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3 years ago

What is the vertex of the parabola graphed below?

Mathematics

2 answers:

Shtirlitz [24]3 years ago

8 0

Answer:

Step-by-step explanation:

<em>The vertex is the point where the axis of symmetry crosses -- in this case, our vertex is a maximum -- since a value, or rate of change, is negative.</em>

dmitriy555 [2]3 years ago

7 0

Answer:

(3,2)

Step-by-step explanation:

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Classify the triangle with the given side lengths as acute, right, obtuse, or not a triangle:

Scorpion4ik [409]

Answer:

Acute

Step-by-step explanation:

An acute triangle has three angles that each measure less than 90 degrees.

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2 years ago

. Tachycardia means ...................heart rate a) fast b) slow c) irregular d) arrhythmic

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Answer:

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2 years ago

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The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.

Lisa [10]

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

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2 years ago

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nata0808 [166]

A pentagon and a abstract shape

8 0

2 years ago

(b) dy/dx = (x - y+ 1)^2

Elanso [62]

Substitute $v(x)=x-y(x)+1$ , so that

$\dfrac{\mathrm dv}{\mathrm dx}=1-\dfrac{\mathrm dy}{\mathrm dx}$

Then the resulting ODE in $v(x)$ is separable, with

$1-\dfrac{\mathrm dv}{\mathrm dx}=v^2\implies\dfrac{\mathrm dv}{1-v^2}=\mathrm dx$

On the left, we can split into partial fractions:

$\dfrac12\left(\dfrac1{1-v}+\dfrac1{1+v}\right)\mathrm dv=\mathrm dx$

Integrating both sides gives

$\dfrac{\ln|1-v|+\ln|1+v|}2=x+C$

$\dfrac12\ln|1-v^2|=x+C$

$1-v^2=e^{2x+C}$

$v=\pm\sqrt{1-Ce^{2x}}$

Now solve for $y(x)$ :

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

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

3 0

3 years ago