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sveta [45]
3 years ago
10

Solve the differential equation

d="TexFormula1" title=" \frac{dy}{dx} = 2cos^{2} y" alt=" \frac{dy}{dx} = 2cos^{2} y" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
avanturin [10]3 years ago
5 0

tany =2x+C is the required differential equation.

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What is the slope intercept from of the equation of the line that that passes through the points (-3, 2) and (1, 5)
viva [34]

The slope-intercept form of a line:

y=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\to slope\\\\b\to y-intercept

We have:

(-3,\ 2)\to x_1=-3,\ y_1=2\\(1,\ 5)\to x_2=1,\ y_2=5

Substitute:

m=\dfrac{5-2}{1-(-3)}=\dfrac{3}{4}

y=\dfrac{3}{4}x+b

Put the values of coordinates of the point (1, 5) to the equation of a line:

5=\dfrac{3}{4}(1)+b\\\\5=\dfrac{3}{4}+b\qquad|-\dfrac{3}{4}\\\\b=4\dfrac{1}{4}

Answer: y=\dfrac{3}{4}x+4\dfrac{1}{4}


5 0
2 years ago
What is the equation of this line? Picture included
enot [183]
A straight line needs two pieces of information to be identified, a gradient and a y-intercept (technically any point will do but the y-intercept is particularly convenient if we have it).

The gradient is calculated by taking two points on the line, and dividing the change in y-coordinate by the change in x-coordinate between them. I'm going to take the points (0,-3) and (2,-2).

The change in y-coordinate is (-2) - (-3) = 1

The change in x-coordinate is (2) - (0) = 2.

Gradient = m = 1/2

Next we identify the y-intercept, the value of y when x = 0. This value is -3, and we call it c.

The equation of a line in slope-intercept form is y = mx + c. Slotting in the values for m and c we have ascertained, we find that the equation of this line is:

y = (1/2)x - 3

I hope this helps :)
7 0
3 years ago
How do I get the third mark have I done something wrong?
Anna11 [10]

Answer:

C (- 4, - 2 )

Step-by-step explanation:

(c)

the x- coordinate of A is - 4

the y- coordinate of B is - 2

coordinates of C = (- 4, - 2 )

8 0
2 years ago
(2x^4-3x^2+4x-9)÷(x+2)
dexar [7]
Working is attached: 2x^3 - 4x^2 + 5x - 6 remainder 3

3 0
3 years ago
A chemist whishes to prepare 100 liters of 45% purity of sulphuric acid .He has two kinds of acid solutions in stock ,one is 55%
tester [92]

Answer:

the chemist should use 60 liters of 55% solution and 40  litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.

Step-by-step explanation:

From the given information,

Let x be the litres of 55% pure solution

Let y be the litres of 30% pure solution

Also;

Given that our total volume of solution is  100 litres

x+y =100  ---- (1)

The total solution of pure by related by the sum of the individual pure concentrations to make up the concentration of final solution.

(0.55)(x)+(0.30)(y) = 0.45(100) ---- (2)

From equation (1)

Let ; y = 100 - x

Replacing the value for y = 100 - x into equation (2)

(0.55)(x)+(0.30)(100-x) = 0.45(100)

0.55x + 30 - 0.30x = 45

0.55x - 0.30x = 45 - 30

0.25x = 15

x = 15/0.25

x = 60 liters of 55% solution

From ; y = 100 - x

y = 100 - 60

y = 40  litres of 30% solution.

Therefore, the chemist should use 60 liters of 55% solution and 40  litres of 30% solution in order to prepare 100 liters of 45% purity of sulphuric acid.

7 0
3 years ago
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