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Nezavi [6.7K]
3 years ago
15

Write 5/3 as a mixed number

Mathematics
2 answers:
Lostsunrise [7]3 years ago
6 0
5 / 3 is improper fraction.
To change it into mixed fraction you have to divide 5 by 3.
i.e. 1 is the quotient, 3 is the divisor, 5 is the dividend, and 2 is the reminder.

To write it in the mixed fraction you will only need the quotient, remainder and divisor.
First you will write quotient in the middle then the remainder divided by divisor
i.e. 1  2/3  where 1 is quotient, 2 is remainder and 3 is divisor.
gogolik [260]3 years ago
3 0
1 2/3 because 3 goes into 5 once n you will have 2 left over
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Consider functions of the form f(x)=a^x for various values of a. In particular, choose a sequence of values of a that converges
sleet_krkn [62]

Answer:

A. As "a"⇒e, the function f(x)=aˣ tends to be its derivative.

Step-by-step explanation:

A. To show the stretched relation between the fact that "a"⇒e and the derivatives of the function, let´s differentiate f(x) without a value for "a" (leaving it as a constant):

f(x)=a^{x}\\ f'(x)=a^xln(a)

The process will help us to understand what is happening, at first we rewrite the function:

f(x)=a^x\\ f(x)=e^{ln(a^x)}\\ f(x)=e^{xln(a)}\\

And then, we use the chain rule to differentiate:

f'(x)=e^{xln(a)}ln(a)\\ f'(x)=a^xln(a)

Notice the only difference between f(x) and its derivative is the new factor ln(a). But we know  that ln(e)=1, this tell us that as "a"⇒e, ln(a)⇒1 (because ln(x) is a continuous function in (0,∞) ) and as a consequence f'(x)⇒f(x).

In the graph that is attached it´s shown that the functions follows this inequality (the segmented lines are the derivatives):

if a<e<b, then aˣln(a) < aˣ < eˣ < bˣ < bˣln(b)  (and below we explain why this happen)

Considering that ln(a) is a growing function and ln(e)=1, we have:

if a<e<b, then ln(a)< 1 <ln(b)

if a<e, then aˣln(a)<aˣ

if e<b, then bˣ<bˣln(b)

And because eˣ is defined to be the same as its derivative, the cases above results in the following

if a<e<b, then aˣ < eˣ < bˣ (because this function is also a growing function as "a" and "b" gets closer to e)

if a<e, then aˣln(a)<aˣ<eˣ ( f'(x)<f(x) )

if e<b, then eˣ<bˣ<bˣln(b) ( f(x)<f'(x) )

but as "a"⇒e, the difference between f(x) and f'(x) begin to decrease until it gets zero (when a=e)

3 0
3 years ago
Find the solution set of 5x&lt;36 when x ∈ n
Margaret [11]

Answer:

5x<36

5x/5 < 36/5

x < 7.2

4 0
3 years ago
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What's the sum of an infinite geometric series if the first term is 156 and the common ratio is 2∕3?
DENIUS [597]

Answer:

468

Step-by-step explanation:

Formula for infinite sum of geometric series is;

S_∞ = a1/(1 - r)

Where;

a1 is first term

r is common ratio

We are given;

a1 = 156

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Thus;

S_∞ = 156/(1 - ⅔)

S_∞ = 156/(⅓)

S_∞ = 468

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stellarik [79]

Hey there! :)

Answer:

Choice B.

Step-by-step explanation:

We can eliminate each graph:

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b). This is an exponential function because the graph is shaped like a geometric equation. This means that the rate of change is exponential. This is the correct choice.

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3 0
3 years ago
I really wish I knew
Yanka [14]
-27 x -2 = 54
The answer would be the square root of 54
3 0
3 years ago
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