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3 years ago

Which mathematical concepts did Euler's legacy include? Check all that apply.

Mathematics

2 answers:

quester [9]3 years ago

7 0

Answer:

a)the notation for the imaginary unit

c) the formalization of a function notation

e) the notation for the base of the natural logarithm

Step-by-step explanation:

it said i was correct :P

jonny [76]3 years ago

5 0

the notation

the formalization of function notation

the notation for the base of natural logarithm

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If 2(4x + 3)/(x - 3)(x + 7) = a/x - 3 + b/x + 7, find the values of a and b.

zmey [24]

Answer:

$a=3$ and $b=5$ .

Step-by-step explanation:

So I believe the problem is this:

$\frac{2(4x+3)}{x-3}(x+7)}=\frac{a}{x-3}+\frac{b}{x+7}$

where we are asked to find values for $a$ and $b$ such that the equation holds for any $x$ in the equation's domain.

So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).

In other words this will clear the fractions.

$\frac{2(4x+3)}{x-3}(x+7)}\cdot(x-3)(x+7)=\frac{a}{x-3}\cdot(x-3)(x+7)+\frac{b}{x+7}(x-3)(x+7)$

$2(4x+3)=a(x+7)+b(x-3)$

As you can see there was some cancellation.

I'm going to plug in -7 for x because x+7 becomes 0 then.

$2(4\cdot -7+3)=a(-7+7)+b(-7-3)$

$2(-28+3)=a(0)+b(-10)$

$2(-25)=0-10b$

$-50=-10b$

Divide both sides by -10:

$\frac{-50}{-10}=b$

$5=b$

Now we have:

$2(4x+3)=a(x+7)+b(x-3)$ with $b=5$

I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.

$2(4\cdot 3+3)=a(3+7)+b(3-3)$

$2(12+3)=a(10)+b(0)$

$2(15)=10a+0$

$30=10a$

Divide both sides by 10:

$\frac{30}{10}=a$

$3=a$

So $a=3$ and $b=5$ .

4 0

3 years ago

Read 2 more answers

15-29=

Dominik [7]

Answer:

15-29= -14

(I need the explanation most importantly)

14+(-4) - 8 =10-8=2

(Explanation please)

-8.4 - (19.5.) = - 27.9, (just add them to each other and write -, because both have - in front of them)

(Explanation)

-15 + 8 - (-19.7) = - 7+19,7=12,7 (there is + and - so it will became - 7, and at next there is two - which will turn them into +)

(Explanation)

29.45 - 56.009 - 78.2=−104,759 (all you have to is to put them all together, and than make it 29.45 less, writing - in front of them)

(Explanation)

LAST ONE

45.9 - (-9.2) + 5= 45.9+9.2+5=55.1+5=60.1 (because when there is 2 minus next to each other it will became plus)

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3 years ago

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NemiM [27]

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Step-by-step explanation:

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3 years ago

What is the equation for the line on the graph

____ [38]

Answer:

x = -1

Step-by-step explanation:

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3 years ago