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Zinaida [17]
3 years ago
13

Which of the following is a solution to the differential equation xy′−3y=6 ?

Mathematics
1 answer:
ololo11 [35]3 years ago
4 0

Answer:

y = 5 {x}^{3}  - 2

Step-by-step explanation:

The given differential equation is :

xy′−3y=6

We want to determine which of the following options is a solution to the differential equations.

The function that satisfies the differential equation is a solution.

We can verify that

y = 5 {x}^{3}  - 2

satisfy this differential equation.

We differentiate to get:

y' = 15 {x}^{2}

We substitute the function and its derivative into the differential equation to get:

x(15 {x}^{2}) - 3(5 {x}^{3}   - 2) = 6

We expand and simplify on the left:

15 {x}^{3}- 15 {x}^{3}   + 6= 6

This simplifies to:

6 = 6

Verified.

We can show that all the other functions do not satisfy this differential equation

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Write an equation to fit the following situation. On Monday, 340 students
lora16 [44]

Answer:

48

Step-by-step explanation:

first you need to subtract the total number of students 340, by 4:00 because four of them had to travel in cars so they weren't on the bus. since there are seven buses and now 336 students going to travel on buses each buses must be split equally so you need to divide 336 by 7 giving you 48

7 0
3 years ago
Explain the difference between evaluating an expression and solving an equation. Use examples to support your explanation.
oee [108]

Answer:

<h3>Evaluating an expression</h3>

Unlike an equation, expression does not have an equal sign.

Example

(x² - 4²) / (x + 2)

So, by evaluating an expression it means to simplify the expression. Let's take a look at the example again

(x² - 4²)

= (x + 2)(x - 2) / (x + 2)

= (x - 2)

<h3>Solving an equation</h3>

Solving an equation involves finding an unknown value given in the equation. It contains an equal to sign (=) so, it result in a solution.

Example

(x² - 4²) / (x + 2) = 0

(x + 2)(x - 2) / (x + 2) = 0

(x - 2) = 0

x = 2

6 0
3 years ago
If f(x) = 2x2 + 3x and g(x) = x – 2, what is (f + g)(2)?
Trava [24]

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5 0
3 years ago
What is the solution of the system of equations?<br> y = 1/8x - 1<br> -5x + 4y = -13
Ann [662]

Answer:

Step-by-step explanation:

y = 1/8x - 1.....sub this back in for y in the other equation

-5x + 4y = -13

-5x + 4(1/8x - 1) = -13

-5x + 1/2x - 4 = -13.....multiple everything by 2 to get rid of the fraction

-5x(2) + 1/2x(2) - 4(2) = -13(2)

-10x + 1x - 8 = - 26

- 9x = -26 + 8

-9x = - 18

x = 18/9

x = 2.....now sub 2 in for x in either of the original equations to find y

y = 1/8x - 1

y = 1/8(2) - 1

y = 1/4 - 4/4

y = -3/4

so ur solution is : (2,-3/4) <===

6 0
3 years ago
Fiona needs $62 to go on a field trip. She has saved $10.50. She earns $6.50 per hour cleaning her neighbor's garden, and she ea
3241004551 [841]

Answer:

Fiona cannot go on the field trip

Step-by-step explanation:

6.5 x 6 = 49

5.25 x 2 = 10.5

49 + 10.5 + 10.5 = 60

3 0
4 years ago
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