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3 years ago

10

PLEASE HELP ME!!

1 answer:

tatiyna3 years ago

3 0

For
y=ax²+bx+c
the x value of the axis of symmetry is -b/(2a)

so test them

A., -b/(2a)=-(-8)/(2*-2)=8/-4=-2, yep
B. -b/(2a)=-2/(2*1/2)=-2/1=-2, yep
C. -b/(2a)=-(-16)/(2*4)=16/8=2, nope, need -2
D. -b/(2a)=-12/(2*3)=-12/6=-2, yep

answer is C

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

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vladimir2022 [97]

Answer:

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Step-by-step explanation:

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3 years ago

2.) What value for c will make the expression a perfect square trinomial?

andre [41]

Answer : $\frac{49}{4}$

Given expression is $x^2 - 7x + c$

To make perfect square trinominal we use completing the square method

In completing the square method we add and subtract the half of square of coefficient of middle term

Here coefficient of middle term is -7

Half of -7 is $\frac{-7}{2}$

Square of $\frac{-7}{2}$ is $(\frac{-7}{2})^2$ = $\frac{49}{4}$

So the expression becomes $x^2 - 7x + [tex] \frac{49}{4}$ that gives perfect square trinomial

Hence , the value of 'c' is $\frac{49}{4}$

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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