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larisa [96]
3 years ago
10

Question 12 Multiple Choice Worth 1 points)

Mathematics
1 answer:
aalyn [17]3 years ago
7 0
B is your answer...
Y = -7
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A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). What are the values of h and
Korolek [52]

The value of a is 1/4 and the value of h and k is (2,-7/4)

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

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

Now to determine the value of focus point , (h,k)

(h = 2)

k = - 2 +1/4 = -7/4

Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)

To know more about Parabola

brainly.com/question/4074088

#SPJ1

7 0
2 years ago
Hi, how do we do this question?​
Nutka1998 [239]

Answer:

\displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{-2(ln|3x + 1| - 3x)}{9} + C

General Formulas and Concepts:

<u>Algebra I</u>

  • Terms/Coefficients
  • Factoring

<u>Algebra II</u>

  • Polynomial Long Division

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]  

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals
  • Integration Constant C
  • Indefinite Integrals

Integration Rule [Reverse Power Rule]:                                                               \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

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

Integration Property [Addition/Subtraction]:                                                       \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

Logarithmic Integration

U-Substitution

Step-by-step explanation:

*Note:

You could use u-solve instead of rewriting the integrand to integrate this integral.

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int {\frac{2x}{3x + 1}} \, dx

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

  1. [Integrand] Rewrite [Polynomial Long Division (See Attachment)]:           \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \int {\bigg( \frac{2}{3} - \frac{2}{3(3x + 1)} \bigg)} \, dx
  2. [Integral] Rewrite [Integration Property - Addition/Subtraction]:               \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \int {\frac{2}{3}} \, dx - \int {\frac{2}{3(3x + 1)}} \, dx
  3. [Integrals] Rewrite [Integration Property - Multiplied Constant]:               \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{2}{3}\int {} \, dx - \frac{2}{3}\int {\frac{1}{3x + 1}} \, dx
  4. [1st Integral] Reverse Power Rule:                                                               \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{2}{3}x - \frac{2}{3}\int {\frac{1}{3x + 1}} \, dx

<u>Step 3: Integrate Pt. 2</u>

<em>Identify variables for u-substitution.</em>

  1. Set <em>u</em>:                                                                                                             \displaystyle u = 3x + 1
  2. [<em>u</em>] Differentiate [Basic Power Rule]:                                                             \displaystyle du = 3 \ dx

<u>Step 4: Integrate Pt. 3</u>

  1. [Integral] Rewrite [Integration Property - Multiplied Constant]:                 \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{2}{3}x - \frac{2}{9}\int {\frac{3}{3x + 1}} \, dx
  2. [Integral] U-Substitution:                                                                               \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{2}{3}x - \frac{2}{9}\int {\frac{1}{u}} \, du
  3. [Integral] Logarithmic Integration:                                                               \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{2}{3}x - \frac{2}{9}ln|u| + C
  4. Back-Substitute:                                                                                            \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{2}{3}x - \frac{2}{9}ln|3x + 1| + C
  5. Factor:                                                                                                           \displaystyle \int {\frac{2x}{3x + 1}} \, dx = -2 \bigg( \frac{1}{9}ln|3x + 1| - \frac{x}{3}  \bigg) + C
  6. Rewrite:                                                                                                         \displaystyle \int {\frac{2x}{3x + 1}} \, dx = \frac{-2(ln|3x + 1| - 3x)}{9} + C

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

Unit: Integration

Book: College Calculus 10e

8 0
3 years ago
PLEASE PLEASE PLLEASE HELPPPPPPPPPPP MEEEEEEE
Arlecino [84]

Answer:

15

Step-by-step explanation:

Please correct me if I'm wrong

8 0
3 years ago
Help with a b and c
djyliett [7]
5/6 x 2/2 = 10/12
1/4 x 3/3 = 3/12
2/3 x 4/4 = 8/12

5/6 + 1/4 = 13/12 (over 1 yard)
1/4 + 2/3 = 11/12 (slightly less than 1 yard)
5/6 + 2/3 = 18/12 (too much)

Here is the answer for a:
a) 5/6 and 1/4
5 0
4 years ago
The width of a triangle is 6 cm less than its length. If it's perimeter is 80 cm then it's lengths and area are respectively
PilotLPTM [1.2K]
The length is 14cm the width is 26cm. And according to my calculations, a=l•w so area would be 364.
5 0
3 years ago
Read 2 more answers
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