Find the length of the curve y=3x^3/2 from x=0 to x=5/9

1 answer:

4 0

$y=3x^{3/2}\implies y'=\dfrac92x^{1/2}$

The length of the curve is

$L=\displaystyle\int_0^{5/9}\sqrt{1+\left(\dfrac92x^{1/2}\right)^2}\,\mathrm dx=\int_0^{5/9}\sqrt{1+\dfrac{81}4x}\,\mathrm dx=\dfrac{335}{243}$

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Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and<br> z ≥ 3.

SashulF [63]

There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1) x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

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-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1 we get 7 combinations, at x =2 we get 6 combinations, at x=3 we get 5 combinations and at x =4 we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

Learn more about combinations here :

brainly.com/question/13387529

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5 0

2 years ago

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Akimi4 [234]

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