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3 years ago

What is the answer to this question ?

Mathematics

1 answer:

Arisa [49]3 years ago

7 0

Answer:

Step-by-step explanation:

h(7)= 7²-1= 49-1= 48

f(h(7))= 48/3 -12

= 16-12

= 4

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Find <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20" id="TexFormula1" title=" \frac{dy}{dx} " alt=" \frac{d

nataly862011 [7]

Answer:

$\displaystyle y' = 2x + 3\sqrt{x} + 1$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Anything to the 0th power is 1
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

$\displaystyle y = (x + \sqrt{x})^2$

Step 2: Differentiate

Chain Rule: $\displaystyle y' = 2(x + \sqrt{x})^{2 - 1} \cdot \frac{d}{dx}[x + \sqrt{x}]$
Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = 2(x + x^{\frac{1}{2}})^{2 - 1} \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}]$
Simplify: $\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}]$
Basic Power Rule: $\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 \cdot x^{1 - 1} + \frac{1}{2}x^{\frac{1}{2} - 1})$
Simplify: $\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2}x^{-\frac{1}{2}})$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2x^{\frac{1}{2}}})$
Multiply: $\displaystyle y' = 2[(x + x^{\frac{1}{2}}) + \frac{x + x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}]$
[Brackets] Add: $\displaystyle y' = 2(\frac{2x + 3x^{\frac{1}{2}} + 1}{2})$
Multiply: $\displaystyle y' = 2x + 3x^{\frac{1}{2}} + 1$
Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = 2x + 3\sqrt{x} + 1$

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

Unit: Derivatives

Book: College Calculus 10e

4 0

3 years ago

You can approximate e by substituting large values for ninto the expression

ratelena [41]

You can approximate e by substituting large values for (1 + 1/n)^n into the expression.

<h3>How to illustrate the expression?</h3>

It should be noted that an expression can simply be used to illustrate the information given in a data.

In this case, you can approximate e by substituting large values for (1 + 1/n)^n into the expression.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

8 0

2 years ago

Find the value of f(g(-2)) f(x) =-2x+14 g(x)=3x^2+6x-2

Rzqust [24]

Answer:

-2

Step-by-step explanation:

f[g(x)

=f(3x^2+6x-2)

=2 (3x^2+6x-2)+14

=6x^2+12x-4+14

=6x^2+12x+10

f[g(-2)]=6 (-2)^2+12×(-2)+10

=12- 24+10

=-2

3 0

3 years ago

An animal shelter has 4/5 of its crates filled with animals. 1/2 of the filled crates are holding cats. What fraction of the tot

max2010maxim [7]

8/10s of the crates are filled with animals, half of those are holding cats so 4/10s are holding cats so I believe 4/10s of the total crates are holding cats

5 0

3 years ago

Read 2 more answers

Write the quadratic function for the parabola having vertex(4,2) and passing through the point (1,11)

Zigmanuir [339]

So the function we are looking for should look like f(x)=a(x-1)2-2, and since the parabola passes through (4,5), we have 5=a(4-1)2-2, which means 5=9a-2, so a = (7/9) and f(x) = (7/9)(x-1)2-2.

3 0

3 years ago