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katrin2010 [14]
3 years ago
13

What is the base of the natural logarithm function f(x) = ln(x)? Explain how you know.

Mathematics
1 answer:
Zarrin [17]3 years ago
4 0

Answer:

base = e

Step-by-step explanation:

The general log function is defined as

f(x)=\log_a x             .... (1)

where, a is the base of the log function.

The natural logarithm function is

f(x)=\ln x

It can be rewritten as

f(x)=\log_e x              .... (2)

where, e is a constant or Euler's number is:

e ≈ 2.71828183

On comparing (1) and (2) we get

a=e

Therefore, the base of the natural logarithm function is e.

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Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. X= 2.5 when y=
puteri [66]

Answer:constant of variation(k) is, 250.

Step-by-step explanation:

The inverse variation says that:

then, the equation is in the form of :

       ....[1] where, k is the constant of variation

As per the statement:

Suppose that y varies inversely with x.

then,

by definition of inverse variation we have;

When x = 2.5 and y = 100 then

Substitute these in [1] we have;

Multiply 2.5 both sides we have;

or

k = 250

⇒

Therefore, the constant of variation is, 250 and the equation we get

Read more on Brainly.com - brainly.com/question/5991656#readmore

Step-by-step explanation:

4 0
3 years ago
Big Enos loves Coors beer but he lives in Georgia and nobody sells Coors east of Texas. So he offers to pay Cletus "The Snowman"
Alik [6]

Answer:

Snowman Expenses:

a) Income Tax deductible expenses:

Payment for 400 cases of beer = $10,000

Payment for fuel = $650

Total = $10,650

b) The expenses above are allowable because they are "ordinary and necessary expenses incurred in carrying on any trade or business."  IRS Code 162.

c) The bribe paid to the Sheriff of $1,000 is not allowable under the same code.

d)  Such payments are not allowable because, according to IRS Code 162  section C: 1 and 2, they are described as "Illegal bribes, kickbacks, and other payments" and "other illegal payments."

Step-by-step explanation:

a) According to the Internal Revenue Code 162 which details trade or business expenses, section A specifically state that "There shall be allowed as a deduction all the ordinary and necessary expenses paid or incurred during the taxable year in carrying on any trade or business, including—

(1)a reasonable allowance for salaries or other compensation for personal services actually rendered;

(2)traveling expenses (including amounts expended for meals and lodging other than amounts which are lavish or extravagant under the circumstances) while away from home in the pursuit of a trade or business; and ..."

b) Bribes are illegal payments prohibited by states law.  Snowman paid the payment in order not to get his vehicle impounded and himself imprisoned, according to the Sheriff's threats.  That he was over-speeding in order to meet his business appointment does not guarantee him the right to bribe a government official.

7 0
4 years ago
You bought 7 packs of trading cards for $37.03 how much did you pay for each pack of trading cards
zhannawk [14.2K]
$5.29 for each pack. You're welcome.
4 0
3 years ago
Read 2 more answers
Bill buys and sells laptops. Last month Bill bought 50 laptops. He paid £400 for each laptop. He sold 40 of these laptops at a p
Ivenika [448]

Answer:

As Bill's sales is £25400, which is greater than £25000, he achieved his target.

Step-by-step explanation:

Cost of each laptop = £400

lets calculate for 40 laptops first

Given, he sold 40 of these at 30% profit

30% of cost price = 30% of  £400  = 30/100 * 400 = 120

Therefore, selling price of these laptops =  £400  +  £120 =  £520

Total sales generated from selling 40 of these laptop = 40*£520

= £520 =£20,800  

lets calculate for 10 laptops now

Given, he sold 10 of these at 15% profit

15% of cost price = 15% of  £400  = 15/100 * 400 = 60

Therefore, selling price of these laptops =  £400  +  £60 =  £460

Total sales generated from selling 10 of these laptop = 10*£460

= £4600

Total sales generated from selling all the 50 laptop =  

Total sales generated from selling 40 of these laptop + Total, sales generated from selling 10 of these laptop = £20,800  + £4600 = £25,400

Target for Bill = £25000

As his sales is £25400, which is greater than £25000, he achieved his target.

6 0
3 years ago
Expand and simplify 2(x-y)-3(x-2y)
hoa [83]
2(x-y) - 3(x-2y) = 0

2(x) - 2(y) -3(x) -3(-2y) = 0

2x - 2y - 3x + 6y = 0

-x + 4y = 0

Value of x:

-x = -4y
-x / -1 = -4y / -1
x = 4y

Value of y:

-x + 4y = 0
4y = x
4y / 4 = x / 4
y = x/4

3 0
4 years ago
Read 2 more answers
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