I want to know the answers to the ones circled

Mathematics

1 answer:

LenaWriter [7]3 years ago

4 0

Hello! I will do my best to help you understand and receive the answers.

Let's begin with our first question..

15.) Dao has 2 3/8 pounds of hamburger meat. He is making 1/4 pound burgers. How many burgers can he make?

For this problem we will have to use division. Our equation (use a calculator if needed) is 2 3/8 divided by 1/4 which equals 3.

Your final answer should be : Dao can make 3 hamburgers total.

I would answer the next question, but I believe from this information above you can try and figure it out. If you are still stuck, message me and i can help you from there.

:))

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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:

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