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marusya05 [52]
3 years ago
6

Divide the number 20 into two parts (not necessarily integers) in a way that makes the product of one part with the square of th

e other as large as possible
use calculus methods
Mathematics
1 answer:
Ilya [14]3 years ago
3 0

Answer:

13 1/3 and  6 2/3.

Step-by-step explanation:

Let the 2 parts be x and (20 - x).

So x^2(20 - x) must be a maximum.

y = x^2(20 - x)

y = 20x^2 - x^3

Finding the derivative):

y' =  40x - 3x^2 = 0   for  maxm/minm value.

x( 40 - 3x) = 0

40 - 3x = 0

3x = 40

x = 40/3.

This is a maximum because the second derivative y" =  40 - 6x = 40 - 6(40/3)) is negative.

So the 2 numbers are 13 1/3 and  6 2/3.

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Serggg [28]

Answer:

so 6x = -6y + 5

divide by 6

x = 5

Step-by-step explanation:

8 0
2 years ago
Calculate the volume of the rectangular prism.
WITCHER [35]

Answer:

189 cm³

Step-by-step explanation:

V = lwh

V = 9*7*3

V = 189 cm³

Hope this helped! :)

7 0
3 years ago
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Use the cosine ratio to find the value of x, to the nearest tenth.
Vsevolod [243]

Answer:

C

Step-by-step explanation:

cos34° = \frac{adjacent}{hypotenuse} = \frac{x}{4.8}

Multiply both sides by 4.8

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3 years ago
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jack has x pence, jill has 6 pence less then jack, write down in terms of x, the number of pence that jill has
Diano4ka-milaya [45]

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x-6

Step-by-step explanation:

6 pencils less than x in terms of x it would be x-6

hope it helps

4 0
3 years ago
A jogger ran 3 miles due east of his house. then he ran 5 miles at a heading of 30o east of north (or 30o ne). how far is he fro
Natasha_Volkova [10]

Magnitude of the net displacement: 7.0 miles

Step-by-step explanation:

In order to find the total displacement of the man, we have to resolve each displacement along the x- and y- direction.

Taking x as positive x direction and y as positive north direction:

- The first motion is 3 miles due east, so

A_x = 3 mi\\A_y = 0

- The second motion is 5 miles at 30^{\circ} east of north, so:

B_x = 5 sin 30^{\circ}=2.5 mi\\B_y = 5 cos 30^{\circ}=4.3 mi

So the components of the net displacement are

R_x = A_x + B_x = 3 + 2.5 = 5.5 mi\\R_y = A_y+B_y = 0 + 4.3 = 4.3 mi

And so the magnitude of the net displacement is

d=\sqrt{R_x^2+R_y^2}=\sqrt{5.5^2+4.3^2}=7.0 mi

So, he is 7.0 miles far from the house.

Learn more about distance and displacement:

brainly.com/question/3969582

#LearnwithBrainly

4 0
3 years ago
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