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3 years ago

Calculate dy/dx if y = Ln (2x3 + 3x).

Mathematics

1 answer:

Strike441 [17]3 years ago

6 0

Differentiate using the chain rule:

d/du [ln(u)] d/dx[2x^3+3x]

derivative of ln(u) = 1/u

1/u d/dx[2x^3+3x]

1/2x^3+3x d/dx[2x^3+3x]

Differentiate

(6x^2+3) 1/2x^3+3x

Simplify

Dy/dx = 3(2x^2+1) / x(2x^2 +3)

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Find the distance and midpoint for A(0,1) and B(2,6)

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I think the answer is (3, 6)

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3 years ago

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Oksanka [162]

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Step-by-step explanation:

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4 years ago

Read 2 more answers

A friend of mine is giving a dinner party. His current wine supply includes 9 bottles of zinfandel, 10 of merlot, and 12 of cabe

e-lub [12.9K]

Answer:

Step-by-step explanation:

From the given information:

The total number of wine = 9 + 10 + 12 = 31

(1)

The number of distinct sequences used for serving any five wines can be estimated by using the permutation of the number of total wines with the number of wines served.

i.e

= $^{31}P_5$

$=\dfrac{31!}{(31-5)!}$

$=\dfrac{31!}{(26)!}$

$=\dfrac{31\times 30\times 29\times 28\times 27\times 26!}{(26)!}$

= 20389320

(2)

If the first two wines served = zinfandel and the last three is either merlot or cabernet;

Then, the no of ways we can achieve this is:

= $^9P_2\times ^{22}P_3$

$= \dfrac{9!}{(9-2)!}\times \dfrac{22!}{(22-3)!}$

$= \dfrac{9!}{(7)!}\times \dfrac{22!}{(19)!}$

$= \dfrac{9*8*7!}{(7)!}\times \dfrac{22*21*20*19!}{(19)!}$

= 665280

(3)

The probability that no zinfandel is served is computed as follows:

Total wines (with zinfandel exclusion) = 31 - 9 = 22

Now;

the required probability is:

$= \dfrac{^{22}P_5 }{^{31}P_5}$

$= \dfrac{\dfrac{22!}{(22-5)!} } {\dfrac{31!}{(31-5)!} }$

$= \dfrac{\dfrac{22!}{17!} } {\dfrac{31!}{(26)! }}$

$= \dfrac{(\dfrac{22*21*20*19*18*17!}{17!})} {(\dfrac{31*30*29*28*27*26!}{(26)! })}$

= 0.1549

≅ 0.155

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3 years ago

Please help me! Write an equation in point-slope form of the line that passes through the given point and has the given slope.

andriy [413]

9514 1404 393

Answer:

y -3 = 5(x -1)
y +1 = -3(x +2)
y +7 = -1/4(x -4)

Step-by-step explanation:

When you are given a point and a slope, and asked for the equation in point-slope form, it is simply a matter of putting the given numbers into the appropriate places in the equation template.

y -k = m(x -h) . . . . . . point (h, k), slope m

1. y -3 = 5(x -1) . . . . . . point (1, 3), slope 5

2. y +1 = -3(x +2) . . . . point (-2, -1), slope -3

note that for k=-1, -k = -(-1) = +1; similarly the value of -h becomes +2

3. y +7 = -1/4(x -4) . . . point (4, -7), slope -1/4

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3 years ago

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THE NEW COODINATES
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