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likoan [24]
3 years ago
15

The function f has a domain of 1,3,5,7 and a range of 2,4,6. Could f be represented by 1,2. 3,4. 5,6. And 7,2. Justify your answ

er
Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0
Yes, a function with those domain and range values could certainly be represented by those points. (1,2) and (7,2) are points with separate domain values but identical range values. This is allowed because every x value is only assigned one y value.
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Question 7
serg [7]

\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

  • Given - <u>a </u><u>cone</u><u> </u><u>with </u><u>volume</u><u> </u><u>7</u><u>6</u><u>9</u><u>?</u><u>3</u><u> </u><u>ft³</u><u> </u><u>,</u><u> </u><u>having </u><u>a </u><u>height </u><u>of </u><u>1</u><u>5</u><u> </u><u>ft</u>

  • To calculate - <u>radius </u><u>of </u><u>the </u><u>cone</u>

We know that ,

\bold{Volume \: of \: cone =  \frac{1}{3}\pi \: r {}^{2}  h }\\

<u>substituting</u><u> </u><u>the </u><u>values </u><u>in </u><u>the </u><u>formula</u><u> </u><u>stated </u><u>above </u><u>,</u>

\bold{769.3 =  \frac{1}{3}  \times 3.14 \times r {}^{2}  \times 15} \\  \\\bold{\implies r {}^{2}  =  \frac{769.3 \times 3}{3.14 \times 15} } \\  \\\bold{\implies  r {}^{2}  =  \cancel\frac{2307.9}{47.1}}  \\  \\\bold{ \implies \: r {}^{2}  = 49} \\  \\ \bold{\implies \: r = 7 \: ft}

therefore ,

<u>radius </u><u>=</u><u> </u><u>7</u><u> </u><u>cm</u>

hope helpful ~

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2 years ago
9.25 the average score for Mrs Myles class was 70% of Mrs Jones i class test average score in Mr. Myles class
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80.2 is the correct answer
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3 years ago
In cos(0.3), what unit would 0.3 be? Is it radians? Also if you were to solve it, would the answer be in radians as well? Please
neonofarm [45]

Answer:

22

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Find the area of the region enclosed by the graphs of the functions
Vaselesa [24]

Answer:

\displaystyle A = \frac{8}{21}

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<u> </u>

Equality Properties

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

<u>Algebra I</u>

  • Terms/Coefficients
  • Functions
  • Function Notation
  • Graphing
  • Solving systems of equations

<u>Calculus</u>

Area - Integrals

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

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

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

Area of a Region Formula:                                                                                     \displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx

Step-by-step explanation:

*Note:

<em>Remember that for the Area of a Region, it is top function minus bottom function.</em>

<u />

<u>Step 1: Define</u>

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

<u>Step 2: Identify Bounds of Integration</u>

<em>Find where the functions intersect (x-values) to determine the bounds of integration.</em>

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

<u>Step 3: Find Area of Region</u>

<em>Integration</em>

  1. Substitute in variables [Area of a Region Formula]:                                     \displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx
  2. [Area] Rewrite [Integration Property - Subtraction]:                                     \displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx
  3. [Area] Integrate [Integration Rule - Reverse Power Rule]:                           \displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}
  4. [Area] Evaluate [Integration Rule - FTC 1]:                                                    \displaystyle A = \frac{2}{3} - \frac{2}{7}
  5. [Area] Subtract:                                                                                               \displaystyle A = \frac{8}{21}

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

Unit: Area Under the Curve - Area of a Region (Integration)  

Book: College Calculus 10e

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3 years ago
Kerry wants to give each student in her class 1/2
qwelly [4]

Answer:

60

Step-by-step explanation:

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