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2 years ago

1 (5x-3x2-6)-(3x2-5x+7) 2 (2m2+7m+8) -(1-2m-2m2)

Mathematics

1 answer:

swat322 years ago

3 0

Answer:

#1 -6

#2 14

Step-by-step explanation:

#1 You would put 5x and then you would subtract it by 3 then you multiply it by 3×2 and your answer will be -6

#2 You would add 2 add 7 add 8 and then you would subtract 1 and subtract 2.and your answer 14

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Find the solution of the differential equation that satisfies the given initial condition. dy/dx=x/y , y(0)=-1

Charra [1.4K]

Separating variables, we have

$\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx$

Integrate both sides.

$\displaystyle \int y\,dy = \int x\,dx$

$\dfrac12 y^2 = \dfrac12 x^2 + C$

Given that $y(0)=-1$ , we find

$\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12$

Then the particular solution is

$\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12$

$y^2 = x^2 + 1$

$y = \pm\sqrt{x^2 + 1}$

and because $y(0)=-1$ , we take the negative solution to accommodate this initial value.

$\boxed{y(x) = -\sqrt{x^2+1}}$

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1 year ago

The three lines given below form a triangle. Find the coordinates of the vertices of the triangle.

LenKa [72]

Answer:

(3, 5), (1, 2) and (5, 1)

Step-by-step explanation:

Make three systems with pairs of lines and solve them to work out the vertices.

1) Line 1 and line 2

-3x + 2y = 1
2x + y = 11

Double the second equation and subtract equations:

-3x + 2y - 2(2x + y) = 1 - 2(11)
-3x - 4x = 1 - 22
-7x = - 21
x = 3

Find y:

2*3 + y = 11
6 + y = 11
y = 11 - 6
y = 5

The point is (3, 5)

2) Line 1 and line 3

-3x + 2y = 1
x + 4y = 9

Triple the second equation and add up equations:

-3x + 2y + 3(x + 4y) = 1 + 3(9)
2y + 12y = 1 + 27
14y = 28
y = 2

Find x:

x + 4*2 = 9
x + 8 = 9
x = 1

The point is (1, 2)

3) Line 2 and line 3

2x + y = 11
x + 4y = 9

Double the second equation and subtract the equations:

2x + y - 2(x + 4y) = 11 - 2(9)
y - 8y = 11 - 18
- 7y = - 7
y = 1

Find x:

x + 4*1 = 9
x + 4 = 9
x = 5

The point is (5, 1)

8 0

1 year ago

For a company picnic, Nick ordered a box of fresh-baked gingerbread cookies and sugar cookies. The box included a total of 36 co

Mekhanik [1.2K]

Answer: 9

Step-by-step explanation:

36 ÷ 4 = 9

4 0

2 years ago

1. General Trades A roofer earns $24 per hour plus $36 per hour overtime. If he puts in 40 hours of regular time during a certai

snow_tiger [21]

Answer:

He should work $6\frac{2}{3}$ hours in overtime.

Step-by-step explanation:

Let x represents the number of hours of regular time and y represents the number of hours of overtime,

Since, earnings are $24 per hour for regular time and $36 per hour for overtime,

Thus, total earning = (24x + 36y) dollars,

Here, x = 40 hours and total earning = $ 1200,

By substituting the values,

1200 = 24(40) + 36y

1200 = 960 + 36y

240 = 36y

⇒ $y = 6\frac{2}{3}\text{ hours}$

Hence, he should work $6\frac{2}{3}$ hours in overtime.

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3 years ago

Solve the equation 1.2x = 5.16 for x.

Kobotan [32]

1.2x = 5.16

x = 5.16/1.2

x = 4.3

5 0

2 years ago

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