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2 years ago

12

A) translation: 6. y) -(-6, y)

1 answer:

trasher [3.6K]2 years ago

8 0

Answer:

idk!!!!! :c

Step-by-step explanation:

SORRY

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Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

6 0

2 years ago

Joe has 16 pounds of fertilizer for his three gardens. He uses 8/3 of the fertilizer in his first garden and 1/4 of the fertiliz

Natasha2012 [34]

Answer:

3/8

Step-by-step explanation:

3 0

2 years ago

The formula d = rt gives the distance traveled in time t at rate r. A bicyclist rides at a

Nesterboy [21]

D = rt

We are given the rate r to be 15 mph.

We are given the time (in hours) to be 3.5.

We need to find D.

D = (15)(3.5)

D = 52.5 miles.

Did you follow?

6 0

2 years ago

How to write three hundred thousand, five thousand sixty three in standard form

anygoal [31]

300,000 <-- three hundred thousand

5,000 <-- five thousand

63 <-- sixty three

300,000
5,000
63

305,063

305,063 is your answer.

Hope this helps.

3 0

2 years ago

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In a game against the Creek Side

frosja888 [35]

Classify the graph as a linear function, nonlinear function, or relation (non- function) 10 O A. Linear function B.

4 0

2 years ago