3 years ago

How do you use an exponent to represent a number such as 16

Mathematics

1 answer:

Vanyuwa [196]3 years ago

4 0

Hey there, well 4×4=16. Therefore, the exponent of 16 is 4²

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Total employment for sheet metal workers in 2016 is projected to be 201,000. If this is a 6.3% increase from 2006,

anastassius [24]

Answer:

Step-by-step explanation:

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3 0

3 years ago

Can someone help me please will give brainlist

nadya68 [22]

Answer:

A) it converges

B) 1998.047

C) 2000

d) The sum is getting smaller and smaller

Step-by-step explanation:

Formula: a_n+a_1*r^(r-1)

(1000*((0.5^10)-1))/(0.5-1)=1998.047

(1000*((0.5^30)-1))/(0.5-1)=2000

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2 years ago

Dexter drove 546 miles on one tank of gasoline. His car’s gas tank holds 15 gallons of gas. Find the average number of miles he

AlexFokin [52]

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3 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

4 years ago

why do whole numbers raised to an exponent get greater while fractions raised to an exponent get smaller?

ehidna [41]

Any number above 1 gets greater, below 1 smaller (when above 0), while 1 itself remains the same. Negative numbers are more unpredictable.

8 0

3 years ago

Read 2 more answers