The price s of a pair of shoes plus 5% sales tax

2. Solve the following system. Show all your work. {3x - 2y + 2z = 30 {-x + 3y - 4z = -33 {2x - 4y + 3z = 42

Semmy [17]

From the system of equations, we have 3 unknowns and 3 equations. Therefore, it can be solved.

3x - 2y + 2z = 30 (1)
-x + 3y - 4z = -33 (2)
2x - 4y + 3z = 42 (3)

We can write equation 2 x as a function of y and z and substitute the new equation to the other equations.
x =3y - 4z + 33 (2)

3 (3y - 4z + 3) - 2y + 2z = 30 (1)
2 (3y - 4z + 3) - 4y + 3z = 42 (3)

We simplify and solve the equations and we get values,

x = 4
y = -7
z = 2

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:

Algebra I

Factoring

Calculus

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:

Step 1: Define

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

Step 2: Integrate Pt. 1

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

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

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

Step 4: Integrate Pt. 2

[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

The answer should look like this. (___,___) plzzz fast.

BartSMP [9]

Answer:

( -1, 15/2) or ( -1, 7 1/2)

Step-by-step explanation:

Formula: ( (x1 + x2)/2, (y1 + y2)/2 )

1. ( (-4 +6)/2, (8 + 7)/2 ) Plug in

2. ( -2/2, 15/2) Add/Subtract

3. ( -1, 15/2) or ( -1, 7 1/2) Divide

5 0

2 years ago

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What is the measure of the largest angle on the triangle!

nalin [4]

Okay, so as you may know the inside angles of a triangle always add up to 180! so you must first find x, so that means add up all equations to find x. your answer is 41

6 0

3 years ago

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What is the quotient of 83.3 and 24.5

Svetradugi [14.3K]

Answer:

3.4

Step-by-step explanation:

83.3 divided by 24.5= 3.4

5 0

2 years ago

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