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2 years ago

X^3+2/3x^4-1/2x^2 integral

Mathematics

1 answer:

Irina-Kira [14]2 years ago

5 0

$\frac{2 {x}^{5} }{15} + \frac{ {x}^{4} }{4} - \frac{ {x}^{3} }{6} + c$

simplified form =

$\frac{ {x}^{3}(8 {x}^{2} + 15x - 10) }{60} + c$

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Evaluate the expression when m=4<br> m^2-9m-5

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X=3<br> 5x+4y=-9<br> -x+4y-2z=-25

Alexandra [31]

Answer:

y=-6 z=-1

Step-by-step explanation:

5(3)+4y=-9

15+4y=-9

-15. -15

4y=-24

/4. /4

y=-6

-x+4y-2z=-25

-3+4(-6)-2z=-25

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2 years ago

Write the sum using summation notation, assuming the suggested pattern continues.

Usimov [2.4K]

Answer:

Sum of the sequence will be 648

Step-by-step explanation:

The given sequence is representing an arithmetic sequence.

Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6

3 - (-3) = 3 + 3 = 6

Since last term of the sequence is 81

Therefore, by the explicit formula of an arithmetic sequence we can find the number of terms of this sequence

$T_{n}=a+(n-1)d$

where a = first term of the sequence

d = common difference

n = number of terms

81 = -9 + 6(n - 1)

81 + 9 = 6(n - 1)

n - 1 = $\frac{90}{6}=15$

n = 15 + 1 = 16

Now we know sum of an arithmetic sequence is represented by

$\sum_{n=1}^{n}(a_{n})=\frac{n}{2}(a_{1}+a_{n})$

Now we have to find the sum of the given sequence

$S_{16}=\frac{16}{2}[-9 + (16-1)6]$

= 8[-9 + 90]

= 8×81

= 648

Therefore, sum of the terms of the given sequence will be 648.

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2 years ago