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Vera_Pavlovna [14]
3 years ago
8

Please help me with this function on a closed interval!

Mathematics
1 answer:
Softa [21]3 years ago
5 0

Answer:

(E) 13

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Functions
  • Function Notation

<u>Calculus</u>

Antiderivatives - Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:                                      \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Rule [Fundamental Theorem of Calculus 2]:                                     \displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<u />\displaystyle \int\limits^4_0 {f'(t)} \, dt = 8<u />

<u />\displaystyle f(4) = \text{unknown}<u />

<u />

<u>Step 2: Integrate</u>

  1. [Integral] Evaluate [Integration Rule - FTC 1 and 2]:                                     \displaystyle \int\limits^4_0 {f'(t)} \, dt = f(4) - f(0)
  2. [Integral] Substitute in variables [Given/Table]:                                           \displaystyle 8 = f(4) - 5
  3. [Addition Property of Equality] Isolate f(4):                                                   \displaystyle 13 = f(4)
  4. Rewrite:                                                                                                           \displaystyle f(4) = 13

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

Unit: Integration

Book: College Calculus 10e

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Which of the following pairs of functions are inverses of each other?
AnnyKZ [126]

Answer:

Step-by-step explanation:

Rearrange each function to solve for x.

Switch x and y,

The resulting equation is the inverse function.

A:

f(x) = y = 5+x

x = y-5

y = x-5

f⁻¹(x) = x-5

g(x) = 5-x ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

:::::

B:

f(x) = y = 2x-9

x = (y+9)/2

y = (x+9)/2

f⁻¹(x) = (x+9)/2

g(x) = (x+9)/2 = f⁻¹(x)

g(x) is the inverse of f(x).

:::::

C:

f(x) = y = 2/x - 6

x = 2/(y+6)

y = 2/(x+6)

f⁻¹(x) = 2/(x+6)

g(x) = (x+6)/2 ≠ f⁻¹(x)

:::::

D:

f(x) = y = x/3 + 4

x = 3y - 12

y = 3x - 12

f⁻¹(x) = 3x - 12

g(x) = 3x - 4 ≠ f⁻¹(x)

g(x) is not the inverse of f(x).

4 0
2 years ago
there are 300 student and teachers at a sports event.Grade k to 2 is students: 137 Grade 3 to 5 students: 145 Teachers: ? what i
AVprozaik [17]

Answer:

6%

Percentage of teachers = 6%

Step-by-step explanation:

Given;

Number of grade k-2 students = 137

Number of grade 3-5 students = 145

Total = 300

Number of teachers = 300 - (137+145) = 18

Percentage of teachers = (number of teachers÷total)× 100%

%T = (18/300) × 100

%T = 6%

8 0
3 years ago
-4 plus the square root of 81​
almond37 [142]
<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ The square root of 81 is 9

We have -4 + 9

Thus, your answer is 5

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

6 0
3 years ago
Read 2 more answers
Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase o
sweet-ann [11.9K]
See also brainly.com/question/8975313

The growth factor is 2.

The increase is (2 -1)*100% = 100% per period.
5 0
3 years ago
An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest cir
Serhud [2]

Answer:

The artist used 8.6\ in more of silver wire

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

The Perimeter of the square is equal to

P=4a

where

a is the length side of the square

P=40\ in

so

40=4a

a=10\ in

so

Each side of the square has a length of 10 in

step 2

Find the circumference of the circle

The diameter of the circle is equal to the length of the side of  the square

The circumference is equal to

C=\pi D

we have

D=10\ in

substitute

C=(3.14)(10)=31.4\ in

step 3

Find the difference

40\ in-31.4\ in=8.6\ in

4 0
3 years ago
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