1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Hoochie [10]
3 years ago
8

Any help with an explanation would be appreciated!

Mathematics
1 answer:
Lilit [14]3 years ago
5 0

Problem 1

We'll use the product rule to say

h(x) = f(x)*g(x)

h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)

Then plug in x = 2 and use the table to fill in the rest

h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)

h ' (2) = f ' (2)*g(2) + f(2)*g ' (2)

h ' (2) = 2*3 + 2*4

h ' (2) = 6 + 8

h ' (2) = 14

<h3>Answer: 14</h3>

============================================================

Problem 2

Now we'll use the quotient rule

h(x) = \frac{f(x)}{g(x)}\\\\h'(x) = \frac{f'(x)*g(x)-f(x)*g'(x)}{(g(x))^2}\\\\h'(2) = \frac{f'(2)*g(2)-f(2)*g'(2)}{(g(2))^2}\\\\h'(2) = \frac{2*3-2*4}{(3)^2}\\\\h'(2) = \frac{6-8}{9}\\\\h'(2) = -\frac{2}{9}\\\\

<h3>Answer:  -2/9</h3>

============================================================

Problem 3

Use the chain rule

h(x) = f(g(x))\\\\h'(x) = f'(g(x))*g'(x)\\\\h'(2) = f'(g(2))*g'(2)\\\\h'(2) = f'(3)*g'(2)\\\\h'(2) = 3*4\\\\h'(2) = 12\\\\

<h3>Answer:  12</h3>
You might be interested in
An investment of $900 earns 6% annual interest and is compounded semi-annually. Write an equation
nalin [4]

Answer:

A=900(1+\frac{0.06}{2})^{2(t)}

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

First, change 6% into a decimal:

6% -> \frac{6}{100} -> 0.06

Since the interest is compounded semi-annually, we will use 2 for n. Lets plug in the values now and your equation will be:

A=900(1+\frac{0.06}{2})^{2(t)}

4 0
2 years ago
22. One kilometer is approximately 0.62 mile. What fraction represents this length?
bixtya [17]

<u><em>Answer:</em></u>

One kilometer is \frac{31}{50} miles

<u><em>Explanation:</em></u>

<u>To convert a decimal to a fraction:</u>

1- Write the decimal as a fraction whose denominator is 1

2- Multiply both numerator and denominator by multiples of 10 to eliminate the decimal point

3- Simplify the fraction you have

<u>Now, for the given problem:</u>

<u>The given decimal is 0.62, following the above steps:</u>

<u>Step 1: </u>

0.62 = \frac{0.62}{1}

<u>Step 2:</u>

We have two digits after the decimal point, so to eliminate the decimal point, we will multiply the numerator and the denominator by 100

0.62 = \frac{0.62}{1} * \frac{100}{100} = \frac{62}{100}

<u>Step 3:</u>

We can note that, in the fraction obtained from step 2, both the numerator and the denominator are divisible by 2, so we simplify as follows:

\frac{62}{100} = \frac{62/2}{100/2} =\frac{31}{50}

Hope this helps :)

6 0
3 years ago
So this is for my geometry I'm trying to work on my review and I'm hoping that maybe one of you guys out here could help me with
alukav5142 [94]
Sorry it’s not that neat but I think the answer would be in the exact surd form root 233

7 0
3 years ago
71.2% of 722.69 what is this​
Alex_Xolod [135]

Answer:

514.5552

Step-by-step explanation:

:)

3 0
2 years ago
Read 2 more answers
Complete each trinomial such that it can be rewritten in the form
lukranit [14]

Answer:

Step-by-step explanation:

1.5x^2+6x+.... so that it can be rewritten in the form a(x+b)^2

Let .... be C

1.5x^2+6x+C

=1.5(x^2+4x+(C/1.5))

Compare above with 1.5(x+2)^2 = 1.5(x^2+4x+4)

C/1.5=4

C=6

So the expression should be 1.5x^2+6x+6

It can be rewritten to 1.5(x+2)^2

8 0
2 years ago
Other questions:
  • 5t-14=-14<br> solve the equation for t
    6·1 answer
  • Joshua scored the same number of points in each of his last 3 basketball games. He
    11·1 answer
  • Why three prime numbers equal 30
    12·2 answers
  • Explain how to find which is greater 1/4 of 12 or 1/3 of 12
    5·2 answers
  • Counting Cookies: Hannah baked 120 peanut butter chocolate chip cookies. She
    5·1 answer
  • Idk this pls help don’t understand.
    13·1 answer
  • Jim's parents keep a chart on the wall where they mark how much Jim grows each year. When Jim was 15, he grew 1/4 of an inch and
    6·1 answer
  • Solve by completing the square​
    11·1 answer
  • Representations of decimals
    8·2 answers
  • I ran 1½ miles in 20 minutes . How fast did I go?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!