I need helpppppppppppppppp

PLEASE HELP ME GUYS OR I WONT PASS this calculus!!!!

KonstantinChe [14]

Answer:

b. $\displaystyle \frac{1}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle H(x) = \sqrt[3]{F(x)}$

Step 2: Differentiate

Rewrite function [Exponential Rule - Root Rewrite]: $\displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}$
Chain Rule: $\displaystyle H'(x) = \frac{d}{dx} \bigg[ [F(x)]^\bigg{\frac{1}{3}} \bigg] \cdot \frac{d}{dx}[F(x)]$
Basic Power Rule: $\displaystyle H'(x) = \frac{1}{3}[F(x)]^\bigg{\frac{1}{3} - 1} \cdot F'(x)$
Simplify: $\displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle H'(x) = \frac{F'(x)}{3[F(x)]^\bigg{\frac{2}{3}}}$

Step 3: Evaluate

Substitute in x [Derivative]: $\displaystyle H'(5) = \frac{F'(5)}{3[F(5)]^\bigg{\frac{2}{3}}}$
Substitute in function values: $\displaystyle H'(5) = \frac{6}{3(8)^\bigg{\frac{2}{3}}}$
Exponents: $\displaystyle H'(5) = \frac{6}{3(4)}$
Multiply: $\displaystyle H'(5) = \frac{6}{12}$
Simplify: $\displaystyle H'(5) = \frac{1}{2}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

5 0

3 years ago

HELP ME I NEED HELP!!!!

eduard

Answer:

D

Step-by-step explanation:

Since they are the same variables

7 0

3 years ago

Can someone help me here pls thanks!

vesna_86 [32]

Using proportions, it is found that the measure of the inscribed angle B is of 30º.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In a circle, the inscribed angle is half the measure of the outside angle. Hence, in this problem, the measure of angle B is of 50% of 60º, hence:

m<B = 0.5 x 60º = 30º.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

4 0

2 years ago

Combine the following expressions:

melisa1 [442]

ANSWER

$(4n - 1)\sqrt{3 n} + 3\sqrt{n}$

EXPLANATION

The given expression is

$\sqrt{48 {n}^{3} } + \sqrt{9n} - \sqrt{3n}$

We remove the perfect squares under the radical sign.

$\sqrt{16 {n}^{2} \times3 n} + \sqrt{9n} - \sqrt{3n}$

We can now take square root of the perfect squares and simplify them further.

$\sqrt{16 {n}^{2}} \times \sqrt{3 n} + \sqrt{9} \times \sqrt{n} - \sqrt{3n}$

This simplifies to:

$4n\sqrt{3 n} + 3\sqrt{n} - \sqrt{3n}$

This further simplifies to:

$(4n - 1)\sqrt{3 n} + 3\sqrt{n}$

3 0

2 years ago

Read 2 more answers

You have $550 in a savings account that earns 3% simple interest each yaer. How much will be in your account in 10 years?

bija089 [108]

Looking at the given question, we can find several important information's and based on thm we can easily calculate the amount after 10 years.
Principal amount = $550
Rate of interest per year = 3%
Number of years the amount is to be kept = 10 years
Now we get put these information's in the formula of finding amount of money kepy in simple interest.
Amount = P(1 + rt)
Where
p = principal amount
r = rate of interest
t = Time
Then
Amount = 550[1 + (3/100) * 10)]
   = 550 [1 + 3/10]
   = 550 * (13/10)
   = 55 * 13
   = 715 dollars
So the total amount in my account will be $715

4 0

2 years ago