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1 year ago

What is the value of x, y, and z?

Mathematics

1 answer:

baherus [9]1 year ago

3 0

The value of x,y, and z 85+ 84 right?

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

5 0

3 years ago

A bag of candy has a mass of 80 g. A chocolate bar has a mass of 110 g. What is the total mass of the bag of candy and the choco

atroni [7]

total mass = mass of a bag of candy + mass of a chocolate bar

total mass = 80g +110g = 190g

3 0

2 years ago

On Monday, Gina ran 1 mile in 9.3 minutes. Her times for

Marta_Voda [28]

Answer:

In order, they would be:

-4.45 min, -1.8 min, -(1 + 2/3) min, -1.375 min

Step-by-step explanation:

Enjoy :)

3 0

2 years ago

Please help me find the length width and area

Lisa [10]

I would say that the length would be 2 inches, the width to be 6 feet and the area to be 144. I would say this because in order to find the area, you would need to convert 6 feet into inches. There are 12 inches in a foot. So it would be 72 inches. In order to find area you multiply the length by the width. So it would be 72 time 2, this is equal to 144. Hope this helps :)

4 0

2 years ago

Read 2 more answers

Is 1. 58 rational or irrational

scZoUnD [109]

Answer:

1.58 is rational

Step-by-step explanation:

"hope this helps"

4 0

3 years ago

Read 2 more answers