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3 years ago

3.141 in expanded notation

Mathematics

2 answers:

Eva8 [605]3 years ago

8 0

3.141 in expanded notation is 3 + 0.1 + 0.04 + 0.001

Hope that helps :)

kari74 [83]3 years ago

6 0

3 + .1 + .04 + .001 is 3.141 in expanded notation.

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The line of symmetry for the quadratic equation y = ax^2 + 8x - 3 is x = 4. What is the value of "a"?

alexdok [17]

Answer:

a = - 1

Step-by-step explanation:

given a quadratic in standard form : y = ax² + bx + c : a ≠ 0

Then the x-coordinate of the vertex is

• $x_{vertex}$ = - $\frac{b}{2a}$

The line of symmetry passes through the parabola, hence x-coordinate is 4

y = ax² + 8x - 3 is in standard form

with a = a, b = 8 and c = - 3, hence

- $\frac{8}{2a}$ = 4 ( multiply both sides by 2a

- 8 = 8a ( divide both sides by 8 )

a = - 1

6 0

3 years ago

Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4

jok3333 [9.3K]

Answer:

$\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10$

General Formulas and Concepts:
Calculus

Integration

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

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

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

Step-by-step explanation:

Step 1: Define

Identify.

y = 2x + 3

x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^4_3 {2x + 3} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx$
[Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx$
[Integrals] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3$
[Integrals] Integrate [Integration Rule - FTC 1]: $\displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)$
Simplify: $\displaystyle A = 10$

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

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Learn more about integration: brainly.com/question/26401241

Learn more about calculus: brainly.com/question/20197752

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

Unit: Integration

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s344n2d4d5 [400]

Step-by-step explanation:

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x-2x-6=8x+12-4

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matrenka [14]

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