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2 years ago

8

To bake 100 of his favorite cookies, Mr. Wallis

1 answer:

Sonja [21]2 years ago

6 0

30 I think good luck

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Suppose n is an integer. Is n2 +n always, sometimes, or never an even integer? Explain.

romanna [79]

Is the 2 an exponent? if so, it is always an even integer.

4 0

2 years ago

5y^2+5−4−4y^2+5y^2−4x^3 −1

vredina [299]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{4 {x}^{3} + 6 {y}^{2} }}}}}$

Step-by-step explanation:

$\sf{5 {y }^{2} + 5 - 4 - 4 {y}^{2} + 5 {y}^{2} - 4 {x}^{3} - 1}$

Collect like terms

⇒ $\sf{ 4 {x}^{3} + 5 {y}^{2} - 4 {y}^{2} + 5 {y}^{2} + 5 - 4 - 1}$

⇒ $\sf{4 {x}^{3} + {y}^{2} + 5 {y}^{2} + 5 - 4 - 1}$

⇒ $\sf{4 {x}^{3} + 6 {y}^{2} + 5 - 4 - 1}$

Calculate

⇒ $\sf{4 {x}^{3} + 6 {y}^{2} + 1 - 1}$

⇒ $\sf{4 {x}^{3} + 6 {y}^{2} }$

Hope I helped!

Best regards! :D

6 0

2 years ago

Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

<u>Algebra I</u>

Factoring

<u>Calculus</u>

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$ <u />

<u />

<u>Step 2: Integrate Pt. 1</u>

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

<u>Step 3: Identify Variables</u>

<em>Set up u-substitution for the arctan trig integration.</em>

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

<u>Step 4: Integrate Pt. 2</u>

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

2 years ago

Are polynomials determined to be a trinomial, binomial, etc. based on the number of operations or the terms?

Mekhanik [1.2K]

Polynomials are determined to be a trinomial, binomial, etc by the amount of terms they have
For example
7x+3 is a binomial

5 0

2 years ago

X=1/16y^2 the directrix of the parabola is

yan [13]

To solve this problem you must apply the proccedure shown below:

1. You have the following equation of a parabola, given in the problem above:

x<span>=1/16y^2

2. Then, based on the graph attached, you have:

p=y^2/4x
p=8^2/(4)(4)
p=64/16
p=4

3. The directrix is:

directrix=h-p
directrix=0-4
directrix=-4

The answer is:-4</span>

3 0

2 years ago