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charle [14.2K]
3 years ago
14

Integrate the following. ∫

ss="latex-formula">
Mathematics
1 answer:
bogdanovich [222]3 years ago
4 0

Answer:

\displaystyle \int {84} \, dx = 84x + C

General Formulas and Concepts:

<u>Calculus</u>

Integration

  • Integrals
  • Definite/Indefinite Integrals
  • Integration Constant C

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int {84} \, dx

<u>Step 2: Integrate</u>

  1. [Integral] Rewrite [Integration Property - Multiplied Constant]:                 \displaystyle \int {84} \, dx = 84\int {} \, dx
  2. [Integral] Reverse Power Rule:                                                                     \displaystyle \int {84} \, dx = 84x + C

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

Unit:  Integrations

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densk [106]

Answer:

<u>The additional 1.3% of increase in the annual interest rate that Jack is receiving in his savings account, from 2.8% to 4.1%, represent an increase of 46.42%.</u>

Step-by-step explanation:

Jacks's savings account annual interest rate before = 2.8%

Jacks's savings account annual interest rate after the increase = 4.1%

Difference of the two rates = 4.1% - 2.8% = 1.3%

How much percentage is that additional 1.3% from the rate before the increase?

(1.3 * 100)/ 2.8 = 130/2.8 = 46.42%

<u>The annual interest rate increased by 46.42% from the previous annual interest rate.</u>

3 0
3 years ago
How do you solve c2+10c+9=0
Valentin [98]

Answer:

Step-by-step explanation:

Step 1: Factor left side of equation.

(c+1)(c+9)=0

Step 2: Set factors equal to 0.

c+1=0 or c+9=0

c=−1 or c=−9

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8 0
4 years ago
The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based o
Lina20 [59]

The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607

<h3>How to determine the regression equation?</h3>

The table of values is given as:

Completion Percentage 57 59 62 63 64

Interception Percentage 5 3.5 3 2.5 1.5

Next, we enter the above values in a graphing calculator.

From the graphing calculator, we have the following summary:

  • Sum of X = 305
  • Sum of Y = 15.5
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  • Mean Y = 3.1
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  • Sum of products (SP) = -14.5
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Regression Equation = ŷ = bX + a

b = SP/SSX = -14.5/34 = -0.42647

a = MY - bMX = 3.1 - (-0.43*61) = 29.11471

So, the regression equation is

y = -0.42647x + 29.11471

And the correlation coefficient is -0.9607

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brainly.com/question/14313391

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7 0
2 years ago
Please explain your answer. THX!!!!
Sidana [21]

Answer:

1)cos(x)sin^{2}x

2)0

Step-by-step explanation:

for part 1:

Given cos(x) - cos^3(x)

= cos(x) (1- cos^2(x))

Using the identity cos^{2}x +sin^{2}x=1\\ sin^{2}x=1-cos^{2}x

= cos(x)sin^2(x)

for part 2:

given

=cos\frac{5\pi }{8}cos\frac{\pi }{8}  + sin\frac{5\pi }{8}sin\frac{\pi }{8}

Using the identity cos(a)cos(b) + sin(a)sin(b)= cos(a-b)

=cos(\frac{5\pi }{8} -\frac{\pi }{8})

=cos\frac{4\pi }{8}

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=0!

5 0
3 years ago
Find all values of θ in the interval 0° ≤ θ &lt; 360° that satisfy the equation sin 2θ = sin θ.
kap26 [50]
Sin 2θ = sin θ
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2cos θ = 1
cos θ = 1/2
θ = arccos(1/2) = 60° and 300°
θ = 60° and 300°
7 0
3 years ago
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