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ki77a [65]
3 years ago
12

Simplify (4a to the fifth power b to the sixth power) to the fourth power

Mathematics
2 answers:
choli [55]3 years ago
6 0
The first person that answered is correct just let you know!
natita [175]3 years ago
5 0

Answer:

(4a^5b^6)^4 = 256a^20b^24

Step-by-step explanation:

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What is the greatest common factor of 25 and 75​
ch4aika [34]
It’s five that’s easy
3 0
3 years ago
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums
gtnhenbr [62]

I'm guessing the sum is supposed to be

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}

Split the summand into partial fractions:

\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}

1=a(5k+4)+b(5k-1)

If k=-\frac45, then

1=b(-4-1)\implies b=-\frac15

If k=\frac15, then

1=a(1+4)\implies a=\frac15

This means

\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}

Consider the nth partial sum of the series:

S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)

The sum telescopes so that

S_n=\dfrac2{14}-\dfrac2{5n+4}

and as n\to\infty, the second term vanishes and leaves us with

\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17

7 0
3 years ago
Can someone please help me with this square root problem?
vovikov84 [41]

Answer:

Rational, Rational, Rational, Irrational, Irrational

Step-by-step explanation:

The first question:

  • -√49
  • -7

This number is rational

Second:

  • -70.8888....

This number is rational. It wouldn't be rational if the digits won't repeat.

Third:

  • 15.91

This number is rational

Fourth:

  • 17π

This is irrational. The digits of pi do not repeat, making it irrational.

Fifth:

  • -√14

Irrational. The square root of a non-perfect square is irrational.

<h3 />

-Chetan K

5 0
2 years ago
Refer to the data above. What number represents the slope of the line, if the points on the graph above were joined?
Dmitrij [34]

Answer:

slope = 40

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (2, 80) and (x₂, y₂ ) = (4, 160) ← 2 points on the line

m = \frac{160-80}{4-2} = \frac{80}{2} = \frac{40}{1} = 40

4 0
3 years ago
On Tuesday Bellagios pizza sold 60 plan pizzas at $5 each 20 meatball pizzas at each 25 Sicilian pizzas at $9 each and 33 large
mixer [17]
$855 but you also have to add the 20 near ball pizzas times however much they were but you must have skipped that by accident
4 0
3 years ago
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