1 year ago

The volume of a barrel of oil is 257166 cm3 round this figure to the nearest hundred thousand

Mathematics

1 answer:

Fudgin [204]1 year ago

3 0

Answer: Hope this helps :D

the answer is 300000 cm3

Step-by-step explanation:

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The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th

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Answer:

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C$

Step-by-step explanation:

To find:

∫ $6x^5(x^6-2)\,dx$

Solution:

Method of substitution:

Let $x^6-2=t$

Differentiate both sides with respect to $t$

$6x^5\,dx=dt$

[use $(x^n)'=nx^{n-1}$ ]

So,

∫ $6x^5(x^6-2)\,dx$ = ∫ $t\,dt$ = $\frac{t^2}{2}+C_1$ where $C_1$ is a variable.

(Use ∫ $t^n\,dt=\frac{t^{n+1} }{n+1}$ )

Put $t=x^6-2$

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1$

Use $(a-b)^2=a^2+b^2-2ab$

So,

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C$

where $C=2+C_1$

Without using substitution:

∫ $6x^5(x^6-2)\,dx$ = ∫ $6x^{11}-12x^5\,dx$ = $\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C$

So, same answer is obtained in both the cases.

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Ellie wants to spend less than 30, so it’ll be less than.

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Emmaline bought a new book for $12 with a coupon for 25% off, how much would it cost without the coupon

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Answer:

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Step-by-step explanation:

$0.75x = 12\\3x = 48\\x = 16$

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Divide 11 into two parts and their product is 24 ?

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divide 11 into 8 and 3 whose product is 24

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