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3 years ago

3xy^4-y^3+15x^2=40 Find y’

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

8 0

Answer:

y' = (y⁴ + 10x) / (y² − 4xy³)

Step-by-step explanation:

3xy⁴ − y³ + 15x² = 40

Take derivative of both sides with respect to x, using product rule and chain rule:

3(x 4y³ y' + y⁴) − 3y² y' + 30x = 0

Simplify and solve for y':

4xy³ y' + y⁴ − y² y' + 10x = 0

y⁴ + 10x = y² y' − 4xy³ y'

y⁴ + 10x = (y² − 4xy³) y'

y' = (y⁴ + 10x) / (y² − 4xy³)

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"Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin

krok68 [10]

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The answer is "(0.461 , 7.206)"

Step-by-step explanation:

In the given question some information is missing, that is data. so, the correct answer to this question can be defined as follows:

UnLogged:

$x_1=17.500\\s_1=3.529\\n_1=12$

Logged:

$x_2=13.667\\ s_2=4.500\\n_2=9\\$

formula of std error:

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$=\sqrt{\frac{3.529^2}{12}+\frac{4.500^2}{9}}\\\\=\sqrt{\frac{3.529^2\times 3+4.500^2\times 4}{36}}\\\\=1.8133$

Point differential estimation = $x_1-x _2$

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For 90 percent t= 1.860 Cl & 8 df

error of margin E = $t\times \ std \ error$

$= 1.860 \times 1.8133\\= 3.373$

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3 years ago

Given the function how do I solve

BARSIC [14]

Answer: (a) -7 (b) $\bold{\dfrac{4}{25}}$ (c) $\bold{-\dfrac{5}{2}}$ (d) 4

Step-by-step explanation:

A) f(x) = 2x - 3 when x is between -5 and -2 (including -5 and -2)

B) f(x) = x² when x is between -2 and 2 (including 2)

C) $f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}$ when x is between 2 and 5 (including 5)

a) Equation A includes x = -2

f(x) = 2x - 3

f(-2) = 2(-2) - 3

= -4 - 3

= -7

b) Equation B includes x = $-\dfrac{2}{5}$

f(x) = x²

$f\bigg(-\dfrac{2}{5}\bigg) = \bigg(-\dfrac{2}{5}\bigg)^2$

$=\dfrac{4}{25}$

c) Equation C includes x = 4

$f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}$

$f(4)=-\dfrac{3}{2}(4)+\dfrac{7}{2}$

$=-\dfrac{12}{2}+\dfrac{7}{2}$

$=-\dfrac{5}{2}$

d) Try each equation to see if x falls within the values given.

A) f(x) = 2x - 3

-2.5 = 2x - 3

0.5 = 2x

0.25 = x NOT VALID since x should be between -5 and -2

B) f(x) = x²

-2.5 = x²

$\sqrt{-2.5}=x$ NOT VALID since x cannot be an imaginary number

C) $f(x)=-\dfrac{3}{2}x+\dfrac{7}{2}$

$-\dfrac{5}{2}=-\dfrac{3}{2}x+\dfrac{7}{2}$

$-\dfrac{12}{2}=-\dfrac{3}{2}x$

$-\dfrac{12}{2}\bigg(\dfrac{2}{3}\bigg)=x$

$4 = x$ VALID since x is between 2 and 5

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4 years ago