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xz_007 [3.2K]
3 years ago
9

What is the result of subtracting the second equation from the first?−4x−2y=-2x−2y=9

Mathematics
1 answer:
FrozenT [24]3 years ago
8 0
The end result would be ( 11/5 , -15/5)
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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>

  1. [Integral] Factor fraction denominator:                                                         \displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx
  2. [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>

  1. [Integral] Substitute u-du:                                                                               \displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du
  2. [Integral] Trig Integration:                                                                               \displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C
  3. [Integral] Simplify:                                                                                           \displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C
  4. [integral] Multiply:                                                                                           \displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C
  5. [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
3 years ago
Show all of your work. Simplify the expression: - 3a + 7 + 5a​
Eva8 [605]

Answer:

2a + 7

Step-by-step explanation:

-3a + 7 +5a

<em>subtract the negative 3 from the 5</em>

2a + 7

4 0
3 years ago
Read 2 more answers
Brian has 75 pieces of candy 45 pieces of his candy or chocolate what percentage of his candy is chocolate
Alik [6]

Answer:

60%

Step-by-step explanation:

45 pieces out of 75 pieces are chocolate

45/75

Divide: 45/75 = 0.6

To get percentage from a decimal, move the decimal point to the right two place values

0.6 => 60%

60% of his candy are chocolate

4 0
3 years ago
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The cost, including sales tax, of a Ford Focus SE is $19,392.70. If the sales tax is 6%, find the cost of the car before the tax
Ilia_Sergeevich [38]

Answer:

the price before taxes was $18,229.13

Step-by-step explanation:

6 0
2 years ago
If x2 + y2 = 14 and xy = 5, find the value of (1/2 x + 1/2 y)2.
aleksley [76]

Answer:

(½x+½y)²=6

Step-by-step explanation:

x^2 + y^2 = 14, xy=5

(A+B)^2=A^2 +2AB+B^2... (*)

(1/2x+1/2y)^2 =(*)

(1/2x)^2 +2(1/2x)(1/2y)+(1/2y)^2 =

1/4x^2 +1/2xy+1/4y^2=

1/4(x^2 +y^2) +1/2(xy)=

1/4*14+1/2*5=

14/4+5/2=

14/4+10/4=

24/4=6

let me know if I'm wrong.

5 0
3 years ago
Read 2 more answers
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