Which function grows at the fastest rate for increasing values of x? g(x)=14x p(x)=12x3+9 f(x)=2x2−x h(x)=3x

1 answer:

5 0

The function that is growing at the fastest rate is p(x) = 12x^3 + 9.

This is a cubic function, meaning that x is raised to the third power. This is the only function that is raised to the third power, so it will increase the fastest.

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5a+c=-8a, for a how do you solve this problem?

BaLLatris [955]

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C= 13A

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3 years ago

I need to solve this equation: x= r-h/ y<br> for h and then for r

ololo11 [35]

X= r-h/y
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3 years ago

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I can't figure this out

andriy [413]

Suppose that equation of parabola is
y =ax² + bx + c

Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c

Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c

Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c

Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5

Solving it we get that
a = −2, b = −4, c = 1

Thus, equation of parabola is
y = −2x²− 4x + 1

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Rewriting in the form of
(x - h)² = 4p(y - k)

i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)

iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)

v) -3(x + 7/6)² = y - 445/36

vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)

vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)

So, after rewriting the equation would be -

(x + 7/6)² = 4(-⅛)(y - 445/36)

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I hope this is what you wanted.

Regards,
Divyanka♪
__________________

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3 years ago

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If you can’t see the bottom part it’s an 8 ..so anybody ??! Help

jolli1 [7]

Multiply both sides by the reciprocal (-8/7). You would get 40/7 or 5.71428571

8 0

3 years ago

Find a fraction equivalent to 5/7 whose squared terms add up to 1184.

bogdanovich [222]

The system of equations of two unknowns is formulated and solved.

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}$

The fraction that satisfies the request is $\bf{\dfrac{20}{28}}$ , since in $\bf{\dfrac{-20}{-28}}$ the negative signs are canceled and the first fraction is obtained.

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1 year ago