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Mathematics

2 answers:

inna [77]2 years ago

4 0

Hello again ;3

8 pounds < 80 ounces

3 pounds > 50 ounces

ollegr [7]2 years ago

3 0

1. 80 ounces = 5 pounds and 8 pounds = 128 ounces so (8>80)
2. 3 pounds = 48 ounces and 50 ounces = 3.1 pounds so (3<50)

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a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the

nlexa [21]

Answer:

The standard equation of the parabola is:

$y=-\frac{3}{2}x^2+12x-18$

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

$y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2$

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

$y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}$

Then the equation of the parabola becomes:

$y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18$

7 0

3 years ago

Differentiating a Logarithmic Function In Exercise, find the derivative of the function.

sp2606 [1]

Answer:

$\dfrac{d(f(x))}{dx} = \dfrac{2}{x}$

Step-by-step explanation:

We are given the following function in the question:

$f(x) = \ln (3x^2)$

We have to derivate the given function.

Formula:

$\dfrac{d(\ln x)}{dx} = \dfrac{1}{x}\\\\\dfrac{d(x^n)}{dx} = nx^{n-1}$

The derivation takes place in the following manner

$f(x) = \ln (3x^2)\\\\\dfrac{d(f(x))}{dx} = \displaystyle\frac{d(\ln(3x^2))}{dx}\\\\=\frac{1}{3x^2}\times \frac{d(3x^2)}{dx}\\\\= \frac{1}{3x^2}\times (6x)\\\\=\frac{6x}{3x^2}\\\\=\frac{2}{x}$