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3 years ago

Hello, Can I get some help with #30 a and b, please? Don't forget to show your work.

Mathematics

2 answers:

Murljashka [212]3 years ago

6 0

Answer:

a. dy/dx = -2/3

b. dy/dx = -28

Step-by-step explanation:

One way to do this is to assume that x and y are functions of something else, say "t", then differentiate with respect to that. If we write dx/dt = x' and dy/dt = y', then the required derivative is y'/x' = dy/dx.

a. x'·y^3 +x·(3y^2·y') = 0

y'/x' = -y^3/(3xy^2) = -y/(3x)

For the given point, this is ...

dy/dx = -2/3

___

b. 2x·x' +x^2·y' -2x'·y^3 -2x·(3y^2·y') + 0 = 2x' + 2y'

y'(x^2 -6xy^2 -2) = x'(2 -2x +2y^3)

y'/x' = 2(1 -x +y^3)/(x^2 +6xy^2 -2)

For the given point, this is ...

dy/dx = 2(1 -0 +27)/(0 +0 -2)

dy/dx = -28

_____

The attached graphs show these to be plausible values for the derivatives at the given points.

tia_tia [17]3 years ago

3 0

a. Answer: $\bold{-\dfrac{2}{3}}$

Step-by-step explanation:

$xy^3=8\\\\\text{Differentiate using ab=a'b+ab'}:\\a=x\qquad a'=1\\b=y^3\qquad b'=3y^2\cdot y'\\\\y^3+3xy^2\cdot y'=0\\\\\text{Subtract }3xy^2\cdot y'\ \text{from both sides}:\\y^3=-3xy^2\cdot y'\\\\\text{Divide }-3xy^2\ \text{from both sides}:\\-\dfrac{y^3}{3xy^2}=y'\\\\\text{Substitute x = 1 and y = 2 to find the derivative at that coordinate:}\\-\dfrac{(2)^3}{3(1)(2)^2}=y'\\\\\\-\dfrac{8}{12}=y'\\\\\\\boxed{-\dfrac{2}{3}=y'}$

b. Answer: -28

Step-by-step explanation:

$x^2y-2xy^3+6=2x+2y\\\\\text{Differentiate each term separately using ab=a'b+a'b}:\\.\quad \qquad x^2y\qquad \qquad \qquad \qquad \qquad -2xy^3\\a=x^2\qquad a'=2x\qquad \qquad a=-2x\qquad a'=-2\\b=y\qquad \ b'=y'\qquad \qquad \ b=y^3\qquad \ b'=3y^2\cdot y'\\\\2xy+x^2\cdot y'-2y^3-6xy^2\cdot y'+0=2+2y'$

$\text{Subtract }x^2y\cdot y',\ \text{Subtract 2, and Add }6xy^2\cdot y'\ \text{on both sides:}\\2xy-2y^3-2=2y'-x^2y'+6xy^2\cdot y'\\\\\text{Factor out y' from the right side:}\\2xy-2y^3-2=y'(2-x^2+6xy^2)\\\\\text{Divide both sides by }2-x^2+6xy^2:\\\dfrac{2xy-2y^3-2}{2-x^2+6xy^2}=y'\\\\\text{Substitute x = 0 and y = 3 to find the derivative at that coordinate:}\\\dfrac{2(0)(3)-2(3)^3-2}{2-(0)^2+6(0)(3)^2}=y'\\\\\\\dfrac{-56}{2}=y'\\\\\boxed{-28=y'}$

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3 years ago

What are the weights (in Newton’s) for the given masses 22.1,33.5,41.3,59.2,78

Blababa [14]

Answer:

1. 216.8 N

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5. 765.18 N

Step-by-step explanation:

1. Let the mass is 22.1 kg, then the weight in Newton will be (22.1 × 9.81) = 216.8 N {Where acceleration due to gravity is 9.81 m/sec²}

2. Let the mass is 33.5 kg, then the weight in Newton will be (33.5 × 9.81) = 328.635 N {Where acceleration due to gravity is 9.81 m/sec²}

3. Let the mass is 41.3 kg, then the weight in Newton will be (41.3 × 9.81) = 405.153 N {Where acceleration due to gravity is 9.81 m/sec²}

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(Answer)

4 0

3 years ago

352 divided by 2 in long division please show work

baherus [9]

Step 1:

Start by setting it up with the divisor 2 on the left side and the dividend 352 on the right side like this:

2 ⟌ 3 5 2

Step 2:

The divisor (2) goes into the first digit of the dividend (3), 1 time(s). Therefore, put 1 on top:

2 ⟌ 3 5 2

Step 3:

Multiply the divisor by the result in the previous step (2 x 1 = 2) and write that answer below the dividend.

2 ⟌ 3 5 2

Step 4:

Subtract the result in the previous step from the first digit of the dividend (3 - 2 = 1) and write the answer below.

2 ⟌ 3 5 2

- 2

Step 5:

Move down the 2nd digit of the dividend (5) like this:

2 ⟌ 3 5 2

- 2

1 5

Step 6:

The divisor (2) goes into the bottom number (15), 7 time(s). Therefore, put 7 on top:

1 7

2 ⟌ 3 5 2

- 2

1 5

Step 7:

Multiply the divisor by the result in the previous step (2 x 7 = 14) and write that answer at the bottom:

1 7

2 ⟌ 3 5 2

- 2

1 5

1 4

Step 8:

Subtract the result in the previous step from the number written above it. (15 - 14 = 1) and write the answer at the bottom.

1 7

2 ⟌ 3 5 2

- 2

1 5

- 1 4

Step 9:

Move down the last digit of the dividend (2) like this:

1 7

2 ⟌ 3 5 2

- 2

1 5

- 1 4

1 2

Step 10:

The divisor (2) goes into the bottom number (12), 6 time(s). Therefore put 6 on top:

1 7 6

2 ⟌ 3 5 2

- 2

1 5

- 1 4

1 2

Step 11:

Multiply the divisor by the result in the previous step (2 x 6 = 12) and write the answer at the bottom:

1 7 6

2 ⟌ 3 5 2

- 2

1 5

- 1 4

1 2

Step 12:

Subtract the result in the previous step from the number written above it. (12 - 12 = 0) and write the answer at the bottom.

1 7 6

2 ⟌ 3 5 2

- 2

1 5

- 1 4

1 2

- 1 2

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 352 divided by 2 calculated using Long Division is:

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