Answers
Answer:
(a) -12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Swapping Limits]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^6_4 {f(x)} \, dx = 5[/tex]
[tex]\displaystyle \int\limits^4_{10} {f(x)} \, dx = 8[/tex]
[tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx[/tex]
Step 2: Solve Pt. 1
[Integral] Rewrite [Integration Property - Addition]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx[/tex]Step 3: Redefine
Manipulate the given integral values.
[Integrals] Combine [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx = \int\limits^6_{10} {f(x)} \, dx[/tex][Integral] Rewrite: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx[/tex][Integral] Substitute in integrals: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = 5 + 8[/tex][Integral] Add: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = 13[/tex][Integral] Rewrite [Integration Property - Swapping Limits]: [tex]\displaystyle -\int\limits^{10}_6 {f(x)} \, dx = 13[/tex][Integral] [Division Property of Equality] Isolate integral: [tex]\displaystyle \int\limits^{10}_6 {f(x)} \, dx = -13[/tex]Step 4: Solve Pt. 2
[Integral] Substitute in integral: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6[/tex][Integral] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)[/tex][Integral] (Parenthesis) Subtract: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)[/tex][Integral] Multiply: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40[/tex][Integral] Add: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12[/tex]Topic: AP Calculus AB/BC
Unit: Integration
Book: College Calculus 10e
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Step-by-step explanation:
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[tex]\frac{8}{3}[/tex]
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
It was correct on edge 2021
The equation that is correct regarding the measure of <MNP is 1/2(x-y)
Circle geometryIn order to determine the measure of m<MNP, we will use the theorem shown below;
The angle at the vertex is half the difference of angles at the intercepted arcs.
The angle at the vertex = m<MNP
angle a the arcs are x and y
Hence;
m<MNO = 1/2 (x - y)
Hence the equation that is correct regarding the measure of <MNP is 1/2(x-y)
Learn more on circle geometry here:https://brainly.com/question/24375372
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Answer:
c
Step-by-step explanation:
Answer:
B
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Answer:
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Step-by-step explanation:
a pile of coins, consisting of only dimes and quarters, is worth 4 dollars and 55 cents. there are 7 more dimes than quarters in the pile. find the number of dimes and quarters in the pile.
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Pupil who scored 60 in her maths test was absent for English predict what her English mark could have been
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Answer:
There is 30% probability for the students who score 60 marks in math.
Step-by-step explanation:
The probability of the students who score 60 marks in math is 30%. There is 70% chance that a student will score less than 60 marks in math. The students who score 60 plus in math will score lesser in English.
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Answer:
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Answer:
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Step-by-step explanation:
your welcome
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Answer:
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Step-by-step explanation:
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Answer:
8 weeks
Step-by-step explanation:
to solve divide the total cost of kindle by the money she saves each week.
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
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see attached
Step-by-step explanation:
The transformations are ...
(x, y) ⇒ (-y, x) . . . . 90° rotation
(x, y) ⇒ (-x, -y) . . . . 180° rotation
(x, y) ⇒ (y, -x) . . . . 270° rotation
Each successive rotation is a 90° rotation from the previous one. This makes writing the formulas in a spreadsheet really easy. The attached shows the transformed coordinates.
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Answers
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Step-by-step explanation: pythagorean theorem
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Step-by-step explanation:
Use the pythagorean theorem to find the height.
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Answers
Answer:
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Step-by-step explanation:
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3360832553 ____ pass___ wZE2XQ
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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A
Step-by-step explanation:
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Submit
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Answers
Answer:
13 x 9 x 5
Step-by-step explanation:
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Step-by-step explanation: