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3 years ago

How many real solution does the equation b^2+8b-3=0 have?

Mathematics

1 answer:

Bumek [7]3 years ago

3 0

Two.

b1 = - 4 + sqrt(19), b2 = - 4 - sqrt(19)

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Show that d^2y/dx^2=-2x/y^5, if x^3 + y^3=1

aalyn [17]

Answer:

y³ + x³ = 1

First, differentiate the first time, term by term:

${3y^{2}.\frac{dy}{dx} + 3x^{2}} = 0 \\\\{3y^{2}.\frac{dy}{dx} = -3x^{2}} \\\\\frac{dy}{dx} = \frac{-3x^{2}}{3y^{2}} \\\\\frac{dy}{dx} = \frac{-x^{2}}{y^{2}}$

↑ we'll substitute this later (4th step onwards)

Differentiate the second time:

$3y^{2}.\frac{dy}{dx} + 3x^{2} = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} + 6x = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{-x^{2} }{y^{2} })^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{x^{4} }{y^{4} }) = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + \frac{6x^{4} }{y^{3} } = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} = - 6x - \frac{6x^{4} }{y^{3} } \\\\$

$3y^{2}.\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{3y^{2}. y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 2xy^{3} - 2x^{4} }{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (y^{3} + x^{3})}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (1)}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x}{y^{5}}$

3 0

2 years ago

Look at this triangle. 8 cm 22 cm Work out length AB.

Dmitry_Shevchenko [17]

Would the answer be 176? I’m not sure but i’m curious

7 0

2 years ago

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Write an explicit formula for an, the nth term of the sequence 33, 30, 27

lawyer [7]

Answer:

aₙ = aₙ₋₁ - 3

Step-by-step explanation:

Given :

First term : 33

Common difference = 30 - 33 = -3

============================================================

Then the formula will be :

aₙ = aₙ₋₁ - 3

8 0

1 year ago

Jane made a poster that had a length of 1 2/3 feet and a width of 5/6 feet. What is the perimeter of her poster?

RoseWind [281]

Answer:

5 feet

Step-by-step explanation:

7 0

3 years ago

Melody want to sell bags of mixed candy at her lemonade stand . She will mix chocolates pieces that cost $4.89 per bag with pean

Alja [10]

Answer:

Bags of chocolates pieces = 10 bags

Bags of peanut butter pieces = 15 bags

Step-by-step explanation:

The ratio of chocolate pieces to peanut butter pieces

($4.23-$ 3.79) : ($ 4.89 - $4.23)

= $0.44 : $0.66

= 2 : 3

Therefore; the fraction of chocolate pieces bag = 2/5

Thus; Number of bags of chocolate pieces = 2./5 × 25

= 10 bags

Fraction of peanut pieces bags = 3/5

Therefore; Number of bags of peanut butter pieces = 3/5 × 25

= 15 bags

7 0

3 years ago

Read 2 more answers