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2 years ago

Helppp me out please :)))) i’ll mark as brainlist who ever gets it right :)

Mathematics

1 answer:

shepuryov [24]2 years ago

8 0

Answer:

y=-6

Step-by-step explanation:

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Identify the property or rule 85+0=

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IdentityProperty of Addition OR Zero Property

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Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,

sweet [91]

Answer:

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

$f'' = x - \frac{3}{2}$

$f' = \int {\left(x-\frac{3}{2}\right) } \, dx$

$f' = \int {x} \, dx -\frac{3}{2}\int \, dx$

$f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C$ , where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ( $f'(4) = 1$ ):

$1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C$

$C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)$

$C = -1$

The first derivative is $y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1$ , and the particular solution is found by integrating one more time and using the initial condition ( $f(0) = 0$ ):

$y = \int {\left(\frac{1}{2}\cdot x^{2}-\frac{3}{2}\cdot x -1 \right)} \, dx$

$y = \frac{1}{2}\int {x^{2}} \, dx - \frac{3}{2}\int {x} \, dx - \int \, dx$

$y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x + C$

$C = 0 - \frac{1}{6}\cdot 0^{3} + \frac{3}{4}\cdot 0^{2} + 0$

$C = 0$

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

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Step-by-step explanation:

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Step-by-step explanation:

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Given the following information: a circle with a radius of 10cm and has a center of (-9, -2).

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Answer:

Equation: (x+9)² + (y+2)² = 100

4 points: (1, -2) (-1, 4), (-3, -10) (-19, -2)

(-3, 6) is on the circle

Step-by-step explanation:

(h, k) (-9, -2)

Equation: (x+9)² + (y+2)² = 100

4 points: (1, -2) (-1, 4), (-3, -10) (-19, -2)

(-3, 6) is on the circle

check: (-3 + 9)² + (6 + 2)² = 36 + 64 = 100 = 10²

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