation:

By logarithm rules

$\ln1+2\ln2+3\ln3+....+10\ln10\\\ln1+\ln2^2+\ln3^3+....\ln10^{10}\\\ln(1\cdot2^{2} \cdot3^{3}\cdot4^{4} ...\cdot10^{10} )$

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Please help I'm lost.

vova2212 [387]

Part 1: Answer:

(x+1)(x+1)(x-6) = x^3 - 4x^2 - 11x - 6

Step-by-step explanation:

To make r a root, include (x-r) as a factor. (-1+1)(-1+1)(-1-6) is zero even though (-1-6) isn't.

(6+1)(6+1)(6-6) is zero.

Part 2 Answer:

Standard form: y = -x^4 + 12

Degree 4

left end goes down, right end goes down.

Step by step: apply the definitions of standard form, polynomial degree, and "end behavior". In other words, read the textbook.

Part 3: Answer: x = 3, x = 8

Step by step:

x^2-11x = -24

x^2-11x+24 = 0

(x-3)(x-8) = 0

x = 3 or x = 8

Part 4a Answer:

quotient 2x^2 + x - 3

remainder 1

Step by step:

2x^2 + x - 3

___________________

x-4 ) 2x^3 - 7x^2 - 7x + 13

2x^3 - 8x^2

__________

0 + x^2 - 7x + 13

x^2 - 4x

____________

0 - 3x + 13

- 3x + 12

______

Part 4b answer:

quotient 2x^2 - 6x + 2

remainder -20

Step by step: you have to know exactly what you are doing. Refer to textbook or Wikipedia.

dividend 2x^3 +14x^2 - 58x

divisor x+10

leading coefficient of divisor must be 1

write coefficients of dividend at top

write coefficients of dividend at left

| 2 14 -58 0

-10 | -20 60 -20

___________

| 2 -6 2 -20

Coefficients of quotient are 2 -6 2

Remainder is -20

quotient = 2x^2 - 6x + 2

7 0

3 years ago

Is rolling a 3 standard doe and then rolling a sum greater than 4 when counting the next roll an independent event?

zhannawk [14.2K]

Answer:

False

Step-by-step explanation:

In this question, you roll 3 from the standard die and then add it with the next roll to see if the sums are greater than 4.

From this explanation you can see that you use the result from your first roll for the second event, so we can conclude that the event is dependent.

Imagine if we change the result of the first roll into 5, without adding the second roll we can know that the sum will be greater than 4. The first event result will influence the second event, so it is a dependent event.

5 0

3 years ago

A water container holds 2 liters. How many

EastWind [94]

Number of containers for 2 litres of water = 1

So, number of containers for 1 litre of water = ½

So, number of containers for 30 litres of water

= ½ × 30

= 30/2

= 15

So, 15 of these containers would be needed to fill a 30-liter drum.

5 0