Find the coordinates of the vertex and the equation of the axis of symmetry for the parabola with the given equation.

Mathematics

1 answer:

ZanzabumX [31]3 years ago

6 0

Answer:

The vertex is at ( 3.5, -0.25)

and the axis of symmetry is x = 3.5.

Step-by-step explanation:

Convert to vertex form:

y = x^2 - 7x + 12

y = (x - 3.5)^2 - 3.5^2 + 12

y = (x - 3.5)^2 - 0.25

y = (x - 3.5)^2 - 0.25.

So the vertex is at ( 3.5, -0.25)

and

the axis of symmetry is x = 3.5.

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A regular pentagon has side lengths of 14.1 centimeters and an apothem with length 12 centimeters.

lina2011 [118]

Answer:

The approximate area of the regular pentagon is 423 sq.cm.

Step-by-step explanation:

Formula of area of regular pentagon = $\frac{Pa}{2}$

P=Perimeter of pentagon

a=Apothem

Side of pentagon = 14.1 cm

Perimeter of pentagon = $5 \times Side = 5 \times 14.1=70.5$

Apothem=12 cm

Area of regular pentagon = $\frac{70.5 \times 12}{2}=423 cm^2$

Hence the approximate area of the regular pentagon is 423 sq.cm.

8 0

3 years ago

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Solve the differential equation dy/dx+4xy=x

Irina-Kira [14]

$\dfrac{\mathrm dy}{\mathrm dx}+4xy=x$
$\dfrac{\mathrm dy}{\mathrm dx}=x(1-4y)$

This ODE is separable, so you can write

$\dfrac{\mathrm dy}{1-4y}=x\,\mathrm dx$

Integrating both sides gives

$-\dfrac14\ln|1-4y|=\dfrac12x^2+C$
$\ln|1-4y|=-2x^2+C$
$1-4y=e^{-2x^2+C}$
$1-4y=Ce^{-2x^2}$
$y=\dfrac{1-Ce^{-2x^2}}4$