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4 years ago

14

Which of the following equations describes the graph?

1 answer:

Artist 52 [7]4 years ago

7 0

Answer:

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

Step-by-step explanation:

The equation of the parabola in vertex form is y = 1/2 (x - 2)^2 - 1. By finding the vertex at (2,-1) we plug in the point into the formula y = a(x-h)^2 + k. To convert it to standard form like the equations listed, multiply through the distributive property to clear the parenthesis.

y = 1/2 (x-2)(x-2) - 1

y = 1/2 (x^2 - 4x + 4) - 1

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

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

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What is the percent change from $24 to $30

Tju [1.3M]

Answer:

25%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Step-by-step explanation:

6 0

3 years ago

Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

$\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)$

$f'(y)=0\implies f(y)=C$

$\implies F(x,y)=x^2y^3+\ln(x+y^2)=C$

With $y(1)=2$ , we have

$8+\ln9=C$

so

$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

8 0

3 years ago

Write an equation in slope-intercept form of the line that passes through (2,0) and is perpendicular to y=1/5 x-2.

Advocard [28]

Answer:

$y = -5x+10$

Step-by-step explanation:

Given

$(x_1,y_1) = (2,0)$

$y = \frac{1}{5}x - 2$

Required

Determine an equation that perpendicular to the equation

An equation has the form:

$y = mx + b$

Where

$m = slope$

By comparison:

$m = \frac{1}{5}$

Next, we determine the slope of the new line.

When two lines are perpendicular, the following relation exist:

$m_2= -\frac{1}{m_1}$

Substitute 1/5 for m1

$m_2= -\frac{1}{1/5}$

$m_2= -5$

The equation of the line is then calculated using:

$y - y_1 = m(x - x_1)$

Where:

$m_2= -5$ and $(x_1,y_1) = (2,0)$

This gives:

$y - 0 = -5(x - 2)$

$y = -5(x - 2)$

$y = -5x+10$

8 0

3 years ago

629x - 476 = 237,286. <br><br> Find x.

Semmy [17]

This is pretty simple-ish, if you think about it. All we're doing is working backwards.

237,286 + 476 = 237,762

237,762/629 = 378.

We could even check it again, if you want.

378*629 = 237,762

237,762 - 476 = 237, 286.

Therefore, x = 378.

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4 years ago

Read 2 more answers

What fraction is between 1/2 and1?

skelet666 [1.2K]

3/4 which is 0.75 in decimal

4 0

3 years ago

Read 2 more answers