MATHEMATICS HIGH SCHOOL

DIFFERENTIAL EQUATIONS
Solve the differential equations.
dy = 4 − x
/
dx

Answers

Answer 1
Answer: anti derivative of 4 is 4x
anti derivative of -x is -1/2 x^2

so  y = 4x - (1/2)x^2 + C
(can't forget constants when doing anti derivatives xD)

is this what you need?

*edit
Anti-derivative of a Constant [just a number] becomes  (constant)*x
for example  integral of 5 = 5x + C

Then there is a Power Rule for integrals
integral of (x)^n = 1/(n+1) *(x)^(n+1) + C
for example: integral of  x^2 = 1/(2+1) * (x)^(2+1) + C = (1/3)*x^3 + C
Answer 2
Answer:

We have dy/dx = (4-x) dx which is a first order linear ODE

dy = (4-x) dx. Now integrating both sides we get:

y = 4x - 1/2 x^2 + C

which is the answer. Note we only wrote +c once since we can combine arbitrary constants under addition and subtraction with each other.

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A box has the shape of a rectangular prism with height of 28 cm. If the height is increased by 0.2 by how much does the surface area of the box increase?
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Solve for m. 99pt reward and brainliest−37m=12−37m=12

−28−28

−26−26

26

28

Answers

-37m = 12

plug in the numbers:

(-28)(-37) ≠ 12

(-26)(-37)≠12

(26)(-37)≠12

(28)(-37) ≠ 12


idk none of the given answers are correct. Sorry.

Answer:

28 i took the test an that was the answer

Approximately 9 out of 10 smokers began smoking before the age of 21. In a group of 400 smokers, about how many of them started before they reached their 21st birthday?

Answers

400 / 10 = 40. 

     40
   X  9
= 360

In a group of 400 smokers, about 360 of them started before they reached their 21st birthday. 

Forty-two people at a Fourth of July picnic equally shared a watermelon that weighed x pounds. What was the weight of each piece of watermelon shared at the picnic? a x/42
b 42/x
c 42x
d x * 42
this broke my head

Answers

Forty-two people at a Fourth of July picnic equally shared a watermelon that weighed x pounds. What was the weight of each piece of watermelon shared at the picnic?


a x/42

What’s the triangle congruence shortcut

Answers

Answer:

Side-Side-Side [SSS]

Step-by-step explanation:

You know this since the little bars sticking outside of the triangle show that those 2 lines are congruent. Then you know of one line being the same for both, so you then know all of the sides. And since all of the side lengths are equal, this triangle is congruent by Side-Side-Side.

How to solve equation 2x/5+1=7?
How to solve equation x/3-4=10?

Answers

If you would like to solve the equation 2x / 5 + 1 = 7, you can do this using the following steps:

2x / 5 + 1 = 7
2x + 5 = 5 * 7
2x = 35 - 5
2x = 30
x = 15

If you would like to solve the equation x/3 - 4 = 10, you can do this using the following steps:

x/3 - 4 = 10
x/3 = 10 + 4
x/3 = 14
x = 14 * 3 = 42

Find the probability of getting a doublet in a throw of a pair of dice.​

Answers

There are six ways to roll 2 dice such that both dice have the same value
These are the outcomes (1,1),(2,2),(3,3),(4,4,)(5,5) and (6,6).

To find the total number of outcomes, note that there are 6 choices for the first die (values 1–6) and there are 6 choices for the second die (again values 1–6) and so by the Multiplication Principle (MP) there are 36 total outcomes from rolling two dice once.

Now we have the following:

P(getting a doublet) =
Total number of outcomes
Number of ways to get double
​
=
36
6
​
=
6
1
​


Thus, the probability of getting a doublet is
6
1
​
.

Question:

Find the probability of getting a doublet in a throw of a pair of dice.

Answer:

The probability is 1 out of 6.

Explanation:

There are a total of 6 possibilities that you get a doublet, which is {1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, and {6, 6}.

The total possibilities of throwing a dice are 6 possibilities for the first dice, and 6 possibilities for the second dice. Which results in a total of 6 × 6 = 36 possibilities available.

Probability = Possibilities of getting doublet ÷ Total possibilities = 6 ÷ 36 = 1 ÷ 6.

Hopefully this answer will help you.
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