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3 years ago

When to use chain rule and product rule?

Mathematics

1 answer:

Olin [163]3 years ago

8 0

Chain rule when it's one function inside another.

d/dx f(g(x)) = f’(g(x))*g’(x)

Product rule when two functions are multiplied side by side.

d/dx f(x)g(x) = f’(x)g(x) + f(x)g’(x)

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The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer in simplest f

musickatia [10]

Answer:

The scale factor is 1 to 1.3

Step-by-step explanation:

Here, we want to get the scale factor

To get the scale factor, we divide corresponding sides by each other

That, we have that

9/7 = 1.3

4 0

3 years ago

What does a negative net worth indicate? a. Your assets exceed your liabilities. b. Your assets equal your liabilities. c. Your

iris [78.8K]

That would be C...when ur liabilities exceed ur assets

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3 years ago

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Write the sign that will make the equation true 57.21 5.721=10

RideAnS [48]

Put a division sign in between 57.21 and 5.721

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3 years ago

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WEDNESDAY: Use the quadratic formula to solve the following: 3x^2 - 6x-12 = 0*

Pepsi [2]

Answer:

a.) 3.236 or -1.236

Step-by-step explanation:

Used an online calculator for this answer...

Using the Quadratic Formula where

$x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\\x = \frac{ -(-6) \pm \sqrt{(-6)^2 - 4(3)(-12)}}{ 2(3) }\\x = \frac{ 6 \pm \sqrt{36 - -144}}{ 6 }\\x = \frac{ 6 \pm \sqrt{180}}{ 6 }$

The discriminant b^2−4ac > 0

so, there are two real roots.

Simplify the radical...

$x = \frac{ 6 \pm 6\sqrt{5}\, }{ 6 }\\x = \frac{ 6 }{ 6 } \pm \frac{6\sqrt{5}\, }{ 6 }\\x = 1 \pm \sqrt{5}\,$

This simplifies to...

$x = 3.23607\\x = -1.23607$

3 0

4 years ago

if a and b are the two odd positive integers such that a>b then one of the two numbers ( a+b) /2 and (a-b) /2is odd and even

Tamiku [17]

If $a$ and $b$ are odd positive integers, they are one more than a non-negative even number, i.e. there exists $m,n \in \mathbb{N}$ such that

$a = 2m+1,\quad b = 2n+1$

So, the first expression become

$\cfrac{a+b}{2} = \cfrac{2m+1+2n+1}{2} = \cfrac{2m+2n+2}{2} = m+n+1$

Similarly, we have

$\cfrac{a-b}{2} = \cfrac{2m+1-2n-1}{2} = \cfrac{2m-2n}{2} = m-n$

Now, the parity of these expressions depend on those of $m$ and $n$ . We have four cases:

If both m and n are even:

$m+n+1$ is odd, since $m+n$ is even, while $m-n$ is even

If one of the two is odd and the other is even:

$m+n+1$ is even, since $m+n$ is odd, while $m-n$ is odd

If both are odd:

$m+n+1$ is odd, since $m+n$ is even, while $m-n$ is even

So, in all cases, one between (a+b)/2 and (a-b)/2 is odd, and the other is even.

7 0

3 years ago